LCM2 Semester 2 Final Exam
determine the coordinates of point b that would prove quadrilateral ABCD is a parallelogram
(a-b,c)
Which transformation could be used to describe a translation along a line parallel to y=x?
(x,y) --> (x+a, y+a)
a circle drawn on the coordinate plane has a diameter with endpoints given by points A(-1,2) and B(3,2)
(x-1)^2 + (y-2)^2 = 4
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
in a bucket filled with four colors of marbles, Event R is pulling a green marble, Event S is pulling a purple marble, Event T is pulling a red marble, and event U is pulling a yellow marble. Select two choices that represent the complement of Event R, the symbol - indicates "not"
-R SN TNU SU TUUU SEE STUDY GUIDE BECAUSE ANSWER USES SPECIAL SYMBOLS
A circle has a central angle of 0, an arc length for the arc formed by 0 of L, and a radius of R, the circumference of the circle can be obtained by solving the equation C = 2π x r
0 = L/R
a regular octagon is inscribed in a circle. radii are drawn from the center of the circle to two consecutive vertices of the octagon. What is the radian measure of the central angle, rounded to the nearest thousandth?
0.785 radians
Carl claims that for some centers of dilation of a line, the line will remain unchanged. He is tasked to prove his claim using the line y=5x-10 and a dilation with a scale factor of 2. Which center of dilation could be used to support Carl's claim
(1,-5)
Consider triangle ABC shown below, where the length of the side opposite angle A is 8 units, the length of the side opposite angle b is 12 units, and the length of the side opposite angle C is 5 units. Which expressions are equivalent to the are of triangle ABC, select all that apply
(6)(5) sin A 1/2(8)(12) sin C
In a computer graphics design program, Mario created a segment with endpoints at (1,5) and (7,3). He then reflected the segment about a vertical line through the segment's own midpoint. what are the coordinates of the endpoints of the new segment?
(7,5) and (1,3)
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 inches. Figure 2 is a cylinder with the same radius and same total height as figure 1, as shown below. To the nearest hundredth, how many times greater is the volume of figure 2 than the volume of figure 1
1.17
Consider triangle XYZ shown below. Which of the following expressions can be used to determine the area of the triangle shown below>
1/2 (y)(x)sin(<Z)
Look at triangle DPX shown below. Which of these represents the area of triangle DPX
1/2 f r sin a
the probability that a basketball player makes any particular free throw is 80%... how many times can the player be expected to make both free throws if they are independent events?
112
In the figure below, triangle MNO =/~ triangle PQR. Determine the length of QR
12
Chad left his house to go on a road trip, he drove due north at 60 mpg for the first two hours of the trip, and then drove due east at 50 mph for the next hour. after those three hours of driving, approximately how far was Chad from his house
130 mi
A bird sitting on top of a stop sign notices a piece of food on the ground, 11 ft from the base of the stop sign. if the bird has to look down at a 39 degree angle of depression in order to see the piece of food. what is the approximate distance from the bird to the food? Assume the stop sign is at a right angle to the ground sin 39 degrees =/~ 0.63 cos 39 degrees =/~ 0.78 tan 39 degrees =/~ 0.81
14.10 ft
Line m is tangent to Circle Q at point S, IF LS = 8 and the diametere RT = 30, how long would a line segment QL be?
17
a farmer is planting seeds on an irregular piece of land. Seeds come in bags that cover 10,000 square feet of land, What is the best estimate of the number of bags of seed that the farmer should purchase to plant seeds on the entire piece of land
18 bags
Omar is building a bookshelf out of 6 boards, as shown in the diagram below. The board are all 6 inches in width and are all 0.75 inch in thickness. Which of the are the lengths of the boards Omar needs to make the bookshelf? Choose all correct.
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
there are twelve students in the checkout line at a school bookstore and three are randomly selected... what is the probability that the students selected are the sixth, seventh, and tenth people in line or the seventh, tenth, or twelfth people in line?
2/12C3
a bag of candy contains 9 peppermints and 4 butterscotch candies. What is the probability that 3 randomly drawn candies will all be butterscotch?
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 degrees
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?
2√a^2+b^2
Marti is filling a 10 inch diameter ball with sand to make a medicine ball that can be used for exercising. To determine if the medicine ball will be too heavy after its completely full of sand, she did some research and found that there is approximately 100 pounds of sand per cubic foot. How heavy will the medicine ball be after it is filled with sand, rounded to the nearest pound?
30 pounds
what is the perimeter of triangle RST
3c + c√2 + c√3
A contractor is building a tower shaped like a tall rectangular prism.... What is the volume of each floor of the building?
