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Geometry B - (MA202) '17

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Given that MATH is a parallelogram, solve for c.

C. 94

Which statement proves that quadrilateral JKLM is a kite?

LM = JM = 3 and JK = LK = √17

What is the perimeter of the octagon? [_______] cm

11.2

Angle D is a circumscribed angle of circle O. What is the perimeter of kite OBDE?

27 units

In circle T, ∠PTQ ≅ ∠RTS. What is the length of PQ?

b. 4 units

The measure of BAC is 240. What is the ratio of the measure of the major arc to the measure of the minor arc?

c. 2:1

What is the approximate value of x? Round to the nearest tenth.

c. 4.6 cm

Which arc is congruent to EH?

c. GE

High population density can cause increases in competition for resources, such as food and shelter. The table shows the number of zebras living in 4 different regions. In which region is competition for resources most likely the greatest?

c. Region C

PR and QS are diameters of circle T. What is the measure of SR?

100°

A regular hexagon is shown. What is the measure of the radius, c, rounded to the nearest inch? Use the appropriate trigonometric ratio to solve.

14 in.

An oblique prism has a base area of 3x2 square units. What expression represents the volume of the prism, in cubic units?

36x2

What is the value of x?

A. 2

A solid right pyramid has a regular hexagonal base with an area of 7.4 units2. The pyramid has a height of 6 units.

B. 14.8 units3

How many vertices does a triangular prism have?

C:6

Which statements are true about triangle QRS? Check all that apply.

The side opposite ∠Q is RS The hypotenuse is QR. The side adjacent to ∠Q is QS.

Consider a circle whose equation is x² + y² + 4x - 6y - 36 = 0. Which statements are true? Check all that apply.

To complete the square for the x terms, add 4 to both sides. The center of the circle is at (-2, 3).

Line segment ST is congruent to line segment ______

The area of the regular hexagon is 10.4 in.2. What is the measure of the apothem, rounded to the nearest tenth of an inch?

b 1.7

Which is the base shape of this prism?

triangle

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

2/3╓x^3

Triangle TUV was dilated to create triangle T'U'V' using point A as the center of dilation. What is the scale factor of the dilation?

2/5 *See Graph #38

Arc CD is 2/3 of the circumference of a circle. What is the radian measure of the central angle?

4π/3 radians

What is the perimeter of square ABCD?

4√37 units

Circle O has a circumference of approximately 28.3 cm. What is the approximate length of the radius, r?

4.5 cm

Circle O has a circumference of approximately 28.3 cm. What is the approximate length of the radius, r?

4.5 cm

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

4.7

What is the radius of a circle given by the equation x² + y² - 2x + 8y - 47= 0?

8 units

Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?

8, 10, 14

Circle F is congruent to circle J, and ∠EFD ≅ ∠GJH. m∠DFE = 80°. What is the measure of ?

What is the perimeter of parallelogram LMNO?

80 cm *See Graph #12

The volume of a solid right pyramid with a square base is V units3 and the length of the base edge is y units Which expression represents the height of the pyramid?

ABCD is a square. What is the length of line segment D.C.?

d. 13 units

In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°. Rounded to the nearest tenth of a centimeter, what is the length of arc LMN?

d. 14.2 cm

What is the length of line segment SV?

d. 16 units

What is the approximate value of y-x?

d. 17.2°

What is the perimeter of trapezoid JKLM?

d. 9 + √2 + √5 units

Line segment BA is tangent to the circle. What is the length of line segment BA? Round to the nearest unit.

d. 98 units

Angle G is a circumscribed angle of circle E. What is the measure of angle G, in terms of x?

x° + x°

Which equation represents the parabola shown on the graph?

y2 = -8x

Which polygon has an interior angle sum of 1080°?

Which polygon is a convex heptagon?

Which sets can be represented using the Venn diagram below?

A = {animals}; B = {mammals}

A soundproofing tile is made of 8 identical solid right pyramids with square bases. The length of the whole tile shown is x inches. Which expression shows the area of the base of each pyramid?

A. in.2

If events A and B are independent, what must be true?

B. P(A|B) = P(A)

Which circle shows AB that measures 60°?

Find the values of w and x that make NOPQ a parallelogram.

D. w = 3, x = 1/2

Which statements are true of all squares? Check all that apply.

The diagonals are perpendicular. The diagonals are congruent to each other. The diagonals bisect the vertex angles. The diagonals bisect each other.

The perimeter of triangle ABC is 82 inches. The triangle is rotated about a line that passes through points B and D. Which best describes the resulting three-dimensional figure?

a cone with base radius of 17 in.

Figure ABCD is a square. Prove BD ≅ AC. What is the missing reason in the proof?

all sides of a square are congruent

What is the missing reason in step 4?

base angles theorem

Figure ABCD is graphed on a coordinate plane. ABCD is an isosceles trapezoid. What is the approximate perimeter of ABCD? Round to the nearest tenth.

c. 20.9 units

Segments AC and BD are diameters of circle O. What is the measure of ADB?

c. 253°

The area of circle Z is 64π ft^2. What is the value of r?

r = 8 ft

A parabola has a vertex at the origin. The focus of the parabola is located at (-2,0). Which is the equation for the directrix related to the parabola?

x = 2

Line segment GJ is a diameter of circle L. Angle K measures (4x + 6)°. What is the value of x?

x = 21

A parabola has a vertex at the origin. The equation of the directrix of the parabola is y = 3. What are the coordinates of its focus?

(0,-3)

A parabola and its directrix are shown on the graph. What are the coordinates of the focus of the parabola?

(0,2)

Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?

(x + 3)² + (y + 5)² = 36

EFGH is a rhombus. Given EG = 16 and FH = 12, what is the length of one side of the rhombus?

10 units

Line segment KL is tangent to circle J at point K. What is the length of the radius, r?

10 units

What is the measure of arc QR?

104°

Consider quadrilateral LMNO. If quadrilateral LMNO is a parallelogram, what must the measure of angle LMN be? m∠LMN =

105°

n circle O, AD and BE are diameters. What is mAE?

132°

A right square prism has a volume of 360 cubic units. Which could be the dimensions, in units, of the prism? Check all that apply.

1345

What must be the length of ZY in order for ZY to be tangent to circle X at point Y?

15 units

What is the sum of the measures of the interior angles of a 12-gon?

1800°

A circular table top has a radius of 24 inches. What is the area of the table top, to the nearest square inch?

1809 in.2

A circular table top has a radius of 24 inches. What is the area of the table top, to the nearest square inch? Use 3.14 for .

1809² in.

A paper hat is folded into the shape of a kite, as shown. What total length of ribbon is needed to line the two long sides of the hat?

22 in.

The volume of a cylinder is 4πx3 cubic units and its height is x units. Which expression represents the radius of the cylinder, in units?

What is the perimeter of rectangle EFGH?

2√10 + 2√29 units

What is the area of triangle DEF?

2√14 square units

What is the length of AB? Round to the nearest tenth.

38.6 m

The oblique pyramid has a square base. The volume of the pyramid is cm3.

The oblique pyramid has a square base. The volume of the pyramid is cm3

The coordinates of rhombus ABCD are A(-4, -2), B(-2, 6), C(6, 8), and D(4, 0). What is the area of the rhombus? Round to the nearest whole number, if necessary.

60 square units

What is the area of the trapezoid?

60 square units

The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm. What is the smallest possible whole-number value of x?

The equation cos-1 (3.4/10) = x can be used to determine the measure of angle BAC. What is the degree measure of angle BAC? Round to the nearest whole degree.

in the diagram of circle c, what is the measure of <1

What is mSU?

77°

The diagram shows isosceles trapezoid LMNP. It also shows how line segment NO was drawn to form parallelogram LMNO.

What is the area of triangle RST?

9 square units

Triangle XYZ is reflected over its hypotenuse to create a kite. What is the approximate distance from Y to Y'? Round to the nearest tenth.

9.2 units

Which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?

(x + 4)² + (y - 9)² = 25

In quadrilateral QRST, < RST measures (5x + 15)o. Angle TQR measures (4x + 3)o. What is the measure of angle RST

105

What is the center of a circle whose equation is x2 + y2 + 4x - 8y + 11 = 0?

(-2, 4)

What is the center of a circle whose equation is x² + y² + 4x - 8y + 11 = 0?

(-2, 4)

What is the center of a circle represented by the equation (x+9)²+(y−6)²=10²

(-9,6)

Which point is on the circle centered at the origin with a radius of 5 units?

(2, 21)

Which point is on the circle centered at the origin with a radius of 5 units?

(2, √21)

What is the area of the composite figure? (2,4,5)

(6π + 10) m^2

What is the area of the composite figure?

(8π + 12) in.2

Which equation represents a circle with the same radius as the circle shown but with a center at (-1, 1)?

(x + 1)² + (y - 1)² = 16

In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x² + y² = r² . If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?

(x - h)² + (y - k)² = r²

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The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x - 1. What is the value of x?

Consider circle Y with radius 3 m and central angle XYZ measuring 70°. What is the approximate length of minor arc XZ? Round to the nearest tenth of a meter.

3.7 meters

What is the value of x?

Which is the best approximation for the measure of angle EGF?

40.2°

Given right triangle DEF, what is the value of tan(F)?

40/9

Consider circle O below. The length of arc BA is 8.4 cm and the length of the radius is 8 cm. The measure of angle AOC is 45°. Rounded to the nearest whole degree, what is the measure of angle BOA? Rounded to the nearest tenth of a centimeter, what is the length of arc BAC?

60° 14.7 cm

What is the measure of angle AFE?

99°

What does most specifically describe?

A major arc

Which expression represents the volume, in cubic units, of the composite figure?

A. π(103) + π(102)(28)

A bag contains eleven equally sized marbles, which are numbered. What is the probability that a marble chosen at random is shaded or is labeled with a multiple of 3?

D. 6/11

Arc QVT measures 156°. Which statement must be true?

Angles QRT and QST both measure 78°

Which could be the base shape of the cylinder?

C. circle

Which arc is congruent to EH?

LMNP is a parallelogram. What additional information would prove that LMNP is a rectangle?

LP ⊥ PN

Which statements are true about triangle QRS? Select three options.

The side opposite ∠Q is RS. The hypotenuse is QR. The side adjacent to ∠Q is QS

What is the measure of ADB?

XXX 107

What is the measure of EBC?

XXX 210 (degrees) XXX 180 (degrees) XXX 201

Joey is building a frame for a sandbox. The sandbox is going to be a quadrilateral that has the lengths shown. If the diagonal of the sandbox measures 14 feet, which best describes the shape of the sandbox?

a quadrilateral, because angle C and angle X are acute

In the diagram of circle P, m∠XYZ is 72°. What is the value of x?

a. 108°

Given right triangle DEF, what is the value of sin(E)?

a. 3/5

Which equation is correct regarding the measure of <MNP?

a. m<MNP = 1/2(x - y)

Figure TUVS is a parallelogram. Which angles equal 91°?

angles T and V

What is the approximate side length of the square?

c. 4.2 units

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

c. obtuse, because 6^2 + 10^2 < 12^2

Given DEF, which is not equal to cos(F)?

c. tan(F)

Consider kite ABCD. What are the values of x and y?

c. x = 5, y = 22

Which concept can be used to prove that the diagonals of a parallelogram bisect each other?

congruent triangles

Use parallelogram ABCD. What are the values of x and y?

x = 17 y = 10

The area of circle Z is 64.pie ftsquared What is the value of r?

it's r = 8 ft

Ramon wants to make an acute triangle with three pieces of wood. So far, he has cut wood lengths of 7 inches and 3 inches. He still needs to cut the longest side. What length must the longest side be in order for the triangle to be acute?

less than √58 inches but greater than 7 inches

Given △DEF, which is not equal to cos(F)?

tan(F).

Which equation can be used to find the length of ?

(10)sin(40o) = AC

Which equation can be used to find the length of AC?

(10)sin(40o) = AC

What is the area of the shaded portion of the circle?(8)

(16π - 32) in2

What is the length of CD?

10.7 cm

What is the approximate area of the octagon?

101 ft²

A survey finds that 48% of people identify themselves as fans of professional football, 12% as fans of car racing, and 9% as fans of both professional football and car racing. Let event F be choosing a person who is a fan of professional football and let event C be choosing a person who is a fan of car racing. Which statements are true? Check all that apply.

1. P(F|C) = 0.75 3. P(C∩F) = 0.09 4. P(C∩F) = P(F∩C)

What is the length of the side opposite B?

4 units

In the diagram, ZY = WX = . What is the perimeter of rectangle WXYZ?

6√10 Units *See Graph #32

Figure ABCD is a parallelogram. What is the value of x?

In a standard deck of cards there are four suits: spades, clubs, hearts, and diamonds. Each suit has one each of 13 cards: ace, king, queen, jack, 2, 3, 4, 5, 6, 7, 8, 9, and 10. If event A is choosing a king, event B is choosing a heart, and event C is choosing a jack, which Venn diagram could represent this description?

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2. Which circle could represent the base of the vase? Use 3.14 for .

Which circle shows AB that measures 60°?

Which polygon has an interior angle sum of 1260°?

Which polygon is a concave octagon?

In which triangle is the value of x equal to tan−1(3.1/5.2)?

Quadrilateral ABDE is a rectangle. AB = 10 cm and AE = 16 cm. Through which two points could a line of rotation be placed so that the base of the resulting cylinder will have a radius of 5 cm?

Which statements are true about the regular polygons? Check all that apply.

Each interior angle measures 108°. All of the angles are congruent l. The sum of the measures of the interior angles is 180(5 - 2)°.

A shoe store owner is designing the layout of the displays in his store. The floor area for the store is 1,600 square feet. The owner wants to have circular displays for the shoes, each with a radius of 6 feet, and a 48-square-foot rectangular cashier's station in the corner. Customers should be able to easily walk around the shoe displays, so there must be at least a 4-foot walkway around each. The owner started drawing the layout shown.

NOT Two circular displays can be placed so they are each the same distance from the cashier's station.

Does the point (2,√6) lie on the circle shown?Explain

No, the distance from (0, 0) to (2,√6) is not 3 units.

Which expression represents the volume, in cubic units, of the composite figure? ~4, 8, 6, 10

a. 1/3(8)(6)(6) + (8)(6)(4)

The table shows the number of resident geese living in four different ponds. Which pond has the greatest population density of resident geese?

Pond B

Angles PTQ and STR are vertical angles and congruent. Which chords are congruent?

QP and SR

The diagonal of rectangle ABCD measures 2 inches in length. What is the length of line segm

Square root of 3 inches

Which statement proves that parallelogram KLMN is a rhombus?

The slope of KM is 1 and the slope of NL is -1. *See Graph #33

Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism. How are the surface areas of the figures related?

The surface area of the larger prism is 4 times the surface area of the smaller prism.

How can you find the perimeter of the rhombus?

Use the distance formula to find QT, then multiply by 4.

Which equation is correct regarding the diagram of circle O?

b. m<XZY = 1/2(a - b)

The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

Use the distance formula to find the length of each side, and then add the lengths.

The diagonal of a square is x units. What is the area of the square in terms of x?

a. 1/2x^2 square units

A quilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus. Which measures are true for the quilt piece? Check all that apply.

a = 60° The perimeter of the rhombus is 16 inches. The length of the longer diagonal is approximately 7 inches.

The isosceles triangle shown is rotated about line k. The perimeter of the triangle is 58 units. Which best describes the resulting three-dimensional shape?

a cone with a base radius of 17 units

Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

c. The triangle is not acute because 2^2 + 4^2 < 5^2.

A parabola can be represented by the equation x2 = 2y. What are the coordinates of the focus and the equation of the directrix?

focus: (0,1/2); directrix: y = -1/2

The triangle shown is rotated about line m. What is the approximate base area of the resulting three-dimensional figure? Area of a circle: A = πr2

B/C/D

The circle is inscribed in triangle AEC. Which are congruent line segments? Check all that apply.

EF and ED CB and CD

Figure ABCD is a parallelogram. Which sequence could be used to prove that AD = BC?

First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles.

Figure ABCD is a parallelogram. Which sequence could be used to prove that AD = BC?

First prove ABC is congruent to CDA, and then state AD and BC are corresponding sides of the triangles. *See Graph #7

In circle D what is a secant?

The volume of the oblique cylinder is 24 ft3. Which statements are true? Check all that apply.

The height of the cylinder is 3.4 ft. The diameter of the cylinder is about 3 ft. A right cylinder with the same height and radius as this oblique cylinder would also have a volume of 24 ft3.

Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other?

The midpoint of both diagonals is , the slope of [(4 1/20), (5 1/2)] *See Graph #28

GHLJ and GSTU are both parallelograms. Why is ∠L ≅ ∠T?

The opposite angles of the parallelogram are congruent. Angle T is congruent to angle G, and angle G is congruent to angle L.

Given right triangle XYZ, which correctly describes the locations of the sides in relation to ∠Y?

a is adjacent, b is opposite, c is the hypotenuse

Which expression can be used to find the area of triangle RST?

a. (8 • 4) -1/2 (10 + 12 + 16)

Three interior angles of a quadrilateral measure 55°, 117°, and 120°. What is the measure of the fourth interior angle?

a. 68°

A right triangular prism is shown. What is the volume of the prism?

a. 900 cubic units

Figure ABCD is a parallelogram. What are the measures of angles B and D?

a. <B = 55° ; <D = 55°

If m<ADC = 100 degrees, is ABCD a parallelogram? Explain.

a. Yes; the alternate interior angles are congruent, so AB || CD. Therefore, one pair of opposite sides is congruent and parallel.

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range possible values for the third side of the triangle?

b. 12.5 < x < 18.9

In circle D, ∠EDH ≅ ∠EDG. What is the measure of EG?

b. 123°

What must be the length of ZY in order for ZY to be tangent to circle X at point Y?

b. 15 units

Given △ABC, sin(A) =

cos(C)

Given △ABC, sin(A) =

cos(c)

Which equation can be used to find the measure of angle LJK?

cos(x) = 10/15

LMNP is a parallelogram. What additional information would prove that LMNP is a rectangle?

d. LP _|_ PN

What type of polygon is shown? (6 angles no dents)

d. convex hexagon

Given right triangle GYK, what is the value of tan(G)?

d. √3

Figure CDEF is a parallelogram. Which measures are correct? Check all that apply.

n = 10 CF = 59 FE = 42

Which trigonometric ratios are correct for triangle ABC?

sin(C) = (square root)3/2 tan(C) =(square root) 3 sin(B) =1/2

In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y - 1) m, and OP = (2x - 1) m. What are the values of x and y?

x = 11 m, y = 2 m

In parallelogram LMNO, what are the values of x and y?

x = 55, y = 14

What value of x would make RQ tangent to circle P at point Q?

x = 6

Which equation represents the general form a circle with a center at (-2, -3) and a diameter of 8 units?

x2 + y2 + 4x + 6y - 3 = 0

The focus of a parabola is located at (4,0), and the directrix is located at x = -4. Which equation represents the parabola?

y2 = 16x

Figure ABCD is a parallelogram. What are the measures of angles B and D?

∠B = 55°; ∠D = 55°

Figure ABCD is a parallelogram. What are the measures of angles B and D?

∠B = 55°; ∠D = 55° *See Graph #11

A regular decagon has a radius of 8 cm. What is the approximate area of the decagon? Recall that a decagon is a polygon with 10 sides.

188 cm²

What is the perimeter of kite KLMN?

2 sq. rt. 2 + 2 sq. rt. 5 units

A right rectangular prism with square bases has a height of 20 centimeters and a volume of 800 cubic centimeters. Which statements describe the prism? Check all that apply.

3 4

A prism is enlarged by a factor of 4. The volume of the new prism is 576 cubic units. What could be the dimensions of the original prism?

3 by 3 by 1

UV and RV are secant segments that intersect at point V. What is the length of TV?

