Math Final Answers
Consider triangle ABC shown below where the length of the side opposite angle A is 8 units, b is 12 and C is 5.
(6)(5) sin A 1/2 (8)(12) sin C
figure 1 is composed of a cylinder and a cone that share the same circular base. the cylindrical portion has a height of 20 inches and the conical portion has a height of 5.7
1.17
Look at DPX shown below. Which of these represents the areas for DPX?
1/2 fr sin a
Chad left his house to go on a road trip.
130 mi
a spinner is divided into 10 equally sized sections. 7 are colored red and 3 are blue.
3/5
What is the perimeter of RST?
3c + Crad2 + Crad3
a contractor is building a tower shaped like a tall rectangular prism.
40,000 feet 3
Two triangles are drawn on a coordinate plane, shown below. Select each statement that is true about these two triangles.
The two triangles are similar. A sequence of rigid motions and dilations carries one triangle to the other.
determine the coordinates of point B that would prove quadrilateral ABCD is a parallelogram
(A-b,c)
what Is the standard form of the equation of a circle with the center (3, -2) and radius 4
(x-3)2 + (y+2)2 = 16
which equation describes a circle with center (4, -7) and radius 9
(x-4)2 + (y+7)2= 81
which of the following equations represents a line that is perpendicular to the line represented by x + 2y=6 and passes through the point (3,-4)
-2x + y = -10
Consider triangle XYZ shown below. Which of the following expressions can be used to find the area?
1/2 (y) (x) sin (<Z)
the probability that a basketball player makes any particular free throw is 80 percent.
112
In the figure below, MNO = PQR. Determine the length of QR.
12
A bird sitting on top of a sign notices a piece of food on the ground, 11 ft from the base of the stop sign.
14.10 ft
Line M is tangent to circle Q at point S. If LS is 8 and Rt is 30 what's QT
17
a farmer is planting seeds on an irregular piece of land. seeds come in bags that cover 10,000 square feet of land.
18 bags.
Omar is building a bookshelf out of 6 boards, as shown in the diagram below.
2 boards that are each 24 inches in length. 2 boards that are each 18 inches in length 2 boards that are each 16.5 inches in length
a bag of candy contains 9 peppermints and 4 butterscotch candies.
2/143
The wheel below is rotated counterclockwise about the center, point C. What is the angle of rotation that maps point A to point B?
288
figure ABCD is a rectangle whose diagonals intersect at the origin. if point B has the coordinates (a, B) what is the length of diagonal AC
2radA2 + b2
A 254 foot tall radio tower is located partway between a building and a tree. The angle of elevation from the base of the building to the top of the tower is 36 and the angle of elevation from base to top is 62. What is the distance from the base of the building to the base of the tree (rounded to nearest foot)
485
a circle is shown below. YZ is parallel WX and WX is 50. what's XZ
65
A manufacturer designs a folding table with straight legs and supports, as shown below. The tabletop is parallel with the ground, and BCD= FED. What is the measure of BAG, the angle the table leg makes with the ground?
68
A fountain is located between two trees. Each tree has h = 60. THe angles of elevation from the base of the fountain to the top of each tree are 64 and 48 as shown below. What is the horizontal distance between the two trees (rounded to nearest foot)
83
On a certain street of 50 houses 20 houses have a 2 car garage 10 have a 1 car garage, and 20 do not have a garage.
87/245
Cheryl started off with ABC, constructed an arc centered at A, constructed arcs of equal radii centered at D and E, and constructed ray AG intercepting side BC at F, as shown in the diagram below. Which statements must be true about Cheryl's construction> Choose all that are correct.
<BAF =<CAF G is equidistant from AB and AC. ADG = AEG
Erin draws two triangles. Two pairs of corresponding angles are congruent. Select each statement that is true for all such pairs of triangles.
A sequence of rigid motions and dilations carry one triangle to the other. The two triangles are similar because they satisfy the AA criterion. All pairs of corresponding angles are congruent because triangles must have an angle sum of 180.
Thomas is attempting to prove the Pythagorean theorem using similar triangles. Which of the following could be Thomas's first ratio that he sets up?
AB/AC = AD/AB
DE || AC in the picture below. Which of the following statements must be true?
AC/DE = BC/BE
The diagram below shows a circular courtyard with 3 straight walkways
Ab= 675 c/b = 35/27
A building was planned to be built in an area north of 8th Street and East of Main Street, as shown below. After additional planning took place, it was determined that, in effect, the building will be reflected about oak street as shown on the map below. Which statement best describes why the second map does not match the written description?
After a reflection about oak street, what was the west side of the building should be on the east and be located exactly one mile west of Main Street. Also, the original shape was rigid during the transformation.
a circle is graphed on a coordinate plane. the circle has center at (-2,4) and has a radius of 5.
B is -8
Lia claims that a reflection over the Y axis will always carry a circle drawn on the coordinate plane to a circle with the same center and same radius. Which statement best describes Lia's claim?
Correct in stating that the reflected circle will always have the same radius but incorrect in stating that the reflected circle will always have the same center.
Determine which figure has been rotated 270 degrees clockwise about the origin.
Image on left is sideways, image on right is normal.
Based on the drawing below, in order for ABC to be similar to DEF by SAS similarity, which of the following needs to be true?
M<F= 38
a bowl is shown below. The diameter of the bowl is 5 inches at its opening and 3 inches at its base. The bowls height is 4 inches.