40,000 ft^3
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 degrees, and the angle of elevation from the base of the tree to the top of the tower is 62 degrees. What is the distance from the base of the building to the base of the tree? (rounded to the nearest foot)
485 feet
a circle is shown below. Diameter YZ is parallel to chord WX and mWX = 50 degreees. what is mXZ
65 degrees
A manufacturer designs a folding table with straight legs and supports, as shown below. The table top is parallel with the ground, and triangle BCD =/~ triangle FED. What is the measure of <BAG, the angle the table leg makes with the ground?
68 degrees
A central angle of 8 radians is drawn in a circle with radius r. Which proportion can be used to derive the are, A8, of the sector of the circle created by the central angle
8/A8 = 2π/πr^2
A fountain is located between two trees. Each tree has a height of 60 feet. The angles of elevation from the base of the fountain to the top of each tree are 64 degrees and 48 degrees as shown below. What is the horizontal distance between the two trees (rounded to the nearest foot)
83 ft
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. if two houses are chosen at random, what is the probability that both houses have a garage?
87/245
a movie critic analyzed hundreds of hollywood movies... according to the data in the table, which of these statements are true? choose all correct
91% of the movies are funny or action packed 6% of the movies are neither funny nor scary 83% of the movies are funny or scary
What is the approximate volume of the right pyramid represented by this net?
965 cm^3
Cheryl started off with triangle ABC constructed an arc centered at A constructed arcs of equal radii centered at D and E, and constricted ray AG intersecting 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 equivalent from AB and AC
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.
?
Anthony draws parallelogram ABCD below and investigates the reflections and rotations that carry it onto itself. Anthony claims that a rotation of 360 degrees is the only transformation that carries parallelogram ABCD onto itself. What is the right answer?
A reflection over diagonal AC (line ontop of AC) A reflection over diagonal BD (line ontop of BD) A rotation of 180 degrees clockwise about its center
a farmer fences a triangular field fro sheep as shown in the graph. each unit of length on the graph represents 100 meters. the farmer wants to provide an area of 2,000 square meters for each sheep, Which of these statements are true? select all that apply.
A segment drawn from point b to (1,-5) us an altitude of the triangle the field will hold a total of 400 sheep a segment drawn from point a to (3,1) is an altitude of the triangle
Thomas is attempting to prove the Pythagorean theorem using similar triangles. Which of the following could be thomas' first ration 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
Given triangle ABC Lance performed a geometric construction. He drew arcs with equal radii centered at A. drew arcs with equal radii centered at D and E. and then drew AF intersecting BC at G. shown in the diagram below. Which statements must be true about lance's construction? select all that apply
AG is an altitude of triangle ABC (AB)^2 - (BG)^2 = (AC)^2 - (GC)^2
Jaimie takes a survey of his class to determine if having brown hair is independent of wearing a watch. There are 21 students in the class... Is having brown hair independent of wearing a watch?
Brown hair is independent of wearing a watch because P(W| BH) = P(W)
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 the same radius. Which statement best describes Lia's claim?
Lia is correct in stating that the reflected circle will always have the same radius, but is incorrect in stating that the reflected circle will always have the same center
Based on the triangles shows below, Theodore claims that triangle TUV is transformed to triangle WXY with a scale factor of 2/3. Is theodore correct?
No, the triangles are similar with a scale factor of 2/3
the region shown below is bounded by x=3, y=0, and y=x. if the region is rotated about the line x=4, which geometric solid is generated?
SEE STUDY GUIDE THIS IS A PICTURE ANSWER cone without a tip and cylinder in the middle
the overhead view of the path formed by a circular road is described by the equation below, where coordinates are measured in kilometers x^2 + y^2 - 0.4x - 0.6y - 0.23 = 0 Shown below is an INCORRECT attempt to find the center and radius of the overhead view of the path formed by the road
Step 4
The city planning commission is looking to put in sidewalks where the three medians of the triangle are located. what would be true about the sidewalks if the model of the city park is an equilateral triangle. Select ALL that apply.
The sidewalks will meet in a single location The sidewalks will bisect the angles of the park The sidewalks divide the park into 6 smaller, noncongruent triangles.
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 scientists claim?