3 units

What is the length of line segment AB, rounded to the nearest tenth?

3.4 cm

In the diagram of circle C, what is the measure of ∠1?

35°

Holly chooses seven out of nine plants for the front of her house with the remaining plants to be used on the side of the house. If order does not matter, in how many ways can she choose the plants for the front of the house?

In the regular decagon shown, what is the measure of angle 1?

QR is tangent to circle P at point Q. What is the measure of angle R?

37°

A greeting card uses a geometric design containing 4 congruent kites. The card is 4 inches wide and 8 inches long. What is the area of one kite?

4 sq. in.

What is the perimeter of square ABCD?

4 sq. rt. 37 units

In circle T, ∠PTQ ≅ ∠RTS. What is the length of PQ?

4 units

What is the radius of a circle whose equation is (x + 5)2 + (y - 3)2 = 4^2?

4 units

What is the approximate value of b, rounded to the nearest tenth? Use the law of sines to find the answer.

4.7 Units

Figure CDEF is a parallelogram. What is the value of r?

Quadrilateral RSTU is a parallelogram. What must be the value of x?

The oblique pyramid has a square base. The volume of the pyramid is ____ cm3.

Consider triangle GHJ. What is the length of line segment HJ?

5 (square 3) units

The hypotenuse of a 45°-45°-90° triangle measures 10 sq. rt. in. What is the length of one leg of the triangle?

5 sq. rt. 10

The area of a rectangle is 15 square inches. What will be the area, in square inches, of the rectangle after it is dilated by a scale factor of 2?

in the diagram of circle o, what is the measure of <ABC

Figure VWYX is a kite. What is the measure of angle VXY?

74°

Circle F is congruent to circle J, and ∠EFD ≅ ∠GJH. m∠DFE = 80°. What is the measure of GH?

80°

Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS. What is the measure of QP?

96°

A briefcase has a three-digit lock code that does not include zero as a digit. What is the probability that the lock code consists of all even digits if the same digit is not used more than once in the lock code?

A. 24 out of 504

What lengths would allow you to calculate the volume of the oblique pyramid with a square base? Check all that apply.

AB and EF AC, CB, and EF AD, DB, and EF

In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?

AC ≅ BD

A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume of the pyramid?

B. 1/3x^2y cm3

A right pyramid with a square base has a base edge length of 24 feet and a slant height of 20 feet. What is the height of the pyramid?

16 feet

A right pyramid with a square base has a base edge length of 24 feet and slant height of 20 feet. The height of the pyramid is _____

16 ft

Two cylinders are similar. The radius of cylinder A is 5.6 inches. The radius of cylinder B is 1.4 inches. If the height of cylinder B is 4 inches, what is the height of cylinder A?

16 inches

The parallelogram shown represents a map of the boundaries of a natural preserve. Walking trails run from points A to C and from points B to D. The measurements shown represent miles. What is the sum of the lengths of the two trails?

16 miles

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, a large farm harvested rice from 690 acres of farmland. The crop yield was 7,553 bushels per acre.

5.2 million bushels

Given right triangle RST, what is the value of sin(S)?

5/13

In parallelogram HGJL, HK = c - 7, JK = 3c - 33, and GK = c + 12. What is the length of segment GL?

50 units

Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. What is OB'?

3 units *See Graph #37

The circumference of the base of a cylinder is 24π mm. A similar cylinder has a base with circumference of 60π mm. The lateral area of the larger cylinder is 210π mm2. What is the lateral area of the smaller cylinder?

33.6π mm2

Twelve education students, in groups of four, are taking part in a student-teacher program. Mark cannot be in the first group because he will be arriving late. How many ways can the instructor choose the first group of four education students?

330

What is the area of the octagon, rounded to the nearest square inch?

332 in.²

In the diagram of circle O, what is the measure of ∠ABC?

What expression represents the volume of the prism, in cubic units? (hypotenuse: 13, opposite: 5)

36x²

The volume of an oblique pyramid with a square base is V units3 and the height is h units. Which expression repr

3v/h units2

The length of the opposite <B measures ______ units.

What is the measure of angle L in parallelogram LMNO?

40°

The measure of central angle XYZ is 1.25 radians. What is the area of the shaded sector?

40π units squared

What is the measure of arc EF in circle H?

41°

The height of a cylinder is equal to the diameter of the base. What expression represents the volume of the cylinder, in cubic units?

In circle A, BAE ~= DAE. What is the length of BE?

c. 27 units

Circle C is inscribed in triangle QSU. What is the perimeter of triangle QSU?

d. 40 units

Right trapezoid WXYZ is shown. What is the measure of angle WXY?

c. 107°

In circle O, what is mAE?

c. 120°

In circle V, angle WXZ measures 30°. Line segments WV, XV, ZV, and YV are radii of the circle V. What is the measure of WUX in circle V?

c. 120°

SU and VT are chords that intersect at point R. What is the length of line segment VT?

c. 13 units

Figure ABCD is a parallelogram. What is the value of n?

c. 17

In circle Z, what is m∠2?

140°

What is the volume of the oblique cone? Round to the nearest tenth.

142.4 cubic units

Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA?

(2π/3)x units

The area of the base of the cube, B, is __________________ square units. The volume of the cube is __________________ cubic units. The height of each pyramid, h, is __________________. Therefore, b = 2h. There are _______ square pyramids with the same base and height that exactly fill the given cube. Therefore, the volume of one pyramid is __________________ or 1/3Bh.

(b)(b) (b)(b)(b) b/2 6 (1/6)(b)(b)(2h)

Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?

(x + 2)² + (y - 1)² = 25

Mrs. Culland is finding the center of a circle whose equation is x2 + y2 + 6x + 4y - 3 = 0 by completing the square. Her work is shown. x2 + y2 + 6x + 4y - 3 = 0 x2 + 6x + y2 + 4y - 3 = 0 (x2 + 6x) + (y2 + 4y) = 3 (x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4 Which completes the work correctly?

(x + 3)2 + (y + 2)2 = 42, so the center is (-3, -2).

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. A state had 424 earthquakes over a given time span and a land area of 71,300 square miles. What is the seismic activity density for this state? Round to the nearest ten thousandth, if necessary.

0.0059

In circle C, r = 32 units. What is the area of circle C?

1024

The figure consists of 12 congruent equilateral triangles. The area of one equilateral triangle is a cm2. The area of the hexagon, shaded slightly darker, is b cm2. Which expressions represent the area of the entire shaded region, including the light and dark shading? Select three options.

12a cm2 2b cm2 (6a + b) cm2

What is the area of parallelogram ABCD?

13 Units

A study found that 23% of the cars manufactured last year were SUVs, 13% of the cars manufactured were white, and 2% of the cars manufactured were white SUVs. To the nearest whole percent, what is the probability that a car is an SUV, given that it is white?

15%

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, the harvest at a farm was 9,396 bushels of soybeans, resulting in a crop yield of 40.5 bushels per acre. To the nearest whole acre, how many acres were harvested?

232

Arc QVT measures 156°. Which statement must be true?

Angles QRT and QST both measure 78°.

Which could be the base shape of the cylinder?

C:circle

Four band members, Harry, Isabel, Jose, and Karen, are all boarding a bus to attend a concert. In each arrangement below, the first initial of each person's name represents that person's position as he or she boards the bus: first, second, third, and fourth. If we know that Karen boards the bus first, which shows the possible outcomes for this event?

D. KHIJ, KHJI, KJHI, KJIH, KIHJ, KIJH

The perimeter of the rectangle shown is 76 cm. It is rotated about line b. Which best describes the resulting three-dimensional figure?

D. a cylinder with a base radius of 14 cm

To get from his house to the lecture hall at school, Lin walked west 651 feet. After class, he walked northeast 910 feet to the gym. Finally, he walked 615 feet back to his house from the gym. What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?

Lin walked southwest, creating an obtuse triangle.

Angle K measures 67º and angle L measures 119°. What are the measures of angles M and N?

M = 113° and N = 61°

In quadrilateral LMNO, LO ∥ MN. What additional information would be sufficient, along with the given, to conclude that LMNO is a parallelogram? Check all that apply.

ML ∥ NO LO ≅ MN

A number cube has faces numbered 1 to 6. What is true about rolling the number cube one time? Check all that apply.

S = {1, 2, 3, 4, 5, 6} If A is a subset of S, A could be {5, 6}. If a subset A represents the complement of rolling a 5, its sample space is A = {1, 2, 3, 4, 6}.

In each circle below, a 50° angle with a vertex at the center of the circle is drawn. How are minor arc lengths CD and EF related?

The arc lengths are proportional: CD = 4EF.

Line segments MP and ML are perpendicular chords in circle O. MP = 10 and ML = 24. Which statements about circle O are true? Check all that apply.

The radius of circle O is 13. LP is a diameter of circle O. ∠LMP intercepts a semicircle.

Which statement proves that △XYZ is an isosceles right triangle?

The slope of XZ is 3/4, the slope of XY is -4/3, and XZ = XY = 5.

Angle K measures 67º and angle L measures 119°. What are the measures of angles M and N?

m = 113° and m = 61°

An oblique cylinder is shown. Which represents the volume of the cylinder, in cubic units?

300π

An oblique cylinder is shown. Which represents the volume of the cylinder, in cubic units?

300π

The diameter of the base of the cone measures 8 units. The height measures 6 units. What is the volume of the cone?

32π cubic units

A cone has a radius of 3 and a height given by the expression 2a. Which expression represents the volume of the cone?

6aπ units3

The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of x√3 units. Which expression represents the area of the base of the pyramid?

6x^2√3 units^2

A cylinder has a radius of 2.8 inches and a height of 2.4 inches. Which cylinder is similar?

A frustum is formed when a plane parallel to a cone's base cuts off the upper portion as shown. What is the volume of the frustum? Express the answer in terms of π.

An oblique prism with a square base of edge length x units has a volume of x3 cubic units. Which expression represents the height of the prism?

What is the volume of the composite figure? Use 3.14 for π and round the answer to the nearest tenth of a cubic unit. ~11, 20, 12

c. 1,582.6 in.^3

The volume of the triangular block is 4 cubic inches. What is the approximate length of y? Round to the nearest tenth of an inch.

not b not a

The right triangular prism has a volume of 1,152 cm3. What is the value of x, the height of the prism?

not c not b

A right pyramid with a square base has a base length of x inches, and the height is two inches longer than the length of the base. Which expression represents the volume in terms of x?

x^2(x + 2)/3 cubic inches

Figure JKLM is a kite. What is the measure of angle K?

118°

Triangle BCD is isosceles and BC ≅ BD. What is the measure of BC

130

Triangle BCD is isosceles and BC ≅ BD. What is the measure of ?

130

What is mST?

130 (degrees)

What is the area of triangle ABC? A(1, 1) B(4, 0) C(3, 5)

7 square units

What is the area of triangle QRS?

7 square units

Which relationship in the triangle must be true?

b. sin(B) = cos(90 - B)

The hypotenuse of a 45°-45°-90° triangle measures units. What is the length of one leg of the triangle?

7 units

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches

Quadrilateral LMNO is a rectangle. Find the perimeter of LMNO. The figure is not drawn to scale.

D. 102

What is the measure of ∠ADC in quadrilateral ABCD?

115°

Hien would like to estimate the area of Nevada using a trapezoid. She uses the dimensions shown as approximations. What is the approximate area of Nevada?

110400

In parallelogram LMNO, what is the measure of angle N?

110° *See Graph #14

What is the area of the shaded region?

(25π - 24) cm2

Michael is finding the area of parallelogram ABCD. To do this, he follows the steps in the table. Step 1. Draw a rectangle around parallelogram ABCD. Step 2. Find the area of the rectangle. Step 3. Find the area of the four right triangles created in the corners of the rectangle. Step 4. Subtract the area of the right triangles from the area of the rectangle. To solve the problem using these steps, what are the dimensions of the rectangle he should draw?

(x) 2 units by 4 units (x) 3 units by 2 units () 4 units by 4 units () 5 units by 6 units

What is the area of triangle ABC?

(x) 7.5 units

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The volume of an object is equal to the ratio of its mass to density, V = m/d. The mass of a spherical grape is 8.4 grams and its density is 2 grams per cubic centimeter. What is the radius of the grape? Round to the nearest tenth of a centimeter.

1.0 cm

Given right triangle QRS, what is the value of sin(30°)?

1/2

A grain silo has a diameter of 4.4 meters. The height of its cylindrical portion is 6.2 meters. What is the approximate total volume of the silo? Use 3.14 for π and round the answer to the nearest tenth of a cubic meter.

130.8 m3

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image. What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7

The perimeter of rhombus ABCD is _____ units.

An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?

24.2 cm

An equilateral triangle has an apothem measuring 2.16 cm and a perimeter of 22.45 cm. What is the area of the triangle, rounded to the nearest tenth?

24.2 cm2

Larissa dives into a pool that is 8 feet deep. She touches the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water. What is the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point?

53.1

In the diagram of circle O, what is the measure of <ABC? (126°, 234°)

54°

In the diagram of circle O, what is the measure of ∠ABC? [_______]

54°

If m = m, what is m?

64 (degrees)

A beach has two floating docks. One is 650 meters east of the lifeguard stand. The other is 60° southeast and 750 meters from the lifeguard stand. Law of cosines: a2 = b2 + c2 - 2bccos(A) Rounded to the nearest meter, the distance between the docks is _____ meters.

705

What is the value of x?

A regular hexagon is shown. What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.

9 in

Two sides of an acute triangle measure 5 inches and 8 inches. The length of the longest side is unknown. What is the greatest possible whole-number length of the unknown side?

9 inches

Joe, Keitaro, and Luis play tennis. To decide who will play against each other in the first match, they put their names in a hat and choose two names without looking. What subset, A, represents the complement of the event in which Joe plays in the first match?

A. A = {KL}

In circle D, what is the tangent to the circle?

Which statement regarding these four states is true?

B. The state with the second lowest population has the lowest population density.

Which three-dimensional figure has the greatest number of faces?

B. octagonal pyramid

Miriam is visiting five friends in her neighborhood, Louise, Mike, Nicole, Oscar, and Pascal. In each arrangement below, the first initial of each person's name represents that person's position as he or she is visited by Miriam. Which shows all the outcomes for this event if she visits with Nicole first and Louise last?

C. NMOPL, NMPOL, NOPML, NOMPL, NPMOL, NPOML

The angle measures of quadrilateral RSTU are shown. m∠R = (2x)° m∠S = (3x - 35)° m∠T = (x + 35)° The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?

C. No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.

Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase. He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet. What is the volume of material he must purchase?

D. 8 ft3

Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. Which statement is true regarding the areas of the two flower beds?

Henry's design would result in a larger flower bed because its area would be 2,500 square feet.

The scale factor of the dilation of segment HG is 1/6

If PG' equals 0.5 units, PG equals 3.0 units. *See Graph #44

What is the measure of EFC?

XXX 54 (degrees)

A circle centered at the origin contains the point (0, -9). Does (8, √17) also lie on the circle? Explain.

Yes, the distance from the origin to the point (8, √17) is 9 units.

A kite has a perimeter of 108 feet. One of the longer sides measures 30 feet. What are the lengths of the other three sides?

a. 24 feet, 24 feet, 30 feet

In circle M, diameters JL and HK each measure 16 centimeters. What is the approximate length of minor arc JH? Round to the nearest tenth of a centimeter.

a. 3.5 cm

Points E, F, and D are located on circle C. The measure of arc ED is 68°. What is the measure of angle EFD?

a. 34°

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. What is the measure of ABC?

a. 36°

What is mPO?

b. 173°

which equation can be used to solve for m<1

m<1= 1/2 (c+d)

Given: RW ≅ WT; UW ≅ WS Prove: RSTU is a parallelogram. Identify the steps that complete the proof.

vertical angles theorem SAS CPCTC

What are the values of x and y?

x = 5, y = 22

Using the side lengths of △PQR and △STU, which angle has a sine ratio of 4/5?

∠P

HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other.

(1,0)

HIJK is a parallelogram because the midpoint of both diagonals is _______ which means the diagonals bisect each other.

(1,0) *See Graph #29

A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm. Which expression represents the volume of the pyramid?

(1/3)5.2(h) cm^3

A soundproofing tile is made of 8 identical solid right pyramids with square bases. The length of the whole tile shown is x inches. Which expression shows the area of the base of each pyramid?

(1/4x)^2 in2

To find the area of parallelogram RSTU, Juan starts by drawing a rectangle around it. Each vertex of parallelogram RSTU is on a side of the rectangle he draws. Which expression can be subtracted from the area of the rectangle to find the area of parallelogram RSTU?

(18 + 4)

What is the area of the composite figure if AB ≅ BC ≅ CD ≅ DA ≅ DN?

(2π + 40) mm2

The center of a circle represented by the equation (x − 5)2 + (y + 6)2 = 42 is

(5, -6)

The center of a circle represented by the equation (x − 5)2 + (y + 6)2 = 42 is

(5,-6)

Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?

(x + 3)2 + (y + 5)2 = 36

Mrs. Culland is finding the center of a circle whose equation is x² + y² + 6x + 4y - 3 = 0 by completing the square. Her work is shown. x2 + y2 + 6x + 4y - 3 = 0 x2 + 6x + y2 + 4y - 3 = 0 (x2 + 6x) + (y2 + 4y) = 3 (x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4 Which completes the work correctly?

(x + 3)² + (y + 2)² = 4², so the center is (-3, -2).

Which equation represents a circle with a center at (2, -8) and a radius of 11?

(x - 2)² + (y + 8)² = 121

Two circles are concentric if they have the same center. Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large?

(x - 4)2 + (y - 6)2 = 16

Which equation represents the circle described? The radius is 2 units. The center is the same as the center of a circle whose equation is x2 + y2 - 8x - 6y + 24 = 0.

(x - 4)² + (y - 3)² = 2²

Two circles are concentric if they have the same center. Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large?

(x - 4)² + (y - 6)² = 16

A circle has a diameter of 12 units, and its center lies on the x-axis. What could be the equation of the circle? Check all that apply.

(x - 6)² + y² = 36 (x + 6)² + y² = 36

Concentric circles are circles with the same center but different radii. Which equations represent concentric circles along with the circle shown in the graph? Check all that apply.

(x - 8)² + (y - 9)² = 3 (x - 8)² + (y - 9)² = 14

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What is the approximate length of the diameter, d? Use 3.14 for π. Round to the nearest tenth of a centimeter. [_______] centimeters

-15.9

Consider a circle whose equation is x2 + y2 - 2x - 8 = 0. Which statements are true? Check all that apply.

-The radius of the circle is 3 units. -The center of the circle lies on the x-axis. -The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

An arc on a circle measures 85°. The measure of the central angle, in radians, is within which range?

0 to π/2 radians

A prize bag contains four country music CDs, eight pop music CDs, and five classic rock CDs. What is the probability of pulling out a classic rock CD and then, without replacing it, pulling out a country music CD? Express your answer in decimal form, rounded to the nearest hundredth.

0.07

A librarian has 10 nonfiction and eight fiction books from which to choose the next three book club selections. What is the approximate probability that she chooses a fiction book, then a nonfiction book, then a fiction book?

0.114

At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives. What is the approximate probability that a student chooses a computer elective and an art elective?

0.22727

Find P(Y|B) from the information in the table. To the nearest tenth, P(Y|B) =

0.4

Ryder shot a model rocket over an area that consists of two grassy areas, shown in green, and an area with no grass, shown in white. What is the probability that his model rocket has landed in a grassy area?

0.4

Quadrilateral ABDE is a rectangle. DE = 4 in. and BD = 6 in. If the rectangle is rotated about a line through CF, cylinder Y is created. If the rectangle is rotated about a line through GH, cylinder Z is created. What is the difference in the measures of the radii of cylinder Y and cylinder Z, in inches?