Models 1 and 3 overestimate the amount of cereal, while model 2 underestimates the amount of cereal.
Based on the triangles shown below, Theodore claims that TUV is transformed to WXY with a scale factor of 3/2. Is he correct?
No, the triangles are similar with a scale factor of 2/3
A geometric figure was created on a coordinate grid. The figure is transformed to create its image using the rule (x,y) -> (x-3-y). Which is another way of describing the transformation of the figure?
Reflection over the X axis , then translation 3 units left
The coordinate grid shows two trapezoids on the design of a new t-shirt. Which sequence of two transformations changes the unshaded trapezoid into the shaded trapezoid?
Rotating 180 degrees about the origin, followed by reflecting about the line x=2.
Quadrilateral ABCD undergoes a dilation of scale factor X, centered at A, to produce AB'C'D. The perimeter of AB'C'D is 45. Determine the scale factor used in the dilation and computer the perimeter of ABCD.
Scale factor: 3, perimeter 15
Xavier's backyard contains a wooden deck shaped like a parallelogram and two grassy lawns shaped like triangles, as shown in the figure below. Which of these statements can be proven to be true? Choose ALL that are correct.
Segment AF has the same length as segment BD The triangles containing lawns 1 and 2 are similar. The large triangle that contains the entire yard is a triangle similar to the triangle that contains lawn 2. <BDF is congruent to <EFD
pablo and his business partner must calculate the area of this window pane to help determine the cost to replace it.
Sin(B)=h/c
The diagram below shows the first steps in copying a triangle using a compass and straightedge. Which is the next step in the construction?
The X is on the top of the drawing and the curve is on the bottom right half of the line.
A student is investigating pairs of triangles that have congruent corresponding angles. The students claims that for such a pair of triangles, a sequence of rigid motions carries one triangle to the other since the triangles are congruent. Which statement best describes the student's claim?
The claim is only true if the triangles have congruent sides, since the definition of congruence requires congruent angles and sides.
The first map below shows a glacier. The second map shows the same glacier in a new position 2 years later. Each unit on the maps represents a distance of one kilometer. One scientist reports that the new position of the glacier is the result of a translation of the form (x,y) -> (x+7, y-8). Which statement BEST supports or refutes the scientist's claim?
The southeast side does translate in the way described. It has also been dilated. The claim is incorrect.
The figure below shows right triangle LMP and right triangle NOP. Segments LN and OM intersect at point P. Which statement best explains why the two triangles are similar?
The two triangles have two pairs of congruent angles because they are both right triangles and by vertical angles LPM = NPO. The AA theorem for two triangles states that if two pairs of corresponding angles of the triangles are congruent, then the triangles are similar.
the diagram below shows the compass and straightedge construction of WA as the angle bisector of angle KWZ. Arcs are numbered as 1 through 4. Select ALL statements that can be part of the justification for why WA is the angle bisector.
WK~= WZ by construction of arcs 1 and 2. KA ~= ZA by construction of arcs 3 and 4.
Anita measured the volume of various 6 inch tall cylindrical cans by pouring water into them.
a can that holds 28 ounces of water has a radius of 1.64 in
a circle has the equation X2 + Y2K + 2x - 12y+33=0
circle has a radius of 2 equation can be written as
if the slope of line AB is M, what is the product of the slopes of ab and a line parallel to AB
m2
Katherine wants to prove that the measures of the interior angles of a triangle have a sum of 180 degrees. She draws a triangle and extends one of the sides through the vertex. She then draws a line through the vertex that is parallel to the opposite side, as shown in the diagram below. Which of the following statements must be true and could be used as part of Katherine's proof? select ALL that apply.
m<1 = m<5 M<2 = m<4 m<3 + m<4 + m<5 = 180
circle O is shown below. m<BC = 116 and m<AOB = 88
m<acb=44 m<ac = 156 m<BAC = 58
NOPQ is a rhombus. Use coordinate geometry to find the length of side ON.
rad A2 + d2
the overhead view of the path formed by a circular road is described by the equation below where coordinates are measured in kilometers. find wrong step.
step 4
If Sin A = Cos B, what must be the relationship between the measures of A and B?
the angle measures need to be complementary.
a square pyramid has a height of 12 feet and a base with a length of 5 feet. in order to double the volume of this pyramid which measurements could be changed.
the area of the base could be increased to 50 feet The height could be increased to 24 feet
in order to better understand the link between being overweight and having type 2 diabetes, a medical student surveys 100 random people.
the chance of having diabetes if you are overweight is much less than the chance of being overweight if you have diabetes.
a biologist is studying species of lizards that live in the desert.
the events 'species observed is a collard lizard's and 'temperature is above 100 f' are independent.
a businessman surveys his employees to determine their overall satisfaction with the company. the two way table shows his data.
the majority of the part time employees were not satisfying. the full time employees were twice as likely to say they were satisfied than the part time employees. over 50 percent of the employees were satisfied with their job.
A hardware store conducts a survey on customers who are doing home improvement projects.
the probability that a customer orders paint given that the customer orders floor tiles is 0.75 a customer ordering paint and a customer ordering floor tiles are dependent events
The figure below is a company logo. Circle containing 2 triangles. circular connections
two triangles are similar but not necessarily congruent
In the circle 0, BD is a diameter. Chose all correct statements.
x=50 m CD is 130 m<BDC = 25