1 inches

A regular hexagon has a radius of 20 in. What is the approximate area of the hexagon?

1,038 in.²

A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute. Approximately how far will a passenger travel during a 5-minute ride?

1,978 feet

Which statements are true about x? Check all that apply.

1. x ∈ B ⋃ C 2. x ∈ B ∩ C 3. x ∈ A ⋃ C 5. x ∈ B 6. x ∈ C

The pentagon below has an area of 8.3 square centimeters. What is the approximate length of the apothem?

1.5 cm

A right triangular prism is constructed so that its height is equal to the leg length of the base. What expression represents the volume of the prism, in cubic units?

1/2 x^3

Consider circle C with radius 5 cm and a central angle measure of 60°. What fraction of the whole circle is arc RS? What is the approximate circumference of the circle? What is the approximate length of arc RS?

1/6 31.4 cm 5.2 cm

The manager of a grocery store reports that there is a 12 percent chance that a customer buys apples during a shopping trip, a 5 percent chance that a customer buy apples and carrots, and a 17 percent chance that a customer buys apples or carrots. What is the probability of a customer buying carrots?

The perimeter of kite WXYZ is 2√53 + 10 units

Consider triangle QRS. The legs each have a length of 10 units. What is the length of the hypotenuse of the triangle?

10 (square 2) Units

The height of trapezoid VWXZ is 8(square 3) units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX. What is the length of the lower base, ZX?

10 + 4 (square 3) Units 10 + 8 (square 3) Units

Triangle ABC is an isosceles triangle in which AB = AC. What is the perimeter of △ABC?

10 + √10 units *See Graph #31

The area of the regular pentagon is 6.9 cm2. What is the perimeter?

10 cm

10 percent

The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

10.2 inches

A ramp leading into a building makes a 15° angle with the ground. The end of the ramp is 10 feet from the base of the building. Approximately how long is the ramp? Round to the nearest tenth.

10.4 feet

The equation tan(55°) = 15/b can be used to find the length of AC. What is the length of AC? Round to the nearest tenth.

10.5

The equation tan(55o)=can be used to find the length of . What is the length of ? Round to the nearest tenth.

10.5 cm

The floor of a gazebo is in the shape of a regular octagon. The perimeter of the floor is 72 feet. The distance from the center of the octagon to one of the vertices is 11.8 feet. What is the approximate length of the apothem? What is the approximate area of the floor of the gazebo?

10.9 392.4

Yolanda is making a banner for a school pep rally. She cuts fabric in the shape of a parallelogram. The angle at the bottom left corner measures 80°. The measure of the angle at the top left corner must measure

100°

Yolanda is making a banner for a school pep rally. She cuts fabric in the shape of a parallelogram. The angle at the bottom left corner measures 80°.

100° *See Graph #2 The measure of the angle at the top left corner must measure.

What are the remaining angle measures if the figure is to be a parallelogram? m∠B = __° m∠C = __° m∠D = __°

101 79 101

A regular octagon has a radius of 6 ft and a side length of 4.6 ft. What is the approximate area of the octagon?

101 ft2

What are the measures of JK and ∠KIJ? Measure of JK = Measure of ∠KIJ =

104° 52°

In quadrilateral QRST, measures (5x + 15)o. Angle TQR measures (4x + 3)o. What is the measure of angle RST?

105°

In quadrilateral QRST, measures (5x + 15)°. Angle TQR measures (4x + 3)°. What is the measure of angle RST?

105°

What is the measure of angle O in parallelogram LMNO? m∠O =

105°

A carpenter is making a 1-inch-wide wooden frame to surround a window. To build the frame, the carpenter needs (5.5π + ______) square inches of wood.

106

in the diagram of circle p m< XYZ is 72, what is the value of X

108

What is the measure of ∠B?

108°

A carpenter cuts the corners of a rectangle to make the trapezoid shown. What is the value of x?

A section of a rectangle is shaded. The area of the shaded section is 63 square units. What is the value of x?

The base of the right triangle drawn in the regular octagon measures 0.7 cm. What is the perimeter of the octagon?

11.2

The measure of ∠B is (3x - 4 )° and the measure of ∠D is (2x - 6)°. What are the measures of angles B and D? m∠B = m∠D =

110° 70°

Consider circle C with angle ACB measuring 3╓/4 radians. If minor arc AB measures 9π inches, what is the length of the radius of circle C? If necessary, round your answer to the nearest inch.

The area of rhombus ABCD is 120 square units. AE = 12 and BD = x - 2. W

12 10

Juan is making a border out of rhombi for his wall. Each rhombus will be connected to the one before it. Each rhombus will be 6 inches tall and 4 inches wide. How much paper does he need for each rhombus? If his wall is 11 feet long, how much paper does he use?

12 396

Circle P has. circumference of approximately 75 inches. What is the approximate length the radius of r? Use 3.14 for 🍰. Round to the nearest inch.

12 inches

Consider circle C with angle ACB measuring 3pi/4 radians. If minor arc AB measures 9π inches, what is the length of the radius of circle C? If necessary, round your answer to the nearest inch.

12 inches

Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse?

12 sq. root 2 cm.

A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the pole. What is the height of the pole?

12 sq. root 3 ft.

Trapezoid ABCD is graphed in a coordinate plane. What is the area of the trapezoid?

12 square units

What is the area of triangle LMN?

12 square units

Consider circle C below, where the central angle is measured in radians. What is the length of the radius?

12 units

FH is tangent to circle G at point F. What is the length of the radius, r?

12 units

FH is tangent to circle G at point F. What is the length of radius, r?

12 units

Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units. What is the length of AC?

12 units

What is the length of a side of rhombus JKLM?

12 units

Rectangle WXYZ was dilated using the rule . What is W'X'?

12 units *See Graph #36

Line segment XY is dilated to create line segment X'Y' using point T as the center of dilation. What is YT?

12 units *See Graph #42

A regular pentagon is shown. What is the measure of the radius, c, rounded to the nearest hundredth? Use an appropriate trigonometric ratio to solve.

12.36 cm

An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown. Which best describes the range of possible values for the third side of the triangle?

12.5 < x < 18.9

Line segment BD passes through the center of circle C, BH = a, and HD = 8. What is the length of the diameter?

12.5 units

The equation sin(40°) = b/20 can be used to determine the length of line segment AC. What is the length of AC? Round to the nearest tenth.

12.9 cm

Given △ABC ~ △XYZ, what is the value of cos(Z)?

12/13

Given right triangle ABC, what is the value of tan(A)?

12/5

How many ways can eight letters be arranged into groups of five where order matters and the first two letters are already chosen?

120

What is the area of the sector that is not shaded?

120

A garden is designed in the shape of a rhombus formed from 4 identical 30°-60°-90° triangles. The shorter distance across the middle of the garden measures 30 feet. What is the distance around the perimeter of the garden?

120 ft.

The measure of minor arc JL is 60°. What is the measure of angle JKL?

120°

The sum of all but one interior angle of a heptagon is 776°. The final angle must have a measure of ___ degrees.

124

The sum of all but one interior angle of a heptagon is 776°. The final angle must have a measure of _______ degrees.

124

Four interior angles of a pentagon measure 156°, 72°, 98°, and 87°. What is the measure of the final interior angle?

127°

A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid. If the height is 6 cm, the volume of the pyramid is cm3.

128

12a cm2, 2b cm2, (6a + b) cm2

What is the length of the two chords shown? The length of the shorter chord is __________ units.

Figure ABCD is a parallelogram. If ABCD is also a rhombus, what must be the value of x?

13 *See Graph #22

A wall in Maria's bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle. Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.

13 ft

For a project, Carlos must provide one cut-out paper model of each type of triangle: acute, right, and obtuse. He sketches each triangle on graph paper before making the models. What is the total area of the three triangles?

13 square units

What is the area of parallelogram ABCD? A(3, 6) D(2, 2) B(5, 6) C(5, 1).

13 square units

What is the length of the shorter of the two chords shown?

13 units

Line segment AB was dilated to create line segment A'B' using the dilation rule DQ,0.15. What is x, the distance between points A and A'?

13.6 units *See Graph #35

What is the perimeter, rounded to the nearest tenth?

13.8 ft

Triangle BCD is isosceles and BC ≅ BD. What is the measure of ?

130

Triangle BCD is isosceles and BC ≅ BD. What is the measure of BC?

130°

What is the value of x?

130°

In circle O, AD and BE are diameters. What is mAE?

132

What is the measure of arc BEC in circle D?

134°

Each angle of a regular octagon has a measure of ___ degrees.

135

Each angle of a regular octagon has a measure of ________ degrees.

135

The corner of a rectangle is cut, creating a right trapezoid. What is the value of x?

135°

Square ABCD and isosceles triangle BUC are drawn to create trapezoid AUCD. What is the measure of angle DCU?

135º

The corner of a rectangle is cut, creating a right trapezoid. What is the value of x?

135º

A hexagon has a radius measuring 23 cm. What is the approximate area of the hexagon?

1374.4 square cm

The law of cosines is used to find the value of m. m2 = 272 + 182 - 2(27)(18)cos(28°) m2 = 729 + 324 - (972)cos(28°) m2 = 1053 - (972)cos(28°) To the nearest whole number, the value of m is ____

The law of cosines is used to find the value of m. m2 = 272 + 182 - 2(27)(18)cos(28°) m2 = 729 + 324 - (972)cos(28°) m2 = 1053 - (972)cos(28°) To the nearest whole number, the value of m is

The sides of a triangle have length x, x + 4, and 20. If the length of the longest side is 20, which value of x would make the triangle acute?

The longest side of an isosceles obtuse triangle measures 20 centimeters. The other two side lengths are congruent but unknown. What is the greatest possible whole-number value of the congruent side lengths?

14 cm

What is the approximate length of the diameter, d? (44 in.)

14 in.

Figure ABCD is a kite. What is the length of line segment BC?

14 units

An oblique prism is created using rhombuses with edge lengths of 25 units. The area of one rhombus is 600 square units. The perpendicular distance between the bases is 24 units. What is the volume of the prism?

14,400 cubic units

Rounded to the nearest tenth of a centimeter, what is the length of arc LMN?

14.2 cm

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25o angle with the ground and when the string makes a 45o angle with the ground? Round to the nearest tenth.

14.2 feet

Kari is flying a kite. She releases 50 feet of string. What is the approximate difference in the height of the kite when the string makes a 25º angle with the ground and when the string makes a 45º angle with the ground? Round to the nearest tenth.

14.2 feet

What is the measure of angle BCD?(25,146,149)

140

Figure ABCD is a parallelogram. Points X and Y are placed so that BX ≅ DY and CD ⊥ XY. The area of BXYC is 71.5 square units. What is the area of ABCD?

143 square units

Evaluate the expression. 4! • 3!

144

What is the sum of the interior angle measures of a regular decagon? What is the measure of each interior angle of a regular decagon?

1440 144

A regular pentagon has an apothem measuring 20 cm and a perimeter of 145.3 cm. What is the area of the pentagon?

1453

Line segment TS is tangent to circle O at point N. If the measure of QNT is 74°, what is the measure of QNP?

148°

Line segment TS is tangent to circle O at point N. If the measure of QNT is 74°, what is the measure of QPN?

148°

What is the measure of EG?

149°

Which expression represents the volume of the prism, in cubic centimeters?

14x² + 7x

In parallelogram WXYZ, what is CY?

What is the value of x in trapezoid ABCD?

What is the value of x of n trapezoid ABCD?

The polygon below is a regular hexagon. What is the approximate length of the apothem? Round to the nearest tenth.

15.6 cm

Consider circle N with radius 30 cm and θ = ╓/6 radians. What is the approximate length of minor arc LM? Round to the nearest tenth of a centimeter.

15.7

Consider circle N with radius 30 cm and θ = pi/6 radians. What is the approximate length of minor arc LM? Round to the nearest tenth of a centimeter.

15.7 cm

In circle O, MP is a diameter. If m is 6 more than 5 times the measure of MN, what is mNP?

151

In circle O, MP is a diameter. If NP is 6 more than 5 times the measure of MN, what is NP?

151°

16 Miles *See Graph #8

Consider triangle PQR. What is the length of side QR? (8 square 3, 8)

16 Units

16.7°

16.7º

A kite has vertices at (2, 4), (5, 4), (5, 1), and (0, -1). What is the approximate perimeter of the kite? Round to the nearest tenth.

16.8 units

What is the measure of angle COA?

160°

A right triangle has one angle that measure 23°. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth.

161.7 cm2

What is the measure of QS?

168°

A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4√3 cm and an area of 12√3 cm2. What is the volume of the pyramid?

16√3

Figure ABCD is a parallelogram. What is the value of n?

In circle A, ∠BAE ≅ ∠DAE. What is the value of x?

In the Venn diagram, consider U = {students in 10th grade at Lee High School}. The diagram shows the electives chosen by the students in the 10th grade. How many student chose to participate in the painting class?

A survey of the 12th grade students at Gaffigan High School found that 84% of the seniors have their driver's licenses, 16% of seniors take the bus every day to school, and 14% of the seniors have driver's licenses and take the bus to school every day. To the nearest whole percent, what is the probability that a senior takes the bus to school every day, given that he or she has a driver's license?

17%

What is the approximate value of y − x?

17.2°

How many square yards of cement are needed to create the walkway around the rectangular pool?

176 square yards

AD and MN are chords that intersect at point B. What is the length of line segment MN

In circle G, r = 3 units. Maria draws a circle with double the area of circle G. What is the area of Maria's circle?

Marina wants to install security cameras in her store, which has dimensions 48 feet by 48 feet. Each camera can view an area of approximately 128 ft2, with a viewing area shaped like a right triangle.

Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle

18 Units 36 Units 36 (square 2) Units

Circle O has a circumference of 36π cm. What is the length of the radius, r?

18 cm

The weather report states that the probability it will rain on Wednesday is 30 percent and the probability that it will rain on Saturday is 60 percent. What is the probability that it will rain on Wednesday and on Saturday?

18 percent

The height of trapezoid VWXZ is units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX. Once you you know the length of YX, find the length of the lower base, ZX?

18 units

18%

What is the area of the shaded sector of the circle?

180

What is the area of the shaded sector of the circle?

180╓ units

Building A and building B are 500 meters apart. There is no road between them, so to drive from building A to building B, it is necessary to first drive to building C and then to building B. About how much farther is it to drive than to walk directly from building A to building B? Round to the nearest whole number.

183 meters

A regular decagon has a radius of 8 cm. What is the approximate area of the decagon? Recall that a decagon is a polygon with 10 sides.

188 cm2

Two sides of an obtuse triangle measure 10 inches and 15 inches. The length of longest side is unknown. What is the smallest possible whole-number length of the unknown side?

19 inches

The perimeter of a square is 56 cm. What is the approximate length of its diagonal?

19.8 cm

Line EF is tangent to circle G at point A. If the measure of CAE is 95°, what is the measure of CBA?

190°

The population density of Peru one year was approximately 23 people per square kilometer. Brazil has a land area of approximately 8.5 million square kilometers.

195,500,000 people

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters. What is the volume of the tissue paper in the packaging box?

198.264 cubic centimeters

Line segment AB is dilated to create line segment A'B' using point Q as the center of dilation. What is the scale factor?

2 *See Graph #41

What is the perimeter of parallelogram WXYZ?

2 sq. rt. 5 + 2 sq. rt. 17 units

Line segment ON is perpendicular to line segment ML. What is the length of segment NP?

2 units

What is the radius of a circle whose equation is (x - 7)2 + (y - 10)2 = 4?

2 units

What is the radius of a circle whose equation is x²+y²+8x−6y+21=0?

2 units

Which sets of three of numbers represent the sides of an obtuse triangle? Check all that apply.

2, 2, 3 3, 5, 6

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area of the heptagon rounded to the nearest whole number? Recall that a heptagon is a polygon with 7 sides.

2,125 cm2

What is the area of triangle ABC?

2.5 square units 3 square units <---- 3.5 square units 4 square units

Bianca calculated the height of the equilateral triangle with side lengths of 10. Then, she used the formula for area of a triangle to approximate its area, as shown below. Calculate the area of the equilateral triangle using the formula for area of a regular polygon, and compare it to Bianca's answer. The apothem, rounded to the nearest tenth, is ___ The perimeter of the equilateral triangle is ____ units. Therefore, the area of the equilateral triangle is ______________, or approximately 43.5 units2. The calculated areas are ________________

2.9 30 1/2(2.9)(30) the same, despite using different formulas

Fiona needs to chose a five-character password with a combination of three letters and the even numbers 0, 2, 4, 6, or 8. If she uses her initials, F, J, and S in order as the first three characters, and she does not use the same digit more than once in her password, how many different possible passwords are there?

In the diagram, AB = 10 and AC = . What is the perimeter of △ABC?

20 + 2√20 units *See Graph #34

When a softball player gets a hit, it can be a single, double, triple, or home run. When Josephine is at bat, the probability that she hits a single is 15 percent and the probability that she hits a double is 5 percent. What is the probability that Josephine hits a single or a double when she is at bat?

20 percent

What is the area of parallelogram ABCD?

20 square units

Rhombus WXYZ is graphed on a coordinate plane. What is the perimeter of the rhombus?

20 units

The equation cos(35°) = a/25 can be used to find the length of BC. What is the length of BC? Round to the nearest tenth.

20.5

The equation cos(35o) = can be used to find the length of . What is the length of ? Round to the nearest tenth.

20.5 inches

A toy company produces rubber balls that have a radius of 1.7 cm. What is the volume of one rubber ball? Round to the nearest hundredth of a centimeter. _______ cm3 If the price of the rubber needed to produce a ball is $0.0045/cm3, what is the cost of producing one ball? Round to the nearest cent. $_______ If the company sells a ball for $0.50, how much profit will it make on each ball? $_______

20.58 0.09 0.41

Consider circle T with radius 24 in. and θ = 5π/6 radians. What is the length of minor arc SV?

20π

What is the length of minor arc SV?

20π in.

What is the area of parallelogram RSTU?`

21 square units

The equation sin(25°) = 9/c can be used to find the length of AB. What is the length of AB? Round to the nearest tenth.

21.3 in.

What is the measure of CED?

212°

Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.

Heron's formula: Area = Triangle PQR has sides measuring 9 feet and 10 feet and a perimeter of 24 feet. What is the area of triangle PQR? Round to the nearest square foot.

22 square feet

The hypotenuse of a 45°-45°-90° triangle measures units. What is the length of one leg of the triangle?

22 units

Points A, B, C, and D lie on circle M. Line segment BD is a diameter. The measure of arc CD equals the measure of arc DA. What is the measure of angle ADM?

22.5°

In circle O, AC and EB are diameters. The measure of arc DC is 50°. What is the meadure of EBC?

220°

A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. The apothem of the hexagon is 2 centimeters. What is the volume of metal in the hex nut, to the nearest tenth? Use 3.14 for π.

23.6 cm3

In the diagram of circle R, m∠FGH is 50°. What is m?

230°

232

Helena has five different flowers. She plans to give one flower to each of her five teachers in any order. She gives the first flower to one of her teachers in the morning. In how many different ways can she give the four remaining flowers to the rest of the teachers in the afternoon?

What is the area of the shaded region? 6mm, 4mm, 2mm, 3mm, 5mm.

24 mm^2

Trapezoid ABCD is graphed in a coordinate plane. What is the area of the trapezoid?

24 square units

What is the area of the rhombus? 3,3,4,4

24 square units

Triangle MNO is an equilateral triangle with sides measuring 16 sq. root 3 units. What is the height of the triangle?

24 units

What is the volume of the right rectangular prism?

240 cm³

A square has an apothem measuring 2.5 cm and a perimeter of 20 cm. What is the area of the square, rounded to the nearest square centimeter?

25 cm²

Circle O has a circumference of approximately 250π ft. What is the approximate length of the diameter, d?

250 ft

Circle O has a circumference of approximately 250π ft. What is the approximate length of the diameter, d?

250 ft

In circle O, AE and FC are diameters. Arc ED measures 17°. What is the measure of EFC?

253°

Points D, E, and F are on circle C and EF ≅ DF. What is the measure of ∠CDF?

The diagram shows the universal set U = {parallelograms}. Set A represents parallelograms with four congruent sides, while Set B represents parallelograms with four congruent angles. How many of the parallelograms fall into the category A B?

In parallelogram RSTU, what is SU?

26 m

What is the area of the composite figure?

264 cm2

What is the area of the composite figures? (6cm, 4cm, 3cm, 10cm, 10cm, 10cm, 5cm, 4cm, 2cm, 6cm)

264 cm^2

Segments RT and SU are diameters of circle O. What is mSRT?

266°

Points D, E, and F are on circle C and EF ≅ DF. What is the measure of ∠CDF?

26°

In circle A, ∠BAE ≅ ∠DAE. What is the length of BE?

27 units

A coach chooses six out of eight players to go to a skills workshop. If order does not matter, in how many ways can he choose the players for the workshop?

Nine wolves, eight female and one male, are to be released into the wild three at a time. If the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed?

Twenty-two percent of the large pieces of mail that Rachel received this week were magazines and the rest were catalogs. Of the catalogs, 36 percent were for clothing. To the nearest whole percent, what is the probability that a randomly chosen large piece of Rachel's mail was a clothing catalog?

28%

In circle O, AD and BE are diameters. The measure of arc AB is 55° and the measure of arc CD is 25°. What is the measure of EAC?

280°

What is the volume of the sphere in terms of π?

288

What is the perimeter of parallelogram WXYZ?

2√5 + 2√17 units

A general formula for a parabola is x2 = 4py. What is the value of p in the equation x2 = 12y?

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

Jamel is asked to create triangles using three of four given sticks. The sticks measure 3 in., 6 in., 7 in., and 8 in. He creates these 4 triangles. Triangle 1: 3 in., 6 in., 7 in. Triangle 2: 3 in., 6 in., 8 in. Triangle 3: 3 in., 7 in., 8 in. Triangle 4: 6 in., 7 in., 8 in. How many of his triangles are obtuse?

The volume of the triangular prism is 54 cubic units. What is the value of x?

What is the value of y?

A right square prism has a volume of 360 cubic units. Which could be the dimensions, in units, of the prism? Check all that apply

3 by 3 by 40 6 by 6 by 10 2.5 by 12 by 12 3.6 by 10 by 10

All tangents to the circle are congruent and form a square. The perimeter of square ACEG is 24 cm. What is the length of line segment BC?

3 cm

UV and RV are secant segments that intersect at point V. What is the length of TV?

3 units

Use the law of sines to find the value of a. What is the best approximation of the value of a?

3.0 cm

What is the best approximation of the value of a?

3.0 cm

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth.

3.2 inches

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°. What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.

3.2 yards

A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest side. Rounded to the nearest tenth, what is the difference between the possible values of x?

3.4 units

Fiona must find the length indicated by the dotted line for the tiles she is installing. She knows that each polygon is a regular hexagon with a perimeter of 7.5 in. The length of the dotted line is 3.75 in. Express the answer to the nearest hundredth.

3.75

The spinner is equally likely to land on any of the five sections. What is the probability that the spinner lands on an even number or on the unshaded section?

3/5

An area reserved for a parking lot is 80 feet long and 77 feet wide. The stalls of the lot are at 90° angles to two one-way aisles. Each aisle is 80 feet by 10 feet. The three areas set aside for the parking spaces are congruent rectangles. Each parking space will be 19 feet by 8 feet. What is the maximum number of parking spaces that will fit in the lot?

The volume of the prism is 840 cubic units. What is the perimeter of the base?

In the kite, AC = 10 and BD = 6. What is the area of kite ABCD?

30 square units

The pentagonal prism has a perpendicular distance of 14 units between the bases. The volume of the prism is 840 cubic units. What is the perimeter of the base?

30 units

Line segment ON is perpendicular to line segment ML, and PN = 10. What is the area of triangle MOL?

300 square units

In the diagram of circle O, what is the measure of <ABC? (210°, 150°)

30°

In the diagram of circle O, what is the measure of ∠ABC?

30°

in circle y what is m<1

In quadrilateral ABCD, AD ∥ BC. What must the length of segment AD be for the quadrilateral to be a parallelogram?

31 units

What is the area of parallelogram RSTU?

What is the area of the pentagon, rounded to the nearest tenth?

32.7 cm²

What is the area of triangle ABC? Round to the nearest square unit.

A sandbox is shaped like a kite. Each unit on the coordinate plane represents one foot. A planner would like to replace the wooden border around the sandbox. How many feet of wood does he need? Round to the nearest whole number, if necessary.

In parallelogram LONM, what is OM?

34 cm

TREC is a rectangle. What is the length of ET?

34 units *See Graph #21

The composite figure is made up of a triangular prism and a pyramid. The two solids have congruent bases. What is the volume of the composite figure?

3465 units

A regular pentagon has a perimeter of 60 cm. What is the measure of central angle CBD? What is the length of segment CD? Which trigonometric ratio can be used to compare BC to CD using angle CBD? What is the approximate length of BC? What is the approximate length of BD?

36 6 tangent 8.3 10.2

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. What is the measure of ABC?

36°

The measure of central angle YCZ is 80 degrees. What is the sum of the areas of the two shaded sectors?

36π units squared

The area of the octagon below is 10,391.9 square millimeters. What is the approximate perimeter of the octagon? Round to the nearest whole number. What is the approximate length of one side of the octagon? Round to the nearest whole number.

371 46

A 15-meter by 23-meter garden is divided into two sections. Two sidewalks run along the diagonal of the square section and along the diagonal of the smaller rectangular section. What is the approximate sum of the lengths of the two sidewalks, shown as dotted lines?

38.2 m

What is the volume of the prism?

384 cubic units

What is the measure of C ?

38°

What is the measure of ∠C ?

38°

Maggie puts together two isosceles triangles so that they share a base, creating a kite. Each leg of the upper triangle measures 41 inches and each leg of the lower one measures 50 inches. If the length of the base of both triangles measures 80 inches, what is the length of the kite's shorter diagonal?

39 inches

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

39.4°

The volume of a solid right pyramid with a square base is V units3 and the length of the base edge is y units. Which expression represents the height of the pyramid?

3V/y^2 units

An arc on a circle measures 295°. The measure of the central angle, in radians, is within which range?

3π/2 to 2π radians

Minor arc KL measures 135°. Which is the radian measure of central angle KOL?

3π/4 radians

In the diagram, KL = , LM = , and MN = . What is the perimeter of isosceles trapezoid KLMN?

3√2 + 2√5 Units *See Graph #27

The Venn diagram shows the number of customers who have purchased different types of pets from a pet store, where C represents customers who have purchased cats, D represents customers who have purchased dogs, and F represents customers who have purchased fish. How many people are in the set C ∩ D?

The equation of a circle is x² + (y - 10)² = 16. The radius of the circle is __ units. The center of the circle is a _____

4 (0,10)

In parallelogram RSTU, SW = 4 cm, WT = 6 cm, RS = 5 cm, and ST = 7 cm. What is the length of line segment WU?

4 cm

The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?

4 cm

Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram?

4 cm and 7 cm

The perimeter of parallelogram ABCD is 46 inches. What is DA?

4 in.

Michael is finding the area of parallelogram ABCD. To do this, he follows the steps in the table. Step 1 Draw a rectangle around parallelogram ABCD. Step 2 Find the area of the rectangle. Step 3 Find the area of the four right triangles created in the corners of the rectangle. Step 4 Subtract the area of the right triangles from the area of the rectangle. To solve the problem using these steps, what are the dimensions of the rectangle he should draw?

4 units by 4 units

The radius of the sphere is 10 units. What is the approximate volume of the sphere? Use π = 3.14 and round to the nearest whole cubic unit.

4,187 cubic units

A right triangle has one side that measures 4 in. The angle opposite that side measures 80o. What is the length of the hypotenuse of the triangle? Round to the nearest tenth.

4.1 inches

A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?

4.5

A solid oblique pyramid has a square base with an edge length of 2 cm. Angle BAC measures 45°. What is the volume of the pyramid?

4.8 cm³

Given right triangle MNL, what is the value of cos(M)?

4/5

What is the measure of angle L in parallelogram LMNO?

Angle G is a circumscribed angle of circle E. Major arc FD measures 280°. What is the measure of angle GFD?

40°

In the regular nonagon shown, what is the measure of angle x?

40°

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

41 units

The regular hexagon has a radius of 4 in. What is the approximate area of the hexagon?

42 in.2

A square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year. Each diagonal of the square window measures 9 inches. What is the approximate total length of iron edging needed to create the square frame and the two diagonals?

43.5 inches *See Graph #25

The measure of angle BAC can be calculated using the equation sin-1 (3.1/4.5) = x. What is the measure of angle BAC? Round to the nearest whole degree.

Circle O has a circumference of 88π cm. What is the length of the radius of the circle?

44 cm

Figure ABCD is a parallelogram. What is the perimeter of ABCD?

44 units

Figure ABCD is a parallelogram. What is the perimeter of ABCD?

44 units *See Graph #6

The perimeter of the rectangle is 146 units. What is the length of the longer side?

45 units

ABCD is a square. What is the measure of angle BAC?

45°

A hole the size of a photograph is cut from a red piece of paper to use in a picture frame. What is the area of the piece of red paper after the hole for the photograph has been cut?

47 square units

In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8. What is the length of line segment DB?

48 units

The area of the regular hexagon is 169.74 ft2. What is the perimeter, rounded to the nearest tenth?

48.5 ft

In circle C, what is mFH?

48°

The equation tan−1(8.9/7.7) = x can be used to find the measure of angle LKJ. What is the measure of angle LKJ? Round to the nearest whole degree.

The measure of arc QS is (4x - 18)°. What is the value of x?

49.5

What is the measure of <LMN in kite KLMN?

49°

A parallelogram has side lengths of 4 and 6 and an angle of measure 55°. Law of cosines: a2 = b2 + c2 - 2bccos(A) What is x, the length of the diagonal, to the nearest whole number?

What is the scale factor of the dilation of line segment BA?

5 *See Graph #39

Marlena has 3 straws. Two straws have the lengths shown. She does not know the length of the shortest straw, but when she forms a triangle with all three, the triangle is obtuse. Which are possible lengths of the shortest straw? Check all that apply.

5 inches 6 inches 7 inches

In circle D, ∠EDH ≅ ∠EDG. What is the length of JG?

5 units

Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides. The area of EFGH is 35 square units. What is the value of x?

5 units

The area of the trapezoid is 40 square units. What is the height of the trapezoid?

5 units

Triangle JKL was dilated using the rule . The image, triangle J'K'L', is the result of the dilation. What is L'L?

5 units *See Graph #40

Which triangle is a 30°-60°-90° triangle?

5-10-5(square 3)

Three out of nine students in the computer club are getting prizes for first, second, and third place in a competition. How many ways can first, second, and third place be assigned?

504

What is the measure of AU?

50°

Jacob is cutting a tile in the shape of a parallelogram. Two opposite angles have measures of (6n − 70)° and (2n + 10)°. What are the two different angle measures of the parallelogram-shaped tile?

50° and 130°

The length of the hypotenuse, line segment AC, in right triangle ABC is 25 cm. The length of line segment BC is 15 cm. Which is the approximate measure of angle ACB?

53.1

Two similar cylinders have surface areas of 24π cm2 and 54π cm2. The volume of the smaller cylinder is 16π cm3. What is the volume of the larger cylinder?

54╓ cm

Crop yield is the ratio of the number of bushels harvested to the number of acres used for the harvest. This year, the harvest at a farm was 94,010 bushels of grain, resulting in a crop yield of 170 bushels per acre. To the nearest whole acre, how many acres were harvested?

553

553 acres

To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. The tree meets the ground at a right angle. At approximately what angle does the wire meet the ground?

56.4°

AB is tangent to ⊙C at point B and AD is tangent to ⊙C at point D. What is m∠A?

56°

Line segment SU is a diameter of circle V. What is the measure of arc ST?

56°

Rhombus LMNO is shown with its diagonals. Angle MLO measures 112°. What is the measure of angle MLP?

56°

Which is the best approximation for the measure of angle ABC?

58.3°

A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile. How many deer live in the county? Round to the nearest whole number, if necessary.

5852

An oblique prism has a volume of 144 cubic units. The area of its base is 24 square units. What is the perpendicular height of the prism?

Figure ABCD is a parallelogram. What is the value of p?

Figure VWYX is a kite. What is the value of x?

The chords intersect at point U. What is the value of y?

Figure ABCD is a parallelogram. What is the value of p?

6 *See Graph #1

The perimeter of parallelogram PQSR is 74 cm. What is QS?

6 cm

A right prism has a rhombus as a base. The height of the prism is 6 inches and the volume is 144 cubic inches. Which could be the lengths of the diagonals of the rhombus?

6 in. by 8 in.

How can you best describe the outside of one of these objects using polygons? The object has __ sides, so it is _____________. It appears to be __________ because the sides and angles appear to be congruent.

6, a hexagon regular

QR is tangent to circle P at point Q. What is the approximate length of RP? Round to the nearest tenth.

6.1 units

The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm. Rounded to the nearest tenth, what is the greatest possible value of x?

6.3

A regular pentagon is shown. What is the length of the apothem, rounded to the nearest tenth?

6.5 cm

The area of a kite is 51.68 square inches. One diagonal measures 15.2 inches. What is the measure of the other diagonal?

6.8 inches

A model of a soccer ball is made up of regular pentagons and hexagons. The side length of one of the pentagons measures 2 inches and the apothem measures about 1.38 inches. What is the area of one of the pentagons? State your answer to the nearest tenth. The side length of one of the hexagons measures 2 inches and the apothem measures about 1.73 inches. What is the area of one of the hexagons? State your answer to the nearest tenth.

6.9 10.4

Nico owns 11 instructional piano books. Two are beginner books, six are intermediate books, and three are advanced books. If two books are randomly chosen from the collection, one at a time, and replaced after each pick, what is the probability that he first chooses an advanced book and then chooses a beginner book?

6/121

Lourdes is making a frame in the shape of a parallelogram. She adds diagonal braces to strengthen the frame. How long is the brace that connects points B and D?

60 cm

The composite figure is made up of two congruent rectangular pyramids joined at their bases. What is the total volume of the composite figure

60 units

What is the measure of each exterior angle of a regular hexagon?

60°

Consider a regular hexagon inscribed in circle C with radius r. Regular hexagons have six congruent sides and six congruent angles. In the figure, angle CAB measures 60°. What is m∠ACB? What is the length of segment AB? What is the perimeter of the hexagon? The perimeter of the hexagon is the circumference of the circle. The circumference of the circle is

60° r 6r slightly less than slightly greater than 6r

A right cylinder has a radius of 2 units and height of 5 units. What is the volume of the cylinder? Round to the nearest tenth.

62.8 cubic units

The hypotenuse of a 45°-45°-90° triangle measures 128 cm. What is the length of one leg of the triangle?

64 sq. root 2 cm.

Consider circle O, in which arc XY measures 16π cm. The length of a radius of the circle is 32 cm. What is the circumference of the circle? What is the ratio of the arc length to the circumference? What is the measure of central angle XOY?

64π units 1/4 90°

The radius of a regular decagon, a 10-sided figure, is 15 units. The length of one side of the polygon measures about 9.3 units. What is the approximate area of the regular decagon rounded to the nearest tenth?

663.1 square units

In circle T, ∠PTQ ≅ ∠RTS. What is the measure of PQ?

66°

A regular hexagon has an apothem measuring 14 cm and an approximate perimeter of 96 cm. What is the approximate area of the hexagon?

672 cm2

Point G is the center of the small circle. Point X is the center of the large circle. Points G, Y, and X are all on line segment GX. Marco wants to create a new circle using GX as a radius. What will be the area of Marco's new circle?

676

Chords DE, EF, and FG are congruent. mFG = m∠ECF =

67° 67°

A plot of land is in the shape of a parallelogram with the dimensions shown. How many feet of fencing are needed to enclose the lot?

68 Feet *See Graph #9

A plot of land is in the shape of a parallelogram with the dimensions shown. How many feet of fencing are needed to enclose the lot?

68 feet

Rhombus LMNO is shown with its diagonals. Angle MNO measures 112°. What is the measure of angle LMN?

68°

What is the length of segment EB in parallelogram ABCD?

69 units

Which expression represents the volume of the prism in terms of w, the width of the base?

6w³ cubic units

In circle O, central angle AOB measures π/3 radians. What is the length of arc AB?

6π cm

Figure JKLM is a parallelogram. The measures of line segments MT and TK are shown. What is the value of y?

7 *See Graph #3

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2. Which circle could represent the base of the vase? Use 3.14 for .

7 cm

Two sides of an obtuse triangle measure 12 in. and 14 in. The longest side measures 14 in. What is the greatest possible whole-number length of the unknown side?

7 in.

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches. What is the greatest possible whole-number length of the unknown side?

7 inches

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches. What is the greatest possible whole-number length of the unknown side?

7 inches

The hypotenuse of a 45°-45°-90° triangle measures units. What is the length of one leg of the triangle?

7 units

What is the value of x?

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?

72.44 in.

What is the measure of ∠A?

72°

What is the measure of angle ACB?

Angle BCD is a circumscribed angle of circle A. Angle BAC measures 53°. What is the measure of angle BCD?

Line segment BD is a diameter of circle E. What is the measure of arc BC?

78°

In the diagram m, WZ = √26. What is the perimeter of parallelogram WXYZ? is 2√26 + _____ units.

The measure of central angle RST is radians. What is the area of the shaded sector?

What is the value of x? 6 8 10 12

In parallelogram WXYZ, WY = 12 in., XZ = 16 in., WX = 10 in., and XY = 9 in. What is the length of line segment MX?

8 in.

The shaded figure is a rhombus. The area of the shaded section is 60 square units. What is the value of x?

8 units

Five students, Adriana, Ben, Chandra, Diana, and Ernesto, would each like one of the four spots at the regional science fair. Their names are placed in a hat, and four names are chosen at random to decide who attends the fair. What is the theoretical probability that Chandra will be chosen as one of the science fair participants?

80%

The measure of ADB is 162°. What is the measure of ∠EAB?

81°

In circle Y, what is TU?

82°

n circle Y, what is m?

82°

The base of a hexagonal prism has an apothem measuring 10 inches and an area of 346.41 square inches. The prism is 12 inches tall. What is the approximate lateral area of the prism? Round to the nearest whole number.

831 square inches

LK is tangent to circle J at point K. What is the length of the radius?

85/12

A farmer grows vegetables on seven acres, fruit on six acres, and flowers on two acres. Out in his fields, he finds a ladybug. To the nearest tenth of a percent, what is the theoretical probability that the ladybug was not found within the acres of flowers?

86.7%

Which equation correctly applies the law of cosines to solve for an unknown angle measure?

8^2 = 7^2 + 11^2 - 2(7)(11)cos(P)

In the diagram, SR = 4√2 and QR = √10. What is the perimeter of parallelogram PQRS?

8√2 + 2√10 units

A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius. Each of the central angles has a measure of 40°. How many sides does the polygon have?

Circle J is congruent to circle P. If OK = 2x, QR = 12, and RT = x + 3, what is the length of chord KM?

The measure of central angle ABC is π/2 radians. What is the area of the shaded sector?

The perimeter of square JKLM is 48 units. What is the value of x?

Two sides of an acute triangle measure 5 inches and 8 inches. The longest side is unknown. What is the greatest possible whole-number length of the unknown side? -------

What is the value of r? What is the length of segment EF?

9 55 units

What is the perimeter of trapezoid JKLM?

9 +√2 +√5 units *See Graph #30

Two sides of an acute triangle measure 5 inches and 8 inches. The longest side is unknown. What is the greatest possible whole-number length of the unknown side?

9 inches

The hypotenuse of a 45°-45°-90° triangle measures 18 cm. What is the length of one leg of the triangle?

9 sq. root 2 cm

In circle P, diameter QS measures 20 centimeters. What is the approximate length of arc QR? Round to the nearest tenth of a centimeter.

9.9 centimeters

LN is tangent to circle O at point M and QM is a diameter. Determine the measure of the following angles. The measure of ∠QML is __ degrees. The measure of ∠PMN is __ degrees.

90 63

What is the volume of the prism? (triangular)

900 cubic units

What is the measure of angle S?

Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch.

The measure of central angle XYZ is radians. What is the area of the shaded sector?

The measure of central angle XYZ is 3╓/4 radians. What is the area of the shaded sector?

96╓

The diagram shows one way to develop the formula for the area of a circle. Pieces of a circle with radius r are rearranged to create a shape that resembles a parallelogram. Since the circumference of the circle can be represented by 2πr, and the area of a parallelogram is determined using A = bh, which represents the approximate area of the parallelogram-like figure?

A = (2πr)(r)

Explain how you can use the inscribed angle theorem to justify its second corollary, that an angle inscribed in a semicircle is a right angle.

A semicircle is 180°. The inscribed angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. 90 is half of 180° A circle measures 360°. A semicircle measures 180°. Half of 180° is 90°. A right angle measures 90°.

In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula . Which best explains the formula?

A) The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

Two different cross sections are taken parallel to the base of a three-dimensional figure. The two cross sections are the same shape, but are not congruent. Which could be the three-dimensional figure? Check all that apply.

A).Cone, E).Triangular Pyramid, & F)Square Pyramid.

A soundproofing tile is made of 8 identical solid right pyramids with square bases. The length of the whole tile shown is x inches. Which expression shows the area of the base of each pyramid?

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

Twenty-five bakery customers were surveyed to determine if they like cake or pie. The results are shown in the Venn diagram. Given that a randomly chosen customer likes cake, what is the probability that the customer also likes pie?

Use the Venn diagram to calculate probabilities. Which probability is correct?

Which equation is correct and can be used to solve for the value of z?

Consider the following sets. U = {ordered pairs on a coordinate plane} A = {ordered pair solutions to y = x} B = {ordered pair solutions to y = 2x} Which ordered pair satisfies A ∩ B?

A. (0, 0)

Which expression represents the volume, in cubic units, of the shaded region of the composite figure?

A. (14)(10)(8) - π(2.52)(8)

A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter.

A. 1,005 cm3

The oblique prism below has an isosceles right triangle base. What expression represents the volume of the prism, in cubic units?

A. 1/2x^3 + x²

Students in a class were surveyed about the number of children in their families. The results of the survey are shown in the table. Two surveys are chosen at random from the group of surveys. After the first survey is chosen, it is returned to the stack and can be chosen a second time. What is the probability that the first survey chosen indicates four children in the family and the second survey indicates one child in the family?

A. 1/50

The four diagonals of a cube are drawn to create 6 square pyramids with the same base and height. The volume of the cube is (b)(b)(b). The height of each pyramid is h. Therefore, the volume of one pyramid must equal one-sixth the volume of the cube, or

A. 1/6(b)(b)(2h) or 1/3Bh.

All freshmen, sophomores, juniors, and seniors attended a high school assembly. The total student attendance is shown in the table. Twice during the assembly, a student is chosen at random to assist with the presentation. After the first student has finished assisting, the student returns to the group and can be chosen a second time. What is the probability that the first student chosen is a senior and the second student chosen is a sophomore?

A. 11/320

What is the volume of the cone? Use π ≈ 3.14.

A. 12.56 cubic units

Seventy-five percent of the flowers in the arrangement are roses and the rest are tulips. Of the tulips, 50 percent are pink. To the nearest whole percent, what is the probability that a randomly chosen flower from the arrangement is a pink tulip?

A. 13%

A. 14,400 cubic units

An oblique cylinder has a radius of 10 units and slant length of 26 units. What is the volume of the cylinder?

A. 2,400π cubic units

Rhombus WXYZ is graphed on a coordinate plane. What is the area of the rhombus?

A. 24 square units

The diameter of a sphere is 4 centimeters. Which represents the volume of the sphere?

A. 32/3π cm^3

In the diagram of circle A, what is the measure of ∠XYZ?

A. 35°

Lori downloaded all the pictures she took at Rita's wedding into a single computer folder. She took 86 of the 134 pictures with her camera and the remainder of them with her cell phone. Of the pictures Lori took with her cell phone, one out of every five was blurry. To the nearest whole percent, what is the probability that when she opens a random picture from the computer folder, it will be a blurry picture she took with her cell phone?

A. 7%

Find m<A.

A. 83

A right triangular prism is shown. What is the volume of the prism?

A. 900 cubic units

Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class. Which statement is true about whether A and B are independent events?

A. A and B are independent events because P(A∣B) = P(A).

Information about the students at Jackson High School is shown in the table. Which statement must be true?

A. Out of the 352 eleventh graders at the school, 173 of them are girls.

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference. Which choice represents the sample space, S, for this event?

A. S = {ABC, ABD, ACD, BCD}

Set V is all the unique three-digit numbers using the digits 1, 2, 3, 4, and 5. Which set would be considered a subset of set V?

A. Set W is all the unique three-digit numbers using the digits 1, 3, and 5.

How do the areas of the parallelograms compare?

A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.

Quadrilateral ABCD is a trapezoid with AB || CD. What must be shown to prove that ABCD is an isosceles trapezoid?

A. The base angles are congruent.

A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0.50, while each cylindrical container costs $0.75. Which packaging should the company use to minimize cost? Explain.

A. The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.

S is a subset within a universal set, U. If S = {x, y, 4, 9, ?), which could describe U?

A. U = {keys on a keyboard}

Figure ABCD is a square. Prove BD ≅ AC. What is the missing reason in the proof? 4. AB ≅ BC ≅ CD ≅ DA | Reason?

A. all sides of a square are congruent

Given: Circle O; < A intercepts BC ; <D intercepts BC Prove: <A congruent <D Two statements are missing reasons. What reason can be used to justify both statements 2 and 3? Number 2 and 3 reasons are missing.

A. inscribed angles theorem

Give the most accurate name for this figure.

A. quadrilateral

Which three-dimensional figure has double the number of edges as faces?

A. rectangular prism

The volume of an oblique pyramid with a square base is V units3 and the height is h units. Which expression represents the area of the base of the pyramid?

A. units2

Angle G is a circumscribed angle of circle E. What is the measure of angle G, in terms of x?

A. x° + x°

A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm. Which expression represents the volume of the pyramid?

A.(x^3 + 2x^2)/3 cm3

The square shown has a perimeter of 32 units. The square is rotated about line k. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr

A/C/D

Figure ABCD is a parallelogram. What are the lengths of line segments AB and BC?

AB = 10; BC = 28 *See Graph #5

Points N, P, and R all lie on circle O. Arc PR measures 120°. How does the measure of angle RNQ relate to the measure of arc PR?

Angle RNQ is equal in measure to arc PR.

In circle C, SQ = 10 cm. Which statements about the circle are correct? Check all that apply.

Arc PQ is congruent to arc SR. The measure of arc QR is 150°. Arc PS measures about 13.1 cm. Arc QS measures about 15.7 cm.

Which circle has a central angle that measures 40°?

Which circle has a radius that measures 10 units?

Which graph represents the equation x2 = 8y?

A circular garden with a radius of 8 feet is surrounded by a circular path with a width of 3 feet. What is the approximate area of the path alone? Use 3.14 for π.

B) 178.98 ft2

What is the area of the shaded sector of the circle? (120°, 9)

B) 27π units squared

The measure of central angle RST is π radians. What is the area of the shaded sector?

B) 8 π units squared

The face of a clock is divided into 12 equal parts. The radius of the clock face is 10 inches. Assume the hands of the clock will form a central angle. Which statements about the clock are accurate? Check all that apply.

B, C, E

Figure WXYZ is a parallelogram. Which angle measures are correct? Check all that apply.

B, C, F

For the soccer banquet, the players and their family members selected their favorite main dish and side dish. Of the 39 people who chose chicken as the main dish, 18 wanted potatoes. Of the 32 people who chose rice as a side dish, 6 chose fish as a main dish. A total of 8 people chose a vegetarian meal with potatoes, and a total of 10 people chose fish as their main dish. Which two-way table correctly displays this data?

The radius of a sphere is 3 inches. Which represents the volume of the sphere?

What is the perimeter of parallelogram WXYZ?

Which circle has a central angle that measures 40°?

Which graph represents the equation x2 = 8y?

The two-way table shows the number of books of each type in Eliza's home. What is the probability that a randomly selected reference book is hardcover?

B. 0.4

In the Venn diagram, consider U = {whole numbers 1 - 100}. Let A represent numbers that are perfect squares, B represent numbers that are perfect cubes, and C represent numbers that are perfect fourths. Which number(s) satisfy A ∩ C?

B. 1, 16, 81

What is the difference of the volumes of the two oblique pyramids, both of which have square bases? Round the volumes to the nearest tenth of a centimeter.

B. 1.2 cm³

A solid right pyramid has a square base with an edge length of s units and a height of h units Which expression represents the volume of the pyramid?

B. 1/3 s^2h units3

What is the approximate base area of the resulting three-dimensional figure?

B. 113 sq. cm

The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table. What is the probability that a person chosen at random from this group has brown or green eyes?

B. 13/25

A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters. Which expression represents the volume of the prism, in cubic centimeters?

B. 14x2 + 7x

A solid right pyramid has a square base. The length of the base edge is 4 cm and the height of the pyramid is 3 cm. What is the volume of the pyramid?

B. 16 cm3

A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday's lunch. What is the theoretical probability that applesauce and broccoli will both be offered on Monday?

B. 20%

An oblique cylinder has a diameter of 14 units. The volume of the cylinder is 1,176π cubic units. What is x, the height of the cylinder?

B. 24 units

A bag contains eleven equally sized marbles, which are numbered. Two marbles are chosen at random and replaced after each selection. What is the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number?

B. 24/121

The Hawaiian language has 12 letters: five vowels and seven consonants. Each of the 12 Hawaiian letters are written on a slip of paper and placed in the bag. A letter is randomly chosen from the bag and then replaced. Then, a second letter is randomly chosen from the bag. What is the probability that two vowels are chosen?

B. 25/144

Galina is finding the area of triangle RST. To do so, she follows the steps in the table. To solve the problem using these steps, what are the dimensions of the rectangle she should draw?

B. 3 units by 4 units

The radius of a sphere is 3 inches. Which represents the volume of the sphere?

B. 36π cubic inches

B. 4 cm and 7 cm

The volume of the sphere is 500/3π cubic units. What is the value of x?

B. 5 units

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the height of the triangular base of the pyramid?

B. 5/2√3 units

An oblique candle with a volume of 270 cubic centimeters is 18 centimeters tall. The width of the triangular candle base is 5 centimeters, and the width of the slanted candle is 7 centimeters. What dimensions of the box are required to fit the candle?

B. 7 by 6 by 18

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches. What is the height of the triangular base of the pyramid?

B. 9 √ 3 in.

The diagonals of parallelogram ABCD intersect at point E. Which of the following statements is not necessarily true?

B. AE = BE

Orchid wants to retile her bathroom floor, which has an area of 40 square feet. She is deciding between two types of custom tiles. The square tile is foot by foot and costs $0.45 per tile. The rectangular tile is 2 feet by foot and costs $0.80 per tile.

B. She should choose the rectangular tiles because the total cost will be $8 less.

A company needs to package 7,560 beads. A wooden container shaped like a rectangular prism can hold 180 beads. A plastic cylindrical container can hold 126 beads. The wooden container costs the company $0.70, while the plastic container costs $0.40. Which container should the company use to minimize cost? Explain.

B. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.

April is randomly choosing five CDs to bring in her car from the following: 6 pop CDs, 8 rock CDs, and 10 R&B CDs. What is the complement of April choosing five pop CD

B. choosing five CDs where all of them are not pop

The diagonals of a parallelogram are congruent. Which could be the parallelogram?

B. rectangle

Which shape could be thought of as being created by stacking congruent polygons?

B. rectangular prism

Quadrilateral ABCD is a parallelogram. AC bisects <DAB and <BCD, BD bisects <ABC and <CDA, AC bisects BD, AC is perpendicular to BD, and the diagonals are not congruent. What is the best name for quadrilateral ABCD?

B. rhombus

A parabola has a vertex at the origin. The focus of the parabola is located at (-2,0). Which is the equation for the directrix related to the parabola?

B. x = 2

The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units. Which expression represents the volume of the prism, in cubic units?

B. x^3 + 3x^2

The diagonals of parallelogram ABCD intersect at point E. If DE = 2x + 2, BE = 3x - 8, CE = 4y, and AE = 16, solve for y.

B. y = 4

Consider U = {x|x is a negative real number}. Which is an empty set?

B. {x|x ∈ U and x has a negative square root}

The radius of a sphere is 6 units. Which expression represents the volume of the sphere, in cubic units?

B.4/3π(6)^3

The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr

B/C/D

Which three-dimensional figure has the greatest number of faces?

B:octagonal pyramid.

Circle A is congruent to circle J. Chords BC, CF, EG, KL, LO, and MP are congruent. Which arcs are congruent? Check all that apply.

BC ≅ MP EG ≅ KL LO ≅ MP

Which shows how to correctly solve for C2, the circumference of any circle with radius r?

Because (1)

Two circles are shown in the diagram. Since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. Substitute the values d1 = 1, C1 = π, and d2 = 2r into the proportion. Which shows how to correctly solve for C2, the circumference of any circle with radius r?

Because π/1 = C2/2r, C2 = 2πr

What is true regarding chords and diameters of circles?

Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle.

The perimeter of the rectangle shown is 76 cm. It is rotated about line b. Which best describes the resulting three-dimensional figure?

The circular face of a watch has an area that measures between 800 and 900 square millimeters. What could be the radius of the watch face? Use 3.14 for π.

C) 16 mm

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ. What is the area of circle C, which passes though points W and Z?

C) 324π units squared

C) A=1/2(2πr)(r)

A cylinder has a radius of 1 inch and height of 1 inch. What is the approximate volume of the cylinder? Round to the nearest hundredth. Use 3.14 for π.

A survey asked about the number of people who eat breakfast almost every day (B) and the number of people who buy cereal at least once a month (C). The results of the survey are shown in the Venn diagram. Given that a randomly chosen person eats breakfast almost everyday, what is the probability that the person also buys cereal at least once a month?

Nadia's bookshelf contains 10 fiction books, two reference books, and five nonfiction books. What is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book?

The oblique pyramid has a square base with an edge length of 5 cm. The height of the pyramid is 7 cm. What is the volume of the pyramid

The spinner is equally likely to land on any of the five sections. What is the probability that the spinner lands on an even number or on the unshaded section?

C. (18 + 4)

Which expression represents the volume, in cubic units, of the composite figure?

C. (52)(13) + (52)(12)

C. 0.4

The oblique prism has a rectangular base with a width of 10 units and a length of 13 units. The top base extends 8 units to the right of the bottom base. What is the volume of the prism?

C. 1,950 cubic units

Four interior angles of a pentagon measure 88°, 118°, 132°, and 100°. What is the measure of the fifth interior angle?

C. 102°

The diagonals of parallelogram QRST, TR and QS, intersect at point U. If RS = 10, ST = 12, and RU = 9.5, find the length of RT.

C. 19

Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees. What is the value of x?

C. 20 *See Graph #10

A three-dimensional model of Lucia's apartment is shown. To cool the whole apartment, an air conditioner must provide 2.5 BTUs per cubic foot. How many BTUs are needed to cool Lucia's apartment?

C. 20,400 BTUs

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth

C. 235.5 cubic units

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth.

C. 235.5 cubic units

Points D, E, and F are on circle C and EF ≅ DF. What is the measure of ∠CDF?

C. 26°

An oblique rectangular prism with a square base has a volume of 539 cubic units. The edges of the prism measure 7 by 7 by 14 units. How many units longer is the slanted edge length of the prism, 14, compared to its perpendicular height?

C. 3 units

A cylinder has a radius of 1 inch and height of 1 inch. What is the approximate volume of the cylinder? Round to the nearest hundredth. Use 3.14 for π.

C. 3.14 cubic inches

A solid oblique pyramid has a regular hexagonal base with an area of 54√3 cm2 and an edge length of 6 cm. Angle BAC measures 60°. What is the volume of the pyramid?

C. 324 cm3

Arc CD is 2/3 of the circumference of a circle. What is the radian measure of the central angle?

C. 4π/3 radians

Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. Which number is missing from the two-way table?

C. 517

The oblique pyramid has a square base with an edge length of 5 cm. The height of the pyramid is 7 cm. What is the volume of the pyramid?

C. 58 cm3

The rectangle shown is rotated about line k. What is the approximate base area of the resulting figure? Area of a circle: A = πr2

C. 79 sq. in.

The rectangle shown is rotated about line k. What is the approximate base area of the resulting figure?

C. 79 sq. in.

Consider U = {x|x is a real number}. A = {x|x ∈ U and x + 2 > 10} B = {x|x ∈ U and 2x > 10} Which statements are true?

C. 8 ∉ A; 8 ∈ B

Which sets can be represented using the Venn diagram below?

C. A = {animals}; B = {mammals}

Information about the recycling drive at school is shown in the table. Let A be the event that the item pulled out of the recycling bin is a plastic bottle, and let B be the event that a tenth grader recycled that item. Which statement is true about whether A and B are independent events?

C. A and B are not independent events because P(A∣B) ≠ P(A).

Which statement is true?

C. An isosceles trapezoid has 2 pairs of congruent angles.

Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel. For the events "shower gel" and "scented" to be independent, what must be shown to be true?

C. Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel. For the events "shower gel" and "scented" to be independent, what must be shown to be true?

Dayshawn can choose two of his four t-shirts to take on a weekend trip. If the t-shirts are labeled A, B, C, and D, which choice represents the sample space, S, for the event?

C. S = {AB, AC, AD, BC, BD, CD}

Four runners, Fran, Gloria, Haley, and Imani, compete on a relay team. Haley is the first runner in the relay. The other runners can run in any order. What is the sample space showing the possible orders of the other three runners?

C. S = {FGI, FIG, GFI, GIF, IFG, IGF}

The two-way table shows the ages of the players on different soccer teams. Which statement is true?

C. The probability that a randomly selected player on Team C is 10 years old is .

The table shows information about Town A in Illinois and Town B in Florida. If the two towns have the same population density, which must also be true?

C. Town B has a population of approximately 5,138.

C. a cone with a base circumference of about 63 mm

The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm. What shape is created by the rotation and what is the approximate circumference of the base?

C. a cone with a base circumference of about 63 mm

The area of rectangle ABDE is 270 square inches. The rectangle is rotated about a line that passes through points C and F. Which best describes the resulting three-dimensional shape?

C. a cylinder with a base radius of 9 inches

Which pair of figures has the same number of faces as vertices?

C. rectangular pyramid and triangular pyramid

Which three-dimensional figure has nine edges?

C. triangular prism

Given that PQRS is a square, find x and y.

C. x = 47, y = 28

An oblique square prism is shown. Which expression represents the volume of the prism?

C. x2(x - 2) cubic units

A frustum is formed when a plane parallel to a cone's base cuts off the upper portion as shown. Which expression represents the volume, in cubic units, of the frustum?

C. π(7.52)(19) - π(3.52)(8)

Circle D is shown with the measures of the minor arcs. Which angles are congruent?

C. ∠GDH and ∠EDH

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units. What is BC, the height of the pyramid?

C.14 units

Which three-dimensional figure has exactly three rectangular faces?

C.triangular prism

The area of rectangle ABDE is 270 square inches. The rectangle is rotated about a line that passes through points C and F. Which best describes the resulting three-dimensional shape?

C/D

The area of rectangle ABDE is 270 square inches. The rectangle is rotated about a line that passes through points C and F. Which best describes the resulting three-dimensional shape?

C: a cylinder with a base radius of 9 inches

C:a cone with a base circumference of about 63 mm

Which three-dimensional figure has nine edges?

C:triangular prism

Given: AD ≅ BC and AD ∥ BC Prove: ABCD is a parallelogram. 1. AD ≅ BC; AD ∥ BC 1. given 2. ∠CAD and ∠ACB are alternate interior ∠s 2.definition of alternate interior angles 3. ∠CAD ≅ ∠ACB 3. alternate interior angles are congruent 4. AC ≅ AC 4. reflexive property 5. △CAD ≅ △ACB 5. SAS congruency theorem 6. AB ≅ CD 6. ? 7. ABCD is a parallelogram 7.parallelogram side theorem What is the missing reason in step 6?

CPCTC *See Graph #17

Which is true regarding secants and chords?

Chords and secants intersect the perimeter of a circle twice. Chords are segments entirely within a circle, while secants are lines or rays that extend through a circle.

In circle G, r = 3 units. Maria draws a circle with double the area of circle G. What is the area of Maria's circle?

D) 18π units squared

The smallest of the three circles with center D has a radius of 8 inches and CB = BA = 4 inches. What is the sum of the areas of all three circles?

D) 464π in. squared

Fiona draws a circle with a diameter of 14 meters. What is the area of Fiona's circle?

D) 49 pie msquared

What is the sum of the areas of circle C and circle D?

D) 98π units squared

Hiro has a stack of cards with one number from the set 1, 1, 2, 2, 3, 3, 3, 4 written on each card. What is the probability that he pulls out a 3 first and then pulls out a 2 without replacing them?

The two-way table shows the number of houses on the market in the Castillos' price range. What is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms?

D. 0.8

The diagonals of kite KITE intersect at point P. If m<KIP = 46 degrees and m<KEP = 34 degrees, find <ITE.

D. 100 degrees

The corner of a rectangle is cut, creating a right trapezoid. What is the value of x?

D. 135o

Jasmine rolls a number cube 72 times. The number 2 is rolled 13 times and the number 3 is rolled nine times. To the nearest whole percent, what is the experimental probability of rolling a 2 or 3?

D. 31%

D. 38.2 m

A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?

D. 5/12

The height of a right rectangular prism is three times the width of the base. The length of the base is twice the width. Which expression represents the volume of the prism in terms of w, the width of the base?

D. 6w³ cubic units

An oblique prism has a square base and height of 3 centimeters. What is the volume of the prism?

D. 75 cm3

An oblique prism has a square base and height of 3 centimeters. What is the volume of the prism?

D. 75 cm3

The radius of the large sphere is double the radius of the small sphere. How many times is the volume of the large sphere than the small sphere?

D. 8

D. 86.7%

The diagonals of parallelogram ABCD intersect at point E. To prove that <ADE = <CBE, all of the following could be used, except for which?

D. ACD = CAB by SSS.

If U = {all positive integers} and A = {x|x ∈ U and x is an odd positive integer}, which describes Ac?

D. A^c = {x|x ∈ U and is an even positive integer}

Which statement is true about whether C and Y are independent events?

D. C and Y are not independent events because P(C∣Y) ≠ P(C).

Find each population density, to the nearest hundredth. Which statement is true?

D. Dish C and Dish D have approximately the same population density.

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president. Which choice represents the sample space, S, for this event?

D. S = {PQ, QP, PR, RP, QR, RQ}

A city's bus line is used more as the urban population density increases. The more people in an area, the more likely bus lines will be utilized. The population of City A, in Texas, is 29,455 and covers an area of 19.42 mi2. The population of City B, in Alabama, is 34,890 and covers an area of 25.4 mi2. Which city's residents are more likely to use public buses? Explain.

D. The residents of City A are more likely to use public transportation because the city has the highest population density.

D. a cylinder with a circumference of about 50 units

Which shape has a vertex that is also an apex?

D. pyramid

The universal set is the set of rational numbers. S is the set of integers. Which represents S^c?

D. {x|x is a rational non-integer}

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is pir^2/4r^2 or pi/4 Since the area of the circle is pi/4 the area of the square, the volume of the cylinder equals

D.the volume of the prism or (4r2)(h) or r2h.

Quadrilateral ABDE is a rectangle. AB = 10 cm and AE = 16 cm. Through which two points could a line of rotation be placed so that the base of the resulting cylinder will have a radius of 5 cm?

D:G and H

The perimeter of the rectangle shown is 76 cm. It is rotated about line b. Which best describes the resulting three-dimensional figure?

D:a cylinder with a base radius of 14 cm

In parallelogram ABCD, what is DC?

DC = 13in. *See Graph #19

In the diagram, DG ∥ EF. What additional information would prove that DEFG is an isosceles trapezoid?

DE ≅ GF *See Graph #26

Rashad is considering two designs for a garden. In Design 1 he would use fencing to surround a square plot of land that has an area of 1,296 square feet. In Design 2 he would divide a plot of land into two rectangular sections, each 15 feet by 36 feet, and surround the plot with fencing, as well as place fencing along the dividing line of the two sections.

Design 1, because it requires 24 fewer feet of fencing than Design 2

Consider the incomplete paragraph proof. Given: Isosceles right triangle XYZ (45°-45°-90° triangle)Prove: In a 45°-45°-90° triangle, the hypotenuse is times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, is times the length of each leg?

Determine the principal square root of both sides of the equation.

1 2 3 4 5 6 7 8 Consider the following sets. U = {all triangles} E = {x|x ∈ U and x is equilateral} I = {x|x ∈ U and x is isosceles} S = {x|x ∈ U and x is scalene} A = {x|x ∈ U and x is acute} O = {x|x ∈ U and x is obtuse} R = {x|x ∈ U and x is right} Which is a subset of I?

Consider the following sets. U = {all triangles} E = {x|x ∈ U and x is equilateral} I = {x|x ∈ U and x is isosceles} S = {x|x ∈ U and x is scalene} A = {x|x ∈ U and x is acute} O = {x|x ∈ U and x is obtuse} R = {x|x ∈ U and x is right} Which is a subset of I?

Circle D is shown with the measures of the minor arcs. Which segments are congruent?

EF and GF

Figure ABCD is a parallelogram. Two trapezoids are created using line segment XY such that AX ≅ CY. What is true about the areas of the trapezoids?

Each area is equal to half of the area of ABCD.

Ella's geometry teacher asked each student to devise a problem and write out its solution. Here is Ella's work: A triangle has side lengths of 10, 11, and 15. What type of triangle is it? Procedure: 102 ?? 112 + 152 100 ?? 121 + 225 100 < 346 Conclusion: This triangle is an acute triangle. Which statement best summarizes Ella's work?

Ella's procedure and conclusion are incorrect.

Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classmate?

First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse.

In circle D, which is a secant?

Quadrilateral RSTU has one pair of opposite parallel sides and one pair of opposite congruent sides as shown. Based on the given information, which statement best explains whether the quadrilateral is a parallelogram?

It cannot be determined from the information given.

Which is a correct description of the polygon?

It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet. Which is true regarding the triangular frame?

It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

Janice examines the given triangle and estimates that the longest side has a length of 25 units―if it is a right triangle. How does her estimate compare to the actual length?

It is under by approximately 0.6 units.

A fast-food restaurant kept information about the drinks that were ordered along with the different-sized kids' meals, as shown in the table. Which statements are true? Check all that apply.

Milk was requested for 16 of the large-sized meal orders. Sixty-three of the orders of soda came with a regular-sized meal. A total of 124 large-sized meals were ordered.

NMOPL, NMPOL, NOPML, NOMPL, NPMOL, NPOML

The table shows the number of resident geese living in four different ponds.

NOT Pond D

The populations and areas of four states are shown.

NOT The state with the lowest population has the lowest population density.

The volume of a cylinder is 4πx3 cubic units and its height is x units. Which expression represents the radius of the cylinder, in units?

NOT B. 4x

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

NOT C. 2πx3

Quadrilateral ABDE is a rectangle. AB = 10 cm and AE = 16 cm. Through which two points could a line of rotation be placed so that the base of the resulting cylinder will have a radius of 5 cm?

NOT C. C and F

Which statements are true regarding the area of circle D? Check all that apply. The area of the circle depends on the square of the radius. The area of circle D is 36. The area of circle D is 324. The area of the circle depends on the square of pi. The area of the circle depends on the central angle.

NOT) 1,2,5) 1,2,4) 1,3,5) 1,3,4

Triangle JKL is equilateral. One side of the triangle, JL, is a diameter of circle M. Which is true about line segments JK and KL?

Neither segment is a chord nor tangent to circle M.

A circle centered at (-1, 2) has a diameter of 10 units. Amit wants to determine whether (2, -2) is also on the circle. His work is shown below. The radius is 5 units. Find the distance from the center to (2, -2). The point (2, -2) doesn't lie on the circle because the calculated distance should be the same as the radius. Is Amit's work correct?

No, he did not calculate the distance correctly.

The angle measures of quadrilateral RSTU are shown. m∠R = (2x)° m∠S = (3x - 35)° m∠T = (x + 35)° The measure of angle U is unknown. Can quadrilateral RSTU be a parallelogram?

No, if x = 35, all three given angles measure 70°. The fourth angle would measure 150°.

The figure is a parallelogram. One diagonal measures 28 units. Is the figure a rectangle? Explain.

No, it is not a rectangle because the sides of the parallelogram do not meet at right angles. *See Graph #24

Does the point (2, 6) lie on the circle shown? Explain.

No, the distance from (0, 0) to (2, ) is not 3 units.

Given: quadrilateral MNOL with MN ≅ LO and ML ≅ NO Prove: MNOL is a parallelogram. Complete the paragraph proof. We are given that MN ≅ LO and ML ≅ NO. We can draw in MO because between any two points is a line. By the reflexive property, MO ≅ MO. By SSS, △MLO ≅ △______. By CPCTC, ∠LMO ≅ ∠______ and ∠NMO ≅ ∠LOM. Both pairs of angles are also ______, based on the definition. Based on the converse of the alternate interior angles theorem, MN ∥ LO and LM ∥ NO. Based on the definition of a parallelogram, MNOL is a parallelogram.

ONM NOM alternate interior angles

In parallelogram PQSR, what is PQ?

PQ = 9 cm *See Graph #13

If quadrilateral PQRS is a kite. which statements must be true? Check all that apply

QP ~= QR PM ~= MR <QPS ~= QRS

If quadrilateral PQRS is a kite, which statements must be true? Check all that apply.

QP ≅ QR PM ≅ MR ∠QPS ≅ ∠QRS

Given right triangle PQR, which represents the value of sin(P)?

RQ/PQ

In circle Q, ∠RQS ≅ ∠SQT. Which statement must be true?

RS ≅ ST

High population density can cause increases in competition for resources, such as food and shelter. The table shows the number of zebras living in four different regions.

Region C

Which events are independent? Check all that apply.

Roll a number cube, and then roll the same number cube again. Flip a coin, and then flip the coin a second time. Draw a card from a deck, replace it, and then draw a second card.

A number cube has faces numbered 1 to 6. What is true about rolling the number cube one time? Check all that apply.

S = {1, 2, 3, 4, 5, 6} If A is a subset of S, A could be {5, 6}. If a subset A represents the complement of rolling a 5, its sample space is A = {1, 2, 3, 4, 6}.

Ariana, Boris, Cecile, and Diego are students in the service club. Three of the four students will be chosen to attend a conference. Which choice represents the sample space, S, for this event?

S = {ABC, ABD, ACD, BCD}

Given: AB ≅ CD and AD ≅ BC Prove: ABCD is a parallelogram. Statements Reasons 1.AB ≅ CD;AD ≅ BC 1. given 2.AC ≅ AC 2. reflexive property 3.△ADC ≅ △CBA 3. ? 4.∠DAC ≅ ∠BCA; ∠ACD ≅ ∠CAB 4. CPCTC 5.∠DAC and ∠BCA are alt. int. ∠s; ∠ACD and ∠CAB are alt. int. ∠s 5. definition of alternate interior angles 6. AB ∥ CD; AD ∥ BC 6. converse of the alternate interior angles theorem 7.ABCD is a parallelogram 7. definition of parallelogram What is the missing reason in step 3?

SSS congruency theorem *See Graph #18

Set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three. Set Y is made up of the possible ways five students can be formed into groups of three if student A must be in all possible groups. Which statements about the situation are true? Check all that apply.

Set X has 10 possible groupings. Set Y = {ABC, ABD, ABE, ACD, ACE, ADE} There are three ways to form a group if persons A and C must be in it.

Fiona chooses three towels from a group of five to pack in her beach bag for herself and her two brothers. Let the five towels be represented by A,B,C,D, and E. If Fiona chooses towel A for herself, which statements about the possible outcomes for her brothers' towels are true? Check all that apply.

She has four choices for the first brother's towel and three choices for the second brother's towel. ABC, ABD, ABE, ACD, ACE, and ADE are the possible outcomes. If Fiona did not choose towel A for herself, there would be more outcomes.

The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density. Which statement about the number of earthquakes the states had for the given time span is true?

State A had approximately 3,362 more earthquakes than State B.

The circle is inscribed in triangle PRT. Which statements about the figure are true? Check all that apply.

TU ~~ TS The length of segment PR is 13 units.

The minor arc measures of circle Z are shown in the figure. Use the drop-down menus to complete each statement. Angle UZT is congruent to angle _____. Angle VZW is congruent to angle ______

TZY YZX

Holly and Tamar completed the work in the table to determine if a triangle with side lengths of 40, 42, and 58 is a right triangle. Holly's Work Tamar's Work mc019-1.jpg The triangle is not a right triangle. mc019-2.jpg The triangle is a right triangle. Which best describes the accuracy of their solutions?

Tamar is correct.

Which best explains whether a triangle with side lengths 2 in, 5 in, and 4 in is an acute triangle

The Triangle is not acute because 2^2 + 4^2 < 5^2

Which statements about finding the area of the equilateral triangle are true? Check all that apply.

The apothem can be found using the Pythagorean theorem. The apothem can be found using the tangent ratio. The length of the apothem is approximately 2.5 cm.

In each circle below, a 50° angle with a vertex at the center of the circle is drawn. How are minor arc lengths CD and EF related?

The arc lengths are proportional: CD = 4EF

Which statements are true regarding the area of circle D? Check all that apply.

The area of the circle depends on the square of the radius. The area of circle D is 324.

How does the area of triangle ABC compare to the area of parallelogram GHJK?

The area of △ABC is 2 square units greater than the area of parallelogram GHJK.

If two pyramids have the same height, what must be true of the pyramids for them to also have the same volume?

The areas of the bases must be the same.

The face of a clock is divided into 12 equal parts. The radius of the clock face is 6 inches. Assume the hands of the clock will form a central angle. Which statements about the clock are accurate? Check all that apply.

The central angle measure when one hand points at 2 and the other points at 4 is 60°. With one hand at 5 and the other at 10, the minor arc formed by the hands is about 15.7 in. The length of the minor arc between 11 and 2 is the same as the length of the minor arc between 7 and 10.

The circumference of the clock is approximately 62.8 inches. The minor arc measure when one hand points at 12 and the other hand points at 4 is 120°. The length of the minor arc between 6 and 7 is approximately 5.2 inches.

A right rectangular prism with square bases has a height of 20 centimeters and a volume of 800 cubic centimeters. Which statements describe the prism?

The diagonal of the base is 4√5 centimeters. The area of a base is 40 square centimeters. The area of a lateral side between the bases is about 126.5 square centimeters

Which statements are true of all squares? Check all that apply.

The diagonals are perpendicular. The diagonals are congruent to each other. The diagonals bisect the vertex angles. The diagonals bisect each other.

A rectangle with a width of 2.5 cm and a length of 3 cm is dilated by a scale factor of 4. Which statements about the new rectangle are true? Check all that apply.

The dimensions of the new rectangle will be 10 cm by 12 cm. The new perimeter will be 4 times the original perimeter. The new area will be 16 times the original area. The new perimeter will be 44 cm.

Dilation Dv 2/5 was performed on a rectangle. How does the image relate to the pre-image? Check all that apply.

The image is a reduction because n < 1. The side lengths of the image are two-fifths the size of the corresponding side lengths of the pre-image. The base of the image is two-fifths the size of the base of the pre-image. *See Graph #43

The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Check all that apply.

The length of segment XY can be found by solving for a in 202 - 7.652 = a2. The measure of the central angle, ∠ZXW, is 45°.

The plastic containers should be used because it will cost $5.40 more to use the wooden containers.

The populations and land areas of four cities in Texas are shown. Which statements are true? Check all that apply.

The population density for City B can be found using the ratio 48,592 : 26. The population density of City B is greater than that of City C. City D has the lowest population density of the four cities.

A cylinder with a base diameter of x units has a volume of πx3 cubic units. Which statements about the cylinder are true? Check all that apply.

The radius of the cylinder is 1/2x units. The area of the cylinder's base is 1/4πx2 square units. The height of the cylinder is 4x units.

A cylinder with a base diameter of x units has a volume of πx3 cubic units. Which statements about the cylinder are true? Check all that apply.

The radius of the cylinder is x units., The area of the cylinder's base is πx2 square units., The height of the cylinder is 4x units.

The more people living in an area, the more likely it is that public buses will be used. City A has a population of 51,242 and covers an area of 89.22 mi2. City B has a population of 50,178 and covers an area of 8.12 mi2. Which statement about use of public buses in the cities is most likely true?

The residents of City B are more likely to use public buses because their city has a greater population density.

Which statements are true about polygons? Check all that apply.

The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint. If all of the sides of convex polygon are extended, none of them will contain any points that are inside the polygon. The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.

Which statement proves that PQRS is a parallelogram? The slopes of SP and RQ are both -2 and SP = RQ

The slopes of SP and RQ are both -2 and SP = RQ = √45.

Two chords intersect at a point inside a circle that is not the center of the circle. Which statement must be true?

The sum of the measures of each pair of vertical angles is equal to the sum of the measures of the intercepted arcs.

What is true regarding two adjacent arcs created by two intersecting diameters?

The sum of their measures is 180°.

A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table. Which statements are true about Yuri's experiment? Check all that apply.

The theoretical probability of spinning any one of the five colors is 20%. The theoretical probability of spinning green is equal to the experimental probability of spinning green. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Which steps would prove the circles similar?

Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3. ***3

Which best explains if quadrilateral WXYZ can be a parallelogram?

WXYZ is not necessarily a parallelogram because it is unknown if WC = CY. *See Graph #16

What is mBC?

XXX 80 (degrees) XXX 100 (degrees)

The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Check all that apply.

YZ= 9 cm XZ= 9 sq. root 2 cm

Based on the measures shown, could the figure be a parallelogram?

Yes, one pair of opposite sides could measure 10 in., and the other pair could measure 13 in.

Does the point (1, 7) lie on the circle shown? Explain.

Yes, the distance from (-2, 0) to (1, ) is 4 units.

Does the point (1,√7) lie on the circle shown?Explain

Yes, the distance from (-2, 0) to (1,√7 ) is 4 units.

a = 60° The perimeter of the rhombus is 16 inches. The length of the longer diagonal is approximately 7 inches.

a cylinder with a circumference of about 50 units

Given right triangle JKM, which correctly describes the locations of the sides in relation to ∠J?

a is the hypotenuse, b is adjacent, c is opposite

An interior angle of a regular polygon has a measure of 108°. What type of polygon is it? The polygon is

a pentagon

a quadrilateral, because angle C and angle X are acute

In which triangle is the value of x equal to cos-1 (4.3/6.7)? (Images may not be drawn to scale.)

Which quadrilateral is a trapezoid?

A circle is inscribed in a regular hexagon with side length 10 feet. What is the area if the shaded region. Recall that in a 30° -60°-90° triangle, if the shortest leg measures x units, then the longer leg measures x√3 units and the hypotenuse measures 2x units.

a. (150√3 - 75π) ft^2

A square is inscribed in a circle of diameter 12√2 millimeters. What is the area of the shaded region? Recall that in a 45° - 45° -90° triangle, if the legs each measure x units, then the hypotenuse measures x√2 units.

a. (72π - 144) mm^2

Which polygon has an interior angle sum of 1080°?

a. (8 sides)

A right triangular prism is constructed so that it's height is equal to the leg length of the base. What expression represents the volume of the prism, in cubic units?

a. 1/2x^3

What is the length of AC? Round to the nearest tenth.

a. 10.5 m

a. 14,400 cubic units

A right triangle has a 30° angle. The leg adjacent to the 30° angle measures 25 inches. What is the length of the other leg? Round to the nearest tenth.

a. 14.4 in.

Consider circle T with radius 24 in. and 0 = 5🍰/6 radians. What is the length of minor arc SV?

a. 20🍰 in.

A greeting card uses a geometric design containing 4 congruent kites. The card is 4 inches wide and 8 inches long. What is the area of one kite?

a. 4 sq. in.

What is the measure of arc EF in circle H?

a. 41°

Line segment XY is tangent to circle Z at point U. If the measure of UV is 84°, what is the measure of YUV?

a. 42°

a. 43.5 inches

Given right triangle JKL, what is the value of cos(L)?

a. 5/13

The longest side of an obtuse triangle measures 20 cm. The two shorter sides measure x cm and 3x cm. Rounded to the nearest tenth, what is the greatest possible value of x?

a. 6.3

Circle C is inscribed in triangle JEG. What is the perimeter of triangle JEG?

a. 60 units

Julian describes an angle in the triangle using these statements. Which angle(s) is Julian describing?

a. <G

Using the side lengths of PQR and STU, which angle has a sine ratio of 4/5?

a. <P

Points N, P, and R all lie on circle O. Arc PR measures 120°. How does the measure of angle RNQ relate to the measure of arc PR?

a. Angle RNQ is equal in measure to arc PR.

Two circles are shown in the diagram. Which shows how to correctly solve for C2, the circumference of any circle with radius r?

a. Because 🍰/1 = C2/2r, C2 = 2r🍰

In the diagram, DG || EF. What additional information would prove that DEFG is an isosceles trapezoid?

a. DE ~= GF

Which statements are true about circle Q? Check all that apply.

a. The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8. The area of the shaded sector depends on the length of the radius. The area of the shaded sector depends on the area of the circle.

a. The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.

Which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm, is a right triangle?

a. The triangle is a right triangle because 5^2 + 12^2 = 13^2

Two students describe the sides of right triangle ABC in relation to <B. Who is correct? Explain.

a. Tomas is correct; AC is opposite <B and BC is adjacent to <B

The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

a. Use the distance formula to find the length of each side, and then add the lengths.

Given right triangle JKM, which correctly describes the locations of the sides in relation to <J?

a. a is the hypotenuse, b is adjacent, c is opposite

Figure TUVS is a parallelogram. Which angles equal 91°?

a. angles T and V

Given: quadrilateral ABCD inscribed in a circle. Prove: <A and <C are supplementary, <B and <D are supplementary. What is the missing information in the paragraph proof?

a. inscribed angle

Right triangle ABC is shown. Which equation can be used to solve for c?

a. sin(50°) = 3/c

Angle X is a circumscribed angle of circle V. Which name best describes figure VWXY?

a. square

Which equation can be used to solve for b?

a. tan(30°) = 5/b

Which equation can be used to solve for the measure if angle ABC?

a. tan(x) = 2.4/10

The figure shown is a rhombus. Which equation is true regarding the angles formed by the diagonals and sides of the rhombus?

a. x + y = z

Which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in.?

acute, because 102+122>152

What is the missing reason in the proof?

all sides of a square are congruent

How can you decompose the composite figure to determine its area?

as a semicircle, a hexagon, and a rectangle

Which quadrilateral is a kite?

Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA?

b. (2 🍰/3) x units

The area of rhombus ABCD is 72 square units. EC = 8 units and DB = x - 1. What is the value of x?

b. 10

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

b. 10, 24, 26

What is the area of the composite figure? (5cm, 13 cm, 5cm, 2cm, 5cm, 14cm)

b. 100 cm^2

Points N and R both lie on circle O. Line segment RQ is tangent to the circle at point R. What is the perimeter of triangle RON?

b. 15.0 units

A kite has a perimeter of 70 centimeters. One of the shorter sides measures 16 centimeters. What are the lengths of the other three sides?

b. 16 centimeters, 19 centimeters, and 19 centimeters

In circle A, ∠BAE ≅ ∠DAE. What is the value of x?

b. 17

If KM is drawn on this quadrilateral, what will be its length?

b. 18 units

The length of the hypotenuse, line segment GH, in triangle GJH measures 6 cm. Line segment JH measures 2 cm. Which is the approximate measure of angle JGH?

b. 19.5°

RT and GJ are chords that intersects at point H. If RH = 10 units, HT = 16 units, and GH = 8 units, what is the length of line segment HJ?

b. 20 units

Payton cut out two shapes, as shown, that she will later put together to resemble a house. What is the total area of the two shapes?

b. 21 square units

What is the area of the trapezoid? 4,8,4

b. 24 square units

Line segment ON is perpendicular to line segment ML. What is the length of chord ML?

b. 24 units

What is the area of triangle ABC? A(0, 0) B(3, 4) C(3, 2)

b. 3 square units

AX and EX are secant segments that intersect at point X. What is the length of DE?

b. 3 units

In the kite, AC = 10 and BD = 6. What is the area of kite ABCD?

b. 30 square units

The figures shows two rectangles. Which expression rectangles the area of the shaded region? (6x, 9x)

b. 34x^2

In the diagram of circle C, what is the measure of <1?

b. 35°

Which is the best approximation for the measure of angle XYZ?

b. 39.8°

Minor arc KL measures 135°. Which is the radian measure of central angle KOL?

b. 3π/4 radians

What is the area of triangle LMN?

b. 4 square units

A right triangle has one side that measures 4 in. The angle opposite that side measures 80°. What is the length of the hypotenuse of the triangle. Round to the nearest tenth.

b. 4.1 in.

Which is the best approximation for the measure of angle EGF? (18.6, 12)

b. 40.2°

Angle KJL measures (7x - 8)°. Angle KML measures (3x + 8)°. What is the measure of arc KL?

b. 40°

In circle C, wha is mFH?

b. 48°

Kite EFGH is inscribed in a rectangle where F and H are midpoints of parallel sides. The area of EFGH is 35 square u it's. What is the value of x?

b. 5 units

What is the length of line segment PQ?

b. 5 units

Which set of numbers can represent the side lengths, in inches, of an acute triangle?

b. 5, 7, 8

b. 5.2 million bushels

If line segment RU is considered the base of parallelogram RSTU, what is the corresponding height of the parallelogram?

b. 5.4 units

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

b. 6 < s < 12.8

What is the area of triangle GHJ?

b. 6 square units

QR is tangent to circle P at point Q. What is the approximate length of RP? Round to the nearest tenth.

b. 6.1 units

Points A, B, C, and D lie on circle M. Line segment BD is a diameter. What is the measure of angle ACD?

b. 67.5°

The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm. What is the smallest possible whole-number value of x?

b. 7

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue. In trapezoid EFGH, EF ≅ HG. What is the measure of the angle between Elm Street and Pine Avenue?

b. 72°

In circle N, KL ≅ ML.What is the measure of JNK?

b. 74°

Line segment BD is a diameter of circle E. What is the measure of arc BC?

b. 78°

What is the value of x? (77°, 59°, 66°, 62°, 12x)

b. 8

The perimeter of square JKLM is 48 units. What is the value of x?

b. 9

A company designs a logo using a kite figure around the letter t. The logo is 12 centimeters wide and 16 centimeters tall. What is the area of the logo?

b. 96 sq. cm

What is the measure of arc ECF in circle G?

b. 98°

Figure ABCD is a parallelogram. What are the measures of angles B and C?

b. <B = 65° ; <C = 115°

In circle D, which is tangent to the circle?

b. AB

Diagonals AC and BD form right angles at point M in parallelogram ABCD. Prove ABCD is a rhombus.

b. AMB ~ CMB ~ CMD ~ AMD

Rashad is considering two designs for a garden..... Which plan would cost less in fencing? Explain.

b. Design 1, because it requires 24 fewer feet of fencing than Design 2.

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support bean that will connect the ends of the two boards measures 20 feet. Which is true regarding the triangular frame?

b. It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

Which statement proves that quadrilateral JKLM is a kite?

b. LM = JM = 3 and JK = LK = √17

Given right triangle MNO, which represents the value of cos(M)?

b. MN/MO

The figure is a parallelogram. One diagonal measures 28 units. Is the figure a rectangle? Explain.

b. No, it is not a rectangle because the sides of the parallelogram do not meet at right angles

Angles PTQ and STR are vertical angles and congruent. Which arcs are congruent?

b. PQ and SR

The table shows the number of resident geese living in four different ponds. Which pond has the greatest population density of resident geese?

b. Pond B

Orchid wants to retire her bathroom floor, which has an area of 40 square feet. She is deciding between 2 types of custom tiles. The square tile is 1/2 foot by 1/3 foot and costs $0.45 per tile. The rectangular tile is 2 feet by 1/4 foot and costs $0.80 per tile. Which tile should Orchid choose to minimize costs? Explain.

b. She should choose the rectangular tiles because the total cost will be $8 less

How are the semicircle and the diameter of a circle related?

b. The degree measure of the diameter and the degree measure of the semicircle are the same.

b. The plastic containers should be used because it will cost $5.40 more to use the wooden containers.

The populations and areas of four states are shown. Which statement regarding these four states is true?

b. The state with the second lowest population has the lowest population density.

What does CDE most specifically describe?

b. a major arc

What type of polygon is shown? (7 sides, 1 dent)

b. concave heptagon

Which equation can be used to find the measures of angle GFE?

b. cos-1 (11.9/14.5) = Ø

Given: Circle O with diameter LN and inscribed angle LMN Prove: <LMN is a right angle. What is the missing reason in step 5?

b. inscribed angle theorem

Which equation can be used to find the measure of EHG?

b. mEHG + 80 + 35 = 360

An interior angle of a regular polygon has a measyre of 135°. What type of polygon is it?

b. octagon

A solid right pyramid has a square base with an edge length of s units and a height of h units. Which expression represents the volume of the pyramid?

b. s2h units3

Which equation can be used to find the measure of angle FGE?

b. sin(x) = 9/15.2

Given: Circle M with inscribed <KJLand congruent radii JM and ML Prove: m<MJL = 1/2 (mKL) What is the missing reason in step 8?

b. substitution property

Which equation can be used to find the measure of angle BAC?

b. tan-1 (12/5) = x

Arc AB is 1/6 of the circumference of a circle. What is the radian measure of the central angle?

b. π/3

Given right triangle XYZ, what is the value of tan(Y)?

b. √3/3

Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?

b.π/2 radians

Which equation can be used to solve for b?

b=(8)tan=(30)

Manuel wants to buy a window shade to cover the window and frame shown. The window is in the shape of a regular octagon. The radius of the window, including the frame, is 2 ft, and the measure of each edge of the octagonal frame is 1.52 ft. What is the approximate area of the window that needs to be covered, including the frame?

c 11.2

A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm. What is the area of the pentagon, rounded to the nearest tenth?

c 32.7

A regular octagon has an apothem measuring 10 in. and a perimeter of 66.3 in. What is the area of the octagon, rounded to the nearest square inch?

c 332

Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square?

c. (64 - 16π) in.^2

Triangle ABC is an isosceles triangle in which AB = AC. What is the perimeter of ABC?

c. 10 + √10 units

The area of a rhombus is 65 square units. The length of one diagonal is 13 units. What is the length of the other diagonal?

c. 10 units

Find the length of AC. Use the length to find the length of CD. What is the length of CD? Round to the nearest tenth.

c. 10.7 cm

Points E, F, and D are located on circle C. The measure of arc ED is 108°. What is the measure of angle ECD?

c. 108°

The diagram shows quadrilateral MNPQ. What is the length of line segment MQ?

c. 11 units

In circle O, SU is a diameter. What is mST?

c. 130°

What is the value of x? (140°, 34°, 56°,x)

c. 130°

In circle N, KL ≅ ML. What is the measure of JM?

c. 132°

Rhombus LMNO is shown with its diagonals. The length of LN is 28 centimeters. What is the length of LP?

c. 14 cm *See Graph #23

What is the length of BC? Round to the nearest tenth.

c. 14.5

In circle Z, what is m<2?

c. 140°

What is the measure of EAB in circle F?

c. 148°

c. 16 miles

What is the length of line segment XZ?

c. 16 units

A secant and a tangent meet at a 90° angle outside the circle. What must be the difference between the measures of the intercepted arcs?

c. 180°

This composite figure is made of two identical pyramids attached at their bases. Each pyramid has a height of 2 units. ~2, 5, 0.25 Which expression represents the volume, in cubic units, of the composite figure?

c. 2(1/3(5)(0.25)(2))

A triangle has angles that measure 30°, 60°, and 90°. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth.

c. 23.7 in.

A cylinder has a radius of 1 inch and height of 1 inch. What is the approximate volume of the cylinder? Around to the nearest hundredth. Use 3.14 for π.

c. 3.14 cubic inches

In circle Y, what is m∠1?

c. 31°

Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y and Z are all on line segment WZ. What is the area of circle C, which passes through points W and Z?

c. 324π units^2

A frustum is formed when a plane parallel to a cone's base cuts off the upper portion as shown. ~6.4, 1.5 ~6.8, 3 fustrum What is the volume of the frustum? Express the answer in terms of π.

c. 34.8π units3

An oblique prism has a base area of 3x^2 square units. What expression represents the volume of the prism, in cubic units?

c. 36x^2

BD and AC are chords that intersect at point Y. What is the length of line segment AY?

c. 4 units

Michael is finding the area of parallelogram ABCD. To do this he follows the steps in the table. To solve the problem using these steps, what are the dimensions of the rectangle he should draw?

c. 4 units by 4 units

If line segment AB measures approximately 8.6 units and is considered the base of parallelogram ABCD, what is the approximate corresponding height of the parallelogram? Round to the nearest tenth.

c. 4.8 units

The figure is a kite. What is the length of the kite's longer diagonal?

c. 40 units

A kite is inscribed in a square with a side length of 9 units. What is the area of the kite?

c. 40.5 square units

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

c. 41 units

What is the perimeter of ABCD?

c. 44 units

What is the measure of angle EFD?

c. 47.5°

Splint G is the center of the small circle. Point X is the center of the large circle. Points G, H, and X are on line segment GX. What would be the area of a new circle that has line segment GX as its diameters?

c. 49π cm^2

Angle BAC measures 56°. What is the measure of angle BDC?

c. 56°

In the diagram, ZY = WX = 2√10. What is the perimeter of rectangle WXYZ?

c. 6√10 units

c. 72.44 in.

What is the measure of circumscribed ∠X?

c. 90°

How do the areas of the parallelograms compare?

c. The area of parallelogram ABCD is equal to the area of parallelogram EFGH.

Which statements is true regarding the diagram of circle P?

c. The difference of z and y must be 2x.

A shoe store owner is designing the layout of the displays in his store...... The distance between grid lines is 4 feet. Which statement about the possible designs is true, given, the owner's requirement?

c. The maximum number of circular displays that can be used is 4.

What is true regarding two adjacent arcs created by two intersecting diameters?

c. The sum of their measures is 180°

Circle X with a radius of 6 units and circle Y with a radius of 2 units are shown. Which steps would prove the circles similar?

c. Translate the circles so they share a common center point, and dilate circle Y by a scale factor of 3.

How can you decompose the composite figure to determine its area? (4 curvy sides)

c. as a square and four semicircles

Given: JKLM is an isosceles trapezoid, KL || JM Prove: KM ~= JL What is the missing reason in step 4

c. base angles theorem

Rectangle PQRS is shown with its diagonals, PR and QS. What type of triangle is STR?

c. isosceles triangle

Which equation is correct regarding the measure of <1?

c. m<1 = 1/2(b - d)

A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches. What are the measures of the angles in triangle ABC?

c. m<A ~~ 73.7°, m<B ~~ 16.3°, m<C~~ 90°

Cavalieri's principle states that if two solids of equal height have equal cross-sectional areas at every level parallel to the respective bases, then the two solids have equal volume. The two shaded solids both have a height of 2r units. At every level, the areas of the cross sections of both solids equal π(r2 - b2). Therefore, the formula for the volume of the sphere can be derived by writing an expression that represents the volume of

c. the solid between the two cones and the cylinder.

Which could be the base shape of the cylinder?

circle

Which classifications apply to the polygon? Check all that apply.

concave hexagon

What type of polygon is shown?

concave heptagon

What type of polygon is shown? convex heptagon concave heptagon concave octagon convex octagon

concave heptagon

cone triangular pyramid square pyramid

Which concept is used to prove that the opposite sides of a parallelogram are congruent?

congruent triangles

What type of polygon is shown?

convex hexagon

Given: ABCD is a kite. Prove: BD bisects AC. What is the missing reason in step 5?

corresponding parts of congruent triangles are congruent

Use the diagram to complete the statement. Given △JKL, sin(38°) equals

cos(52°).

For ΔABC, which one is equivalent to sin(A)?

cos(C)

Which expressions can be used to find m<ABC? Check all that apply.

cos-1 (6.3/9.8) sin-1 (7.5/9.8)

Which expressions can be used to find m<BAC? Check all that apply.

cos-1 (6.9/12) sin-1 (9.8/12) tan-1 (9.8/6.9)

Which equation can be used to find the measure of angle GFE?

cos−1( 11.9/14.5) = θ

Which polygon has an interior angle sum of 900°?

d. (7 sides)

If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?

d. 1.6 units

Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°. What is the measure of minor arc BD?

d. 100°

Angle ABD measures (4x + 10)°. Angle ACD measures (5x - 2)°. What is the measure of arc AD?

d. 116°

Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units. What is the length of AC?

d. 12 units

Kite WXYZ is graphed on a coordinate plane. What is the approximate perimeter of the kite? Round to the nearest tenth.

d. 16.2 units

Marina wants to install security cameras in her store, which has dimensions 48 feet by 48 feet. Each camera can view an area of approximately 128 ft^2, with a viewing area shaped like a right triangle. How many cameras will be necessary to cover the entire store?

d. 18

In circle V, r = 14ft. What is the area of circle V?

d. 196π ft^2

Figure LMNO is a parallelogram. What is the value of x?

d. 20

In the diagram, AB = 10 and AC = 2√10. What is the perimeter of ABC?

d. 20 + 2√10 units

Line segment QP is tangent to the circle. What is the length of line segment QP? Round to the nearest unit.

d. 20 units

Point O is the center of the circle. What is the perimeter of quadrilateral DOBC?

d. 28 units

What is the length of AB? Round to the nearest tenth?

d. 38.6 m

The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

d. 5.7 cm

The figure is a square. Its diagonals meet to form four right angles. What is the approximate value of x?

d. 5.7 units

Larissa dives into a pool that is 8 feet deep. She touched the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water. What is the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point?

d. 53.1°

The radius of the large sphere is souble the radius of the small sphere. How many times is the volume of the large sphere than the small sphere?

d. 8

What is the perimeter of LMN?

d. 8 + √10 units

The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

d. 8.5 cm

A scientist has four petri dishes of different sizes. Each dish contains a different number of bacteria. Find each population density, to the nearest hundredth. Which statement is true?

d. Dish C and Dish D have approximately the same population density.

In circle D, which is a secant?

d. GH

Which is correct description of the polygon?

d. It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other?

d. The midpoint of both diagonals is (4 1/2, 5 1/2), the slope of RP is 7, and the slope of SQ is -1/7

A city's bus line is used more as the urban population density increases. The more people in an area, the more likely bus lines will be utilized. Which city's residents are more likely to use public buses? Explain.

d. The residents of City A are more likely to use public transportation because the city has the highest population density.

Which statement proves that parallelogram KLMN is a rhombus?

d. The slope of KM is 1 and the slope of NL is -1.

Given right triangle XYZ, which correctly describes the locations of the sides in relation to <Y?

d. a is adjacent, b is opposite, c is the hypotenuse

A square is inscribed in an equilateral triangle that is inscribed in a circle. Which represents the area of the shaded region?

d. area of the circle - area of the triangle + area of the square

How can you decompose the composite figure to determine its area? (dinosaur looking)

d. as a semicircle, a trapezoid, and two rectangles

How can you decompose the composite figure to determine its area?

d. as a trapezoid, a rectangle, and two squares

Consider the diagram and proof below. Given: WXYZ is a parallelogram, ZX ~= WY Prove: WXYZ is a rectangle. What is the missing reason in Step 7?

d. consecutive <s in a ~~ are supplementary

Which equation can be solved to find one of the missing side lengths in the triangle?

d. cos(60°) = a/12

Major arc JL measures 300°. Which describes triangle JLM?

d. equilateral

A parabola can be represented by the equation y2 = -x. What are the coordinates of the focus and the equation of the directrix?

focus: (-1/4,0); directrix: x = 1/4

Given: Circle O with diameter LN and inscribed angle LMN Prove: LMN is a right angle. What is the missing reason in step 5?

inscribed angle theorem

Given: ∠KJL and ∠KML intercept arc KL. Prove: m∠KJL = m∠KML

inscribed angle thm inscribed angle thm substitution property

Given: Circle O; angle A intercepts BC ; angle D intercepts BC Prove: Angle A is Equivelant to Angle D Two statements are missing reasons. What reason can be used to justify both statements 2 and 3?

inscribed angles theorem

Given: Circle O; angle A intercepts BC ; angle D intercepts BC Prove: angle A is equivelent to angle D Two statements are missing reasons. What reason can be used to justify both statements 2 and 3?

inscribed angles theorem

Given: Circle O; intercepts ; D intercepts Prove: Two statements are missing reasons. What reason can be used to justify both statements 2 and 3?

inscribed angles theorem

Given: Circle O; intercepts ; D intercepts Prove: Two statements are missing reasons. What reason can be used to justify both statements 2 and 3? Statements Reasons 1. circle O; 1. given 2. 2. ? 3. 3. ? 4. 4. substitution property 5. 5. definition of congruent angles

inscribed angles theorem

Two statements are missing reasons. What reason can be used to justify both statements 2 and 3?

inscribed angles theorem

Rectangle PQRS is shown with its diagonals, PR and QS. What type of triangle is △STR?

isosceles triangle *See Graph #20

which equation is correct regarding the measure of <1

m<1=1/2(b-d)

which equation is correct regarding the measure of <mnp

m<mnp=1/2(x-y)

which equation is correct regarding the diagram of circle o

m<xyz=1/2(a+b)

Which equatino can be used to find the measure of EHG?

mEHG + 80 + 35 = 360

In ⊙H, IK ≅ JK, mIK = (11x + 2)°, and mJK = (12x - 7)°. What is the measure of IKJ?

mIKJ = 202°

Complete the steps, which describe how to find the area of the shaded portion of the circle. 1.Find the area of the sector by multiplying the area of the circle by the ratio of the _________________________ to 360. 2.Subtract the area of the triangle from the area of the sector.

measure of the central angle

Which equation is correct regarding the measure of ∠1?

m∠1 = ½(b - d)

Which equation can be used to solve for m∠1?

m∠1 =1/2 (a + b)

What are the angle measures of triangle ABC?

m∠A = 90°, m∠B = 60°, m∠C = 30°

A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches. What are the measures of the angles in triangle ABC?

m∠A ≈ 46.2°, m∠B ≈ 43.8°, m∠C ≈ 90° m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90° m∠A ≈ 74.4°, m∠B ≈ 15.6°, m∠C ≈ 90°

Which equation is correct regarding the measure of ∠MNP?

m∠MNP = 1/2(x - y)

What are the missing angle measures in parallelogram RSTU?

m∠R = 110°, m∠T = 110°, m∠U = 70°

What are the angle measures of triangle VUW?

m∠V = 60°, m∠U = 90°, m∠W = 30°

Figure WXYZ is a parallelogram. Which angle measures are correct? Check all that apply.

m∠X = 55° m∠W = 125° m∠Z = 55°

Figure WXYZ is a parallelogram. Which angle measures are correct? Check all that apply.

m∠X = 55° m∠W = 125° m∠Z = 55°

Figure CDEF is a parallelogram. Which measures are correct? Check all that apply.

n = 10 CF= 59 FE = 42

On the packaging for a triangular sail, the edge measurements for the sail are listed as 7 ft × 15 ft × 17 ft. Without unfurling the sail, you want to determine if the sail forms a right triangle, an acute triangle, or an obtuse triangle. Using the tools from this lesson, you determine that the general shape of the sail is a(n) ________ triangle.

obtuse

An interior angle of a regular polygon has a measure of 135°. What type of polygon is it?

octagon

A point is on a circle if the distance from the center of the circle to the point is equal to the

radius

The diagonals of a parallelogram are congruent. Which could be the parallelogram?

rectangle

Which three-dimensional figure has double the number of edges as faces?

rectangular prism

For a craft project, two equilateral triangles are taped together to create a quadrilateral. What is the quadrilateral?

rhombus

A parabola has a vertex at (0,0). The equation for the directrix of the parabola is x = -4. In which direction does the parabola open?

right

In the diagram below, Θ is measured in radians. Which equation represents the relationship between the radius, r, and arc length, s?

s = Θ • r

The base of a solid oblique pyramid is an equilateral triangle with an edge length of s units. Which expression represents the height of the triangular base of the pyramid?

s/2(√3) units

Given: ABCD is a parallelogram. Prove: ∠A and ∠D are supplementary. By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are ____________ angles. Because AB and DC are ____________, the same-side interior angles must be ____________ by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.

same-side interior parallel supplementary

Which equation is correct and can be used to solve for the value of z?

sin(51°)/2.6 = sin(76°)/z

Which trigonometric rations are correct for triangle ABC? Check all that apply.

sin(C) = √3/2 tan (C) = √3 sin(B) = 1/2

Which trigonometric ratios are correct for triangle ABC? Check all that apply.

sin(C) = √3/2 tan(C) = √3 sin(B) = 1/2

Which trigonometric ratios are correct for triangle DEF? Check all that apply.

sin(D) = 24/25 tan(D) = 24/7 sin(E) = 7/25

Which equation can be used to find the measure of angle LKJ?

sin-1(8.9/10.9)=x

Complete the proof to show that ABCD is a parallelogram. The slope of BC is . The slope of AD is . The slope of CD is . The slope of BA is . BC ∥ AD and CD ∥ BA because the __________________________________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.

slopes of opposite sides are equal

Every possible cross section of a three-dimensional figure is a circle. What is the figure?

sphere

A cross section is made by the intersection of a plane and a square pyramid at an angle either parallel or perpendicular to the base. The cross section can be which of these shapes? Check all that apply.

square triangle trapezoid

Triangle ABC is a right triangle and cos(22.6°)= b/13. Solve for b and round to the nearest whole number. Which equation correctly uses the value of b to solve for a?

tan(22.6°) = a/12

Which equation can be used to solve for the measure of angle ABC?

tan(x) = 2.4/10

Which equation can be used to solve for the measure of angle ABC? (2.4, 10.3, 10)

tan(x) = 2.4/10 tan(x) = 10/2.4 sin(x) = 10.3/10

A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism. The company wants to use the package that has the least amount of wasted space. The company should choose

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.

Which three-dimensional figure has exactly three rectangular faces?

triangular prism

To derive the standard formula of a circle, a radius r is constructed as the hypotenuse of a right triangle as shown. What are the lengths of the sides of the right triangle that is formed? Check all that apply.

x - h y - k

A parabola and its focus are shown on the graph. The vertex of the parabola is at (0,0). What is the equation of the directrix of the parabola?

x = -3

LMNO is a parallelogram, with ∠M=(11x)° and ∠N=(6x-7)°. Which statements are true about parallelogram LMNO? Select three options.

x = 11 m∠N = 59° m∠O = 121°

A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis. Which could be the equation of the parabola?

x2 = 4y

Which equation represents the parabola shown on the graph?

x2 = 6y

Angle G is a circumscribed angle of circle E. What is the measure of angle G, in terms of x?

x° + x°

What is the equation of the circle shown in the graph?

x² + (y + 3)² = 4

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Check all that apply.

x² + (y - 3)² = 36 x² + (y + 8)² = 36

An arc on a circle measures 250°. Within which range is the radian measure of the central angle?

π to 3π/2 radians

Arc CD is 1/4 of the circumference of a circle. What is the radian measure of the central angle?

π/2

An arc on a circle measures 125°. The measure of the central angle, in radians, is within which range?

π/2 to π radians

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD. Which statements about the arcs and angles are true? Check all that apply.

∠EFD ≅ ∠EGD ED ≅ FD mFD = 120°

∠FAE measures 72°. What other angle must measure 72°?

∠FBE

A partial proof was constructed given that MNOP is a parallelogram. By the definition of a parallelogram, MN ∥ PO and MP ∥ NO. Using MP as a transversal, ∠M and ∠P are same-side interior angles, so they are supplementary. Using NO as a transversal, ∠N and ∠O are same-side interior angles, so they are supplementary. Using OP as a transversal, ∠O and ∠P are same-side interior angles, so they are supplementary. Therefore, __________ and _________ because they are supplements of the same angle. Which statements should fill in the blanks in the last line of the proof?

∠M ≅ ∠O; ∠N ≅ ∠P

To prove quadrilateral WXYZ is a parallelogram, Travis begins by proving △WZY ≅ △YXW by using the SAS congruency theorem. Which reasons can Travis use to prove the two triangles are congruent? Check all that apply.

∠ZWY ≅ ∠XYW by the alternate interior ∠s theorem. WY ≅ WY by the reflexive property. WZ ≅ XY by the given.

Given: RT ≅ TV and ST ≅ TU Prove: RSVU is a parallelogram. What is the missing statement in step 4?

△RTS ≅ △VTU and △RTU ≅ △VTS

What is the missing statement in step 4?

△RTS ≅ △VTU and △RTU ≅ △VTS

Which statement is true regarding the diagram of circle P?

🚫 difference of z and y must be 1/2x

What is the approximate length of the radius, r? Use 3.14 for π. Round to the nearest inch. [_______] inches

🚫24

What dimensions of the box are required to fit the candle?

🚫5 by 3 by 18

Which is the radian measure of its corresponding central angle?

🚫5π/6 radians

A community pool that is shaped like a regular pentagon needs a new cover for the winter months. The radius of the pool is 20 ft. The pool is 24 ft on each side. To the nearest square foot, the area of the pool that needs to be covered is [_______] ft².

🚫991

What expression represents the volume of the prism, in cubic units?

🚫¹/₂x² + x

What expression represents the volume of the prism, in cubic units?

🚫¹/₂x³ + ³/₂x²🚫x³ + 3x²

Since all circles are similar, a proportion can be set up using the circumference and diameter of each circle. Substitute the values d₁ = 1, C1 = π, and d₂ = 2r into the proportion.

🚫π/2r = C₂/1, C₂ = π/2r

The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units. Which expression represents the area of the base of the pyramid?

not b

The base diameter and the height of a cone are both equal to x units. Which expression represents the volume of the cone, in cubic units?

1/12πx3

A rectangle has an area of 6 square meters. What will be the area of the rectangle if each side length is increased by a factor 5?

150 square meters

A solid oblique pyramid has a regular pentagonal base. The base has an edge length of 2.16 ft and an area of 8 ft2. Angle ACB measures 30°. What is the volume of the pyramid, to the nearest cubic foot?

19 ft3

The volume of the triangular block is 4 cubic inches. What is the approximate length of y? Round to the nearest tenth of an inch.

2.8 in.

A rectangular prism with a square base is cut from the center of a triangular prism. Each side of the square base measures 1.7 units. ~5.7, 1.7, 5, 4 What is the volume of the shaded solid? Round to the nearest tenth of a cubic unit.

45.4 units ^3

A cylindrical metal pipe has a diameter of 8.4 millimeters and a height of 10 millimeters. A hole cut out of the center has a diameter of 6 millimeters. What is the volume of metal in the pipe? Use 3.14 for π and round the answer to the nearest tenth of a cubic millimeter.

An oblique cone has a height equal to the diameter of the base. The volume of the cone is equal to 18π cubic units. What is the radius of the cone?

B. 3 units

Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid?

The height of each pyramid is 1/2h units.

The perimeter of the rectangle shown is 76 cm. It is rotated about line b. Which best describes the resulting three-dimensional figure?

a cylinder with a base radius of 14 cm

A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A cylindrical hole cut out of the center has a radius of 6 millimeters. ~20, 21, 6 Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Check all that apply.

a. 21π(10)^2 - 21π(6)^2 c. 2,100π - 756π

The volume of a cylinder is 4πx^3 cubic units and its height is x units. Which expression represents the radius of the cylinder, in units?

a. 2x

Which expression represents the volume, in cubic units, of the composite figure? ~20, 28

a. 4/3π(10^3) + π(10^2)(28)

A frustum is formed when a plane parallel to a cone's base cuts off the upper portion as shown. ~8, 3.5 ~11, 7.5 fustrum Which expression represents the volume, in cubic units, of the frustum?

c. 1/3π(7.5^2)(19) - 1/3π(3.5^2)(8)

A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is ╓r^2/4r√2 or ╓/4. Since the area of the circle is the area of the square, the volume of the cone equals

╓/4 the volume of the pyramid or ╓/4 [(2r^2)(h)/3] or 1/3╓r^2h

In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be ╓/4 times the volume of the pyramid that it fits inside. Which expression represents the volume of the cone that is ╓/4 times the volume of the pyramid that it fits inside?

╓/4(4r^2h/3)

-----

--------

Two cones are similar. The surface area of the larger cone is 65π square inches. The surface area of the smaller cone is 41.6π square inches. The radius of the smaller cone is 6.4 inches. What is the radius of the larger cone?

8 inches

The two square pyramids are similar. The side length of the smaller pyramid is 3/4 the side length of the larger pyramid. Which fraction represents the ratio of the base area of the smaller pyramid to the base area of the larger pyramid?

9/16

The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 18 inches. What is the height of the triangular base of the pyramid?

9√3

-----

------

-----

-------

------

-------

1,005 cm3

How many edges does a rectangular prism have?

What is the volume of the composite figure? ~4in, 7in, 3in, 12in

140 cubic inches

An oblique cylinder has a diameter of 14 units. The volume of the cylinder is 1,176π cubic units. What is x, the height of the cylinder?

24 units

A cylinder has a radius of 1 inch and height of 1 inch. What is the approximate volume of the cylinder? Round to the nearest hundredth. Use 3.14 for π.

3.14 cubic inches

The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times longer than the base edge. The height of the pyramid can be represented as ______. The ______ of an equilateral triangle with length x is x^2√3/4 units2. The area of the hexagon base is ______ times the area of the equilateral triangle. The volume of the pyramid is ______ x^2√33 units3.

3x area six 3/2

A can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company's clients needs a cylindrical can that has the same volume but is 15 cm tall. What must the new radius be to meet the client's need? Round to the nearest tenth of a centimeter.

4.9 cm

A gardener uses a tray of 6 conical pots to plant seeds. Each conical pot has a radius of 3 centimeters and a depth of 8 centimeters. About how many cubic centimeters of soil are needed to plant the full tray? Round to the nearest cubic centimeter.

452 cm3

Kabir wants to know the volume of a solid right pyramid with a square base. He uses a ruler to measure the length of the base as 8 inches. He then measures the slant height to be 5 inches. The hypotenuse of the right triangle used to determine the height is ___ inches. The leg of the right triangle that lies on the same plane as the base is ___ inches. The height of the pyramid is ___ inches. The volume of the solid pyramid is ___ cubic inches.

5 4 3 64

The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m. The area of the base is __________________ m2. The volume is __________________ m3.

52900 2645000

How many vertices does a triangular prism have?

The area of the base of the oblique pentagonal pyramid is 50 cm2 and the distance from the apex to the center of the pentagon is 6 cm. The measure of ∠ACB is 45°. The height, AB, is __ cm. The volume of the pyramid is ___ cm3.

6 100

The height is ____ units. The radius is ____ units. The volume is ____π cubic units.

6 8 128

The composite figure is made up of two congruent rectangular pyramids joined at their bases. What is the total volume of the composite figure?

60 units^3

A right cylinder has a radius of 2 units and height of 5 units. What is the volume of the cylinder? Round to the nearest tenth.

62.8 cubic units

A solid oblique cone with a slant length of 17 units is placed inside an empty cylinder with a congruent base of radius 8 units and a height of 15 units. What is the unfilled volume inside the cylinder?

640π cubic units

A volleyball of radius 13 inches fits exactly in a cylinder with the same radius. ~26in cylinder Inside the container there is empty space not taken up by the volleyball. What is the volume of that empty space? Use 3.14 for π and round the answer to the nearest cubic inch.

B. 4,599 in.^3

A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is πr^2/4π^2 or π/4. Since the area of the circles is π/2 the area of the square, the volume of the cone equals

B. π/4 the volume of the pyramid or π/4 ((2r)(h^2)/3) or 1/3πr^2h.

A circle with a radius of 1/2ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all that apply.

The length of the new radius will be 4 feet. The new circumference will be 8 times the original circumference The new area will be 64 times the original area. The new circumference will be 8╓ feet. The new area will be 16╓ square feet.

During practice, the Northwood football team drinks water from a cylindrical cooler that has a radius of 6 inches and a height of 20 inches. Players use conical paper cups, as shown below. If the water cooler is filled completely, can each of the 38 players have two full paper cups of water during practice? Explain.

Yes, because there is enough water in the cooler for about 81 cups total.

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

a. 2/3πx^3

The height of a cylinder is twice the radius of its base. What expression represents the volume of the cylinder, in cubic units?

b. 2πx^3

The radius of a sphere is 3 inches. Which represents the volume of the sphere?

b. 36π cubic inches

The large sphere has a diameter of 20 feet. ~4ft Which expression represents the volume, in cubic units, of the shaded part of the sphere?

b. 4/3π(10^3) - 4/3π(4^3)

A gardener uses a tray of 6 conical pots to plant seeds. Each conical pot has a radius of 3 centimeters and depth of 8 centimeters. About how many cubic centimeters of soil are needed to plant the full tray? Round to the nearest cubic centimeter.

c. 452 cm^3

The perimeter of the rectangle shown is 76 cm. It is rotated about line b. Which best describes the resulting three-dimensional figure?

The base diameter and the height of a cone are equal to x units. Which expression represents the volume of the cone, in survival units?

d. 1/12πx^3

The density of water is 1 gram per cubic centimeter. A more dense object will sink, and a less dense object will float. Will a marble with a radius of 1.4 cm and a mass of 9 grams sink or float in water? The marble will ___________ because the density of the marble is about ___________ grams per cubic centimeter.

Geometry B - (MA202) '17

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