The southeast side of the glacier does translate in the way the scientist describes. The glacier in the second map is congruent to the glacier in the first map. The scientist's claim is correct.
the figure below shows a slice of metallic wire. the slice is in the shape of an oblique, circular cylinder with a radius of r millimeters and a height of h millimeters, which of these are possible cross sections of the figure? choose all correct
half a circle on top of a line named r oval with a vertical line on the side of it circle with a horizontal line on the bottom parallelogram with a vertical and horizontal lines on both sides SEE STUDY GUIDE THIS IS A PICTURE ANSWER
The diagram below shows the compass and straight edge 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
fran's remote controlled toy helicopter flies in a horizontal 10 yard radius circle described by the equation below, where a and b are real constants, and the coordinates are measured in yards. x^2 + ax +y^2+by = 0 which of the following could be the values of a and v? choose all that are correct
a = 16 and b = -12 a = 20 and b =0
Anita measured the volume of various 6 inch tall cylindrical cans by pouring water into them. She then locked on the internet and found that 1 cubic inch is approximately equivalent to 0.554 fluid ounces. what statement is true?
a can that holds 28 ounces of water has a radius of 1.64 inches
a gumball machine contains blue, pink, white, and green gumballs.... if event a is Jane turning the knob of the gumball machine and a blue gumball dropping out, then the complement of event a is
a pink, white, or green gumball dropping out when she turns the knob
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 carries one triangle onto the other the two triangles are similar because the triangles satisfy the Angle-Angle criterion All pairs of corresponding angles are congruent because the triangles must have an angle sum of 180 degrees
The diagram below shows a circular courtyard with three straight walkways. All measurements are in meters. Which equations must be true? select all that apply
ab=675 c/b = 35/27
A building was planned to b built in an area north of 8th street and east of Main street, after additional planning took place....Which statement best explains 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 not rigid during the transformation
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 a vertex. she then draws a line through this vertex that is parallel to the opposite side, as shown in the diagram below.
m<1 = m<5 m<2 = m<4 m<3 + m<4 + m<5 = 180 degrees
Based on the drawing below, in order for triangle ABC to be similar to triangle DEF by SAS similarity, which of the following needs to be true?
m<F = 38 degrees
if the slope of line AB is m, what is the product of the slopes of ab and a line parallel to ab?
m^2
A bowl is shown below. the diameter of the bowl is 5 inches at its opening and 3 inches at its base, the bowl's height is 4 inches. Kellie develops the three models below to estimate the amount of cereal that can be placed in the bowl. Model 1... Model 2... Model 3... Which statement is true regarding the amount of cereal that can be placed in the bowl
models 1 and 3 overestimate the amount of cereal, which model 2 underestimates the amount of cereal
Prove that circle R and circle S are similar. Circle R: (x-4)^2+(y+2)^2 =36 Circle S: (x+1/2)^2+(y-4)^2 = 81 Select the option that BEST shows the necessary transformations from Circle R to Circle S
move left 4.5 units, up 6 units, and an increase of the radius by 3/2
Which cross section is not possible when slicing a square prism with a plane?
octagon
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?
rotation 180 degrees about the origin, followed by reflecting about the line x = 2
the figure below shows concentric circles, in the figure, OH = 1/2 OQ. what is the relationship between the lengths of arc GH and arc PQ
s=1/2t
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
scale factor = 3, perimeter = 15
Pablo and his business partner must calculate the area of this window pane to help determine the cost to replace it... Pablo isn't familiar with the formula, so he wants to confirm that it is correct. Which equation should Pablo use to help derive the formula
sin(B) = h/c
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. select all that apply
the area of the base could be increased to 50 feet^2 the height of the pyramid 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... if you are overweight to the chance of being overweight if you have diabetes?
the chance of having diabetes if you are overweight is much less than the chance of being overweight if you have diabetes
A student is investigating pairs of triangles that have congruent corresponding angles. The student 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.
a biologist is studying a species of lizards that live in the desert. he wants to determine how the temperature affects the number of each species he observes. the two way tables shows his data. using the data, which statements are true?
the events' species observed is a collared lizard and temperature is above 100 degrees F are independent
a package has ten boxes of medicine that are identical except... three of these 10 boxes are expire. three are randomly selected without replacement from the package? which statements are true? choose all correct
the probability that at least one of the selected boxes is expired is 17/24 the probability that none of the selected boxes are expired is 7/24 the probability that all the selected boxes are expired is 1/120 the probability that no more than two of the selected boxes are expired is 119/120
the figure below shows a company logo. the logo is a circle containing two triangles drawn in a circle with four vertices of the triangles lying on the circle. Which of these statements can be shown to be true?
the two triangles are similar but are not necessarily congruent
The figure below shows right triangle LMP and right triangle NOP. Segments LN and OM intersect at point P. Which statement best describes 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, <LMP =/~ <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
A circle is graphed on the coordinate plane. The circle has center (-2,4) and has a radius of 5. The equation of the circle can be expressed as x^2 + y^2 + Ax + By +C = 0, where A,B,and C are integers. Which of the following statements is true?
the value of b is -8
a businessman surveys his employees to determine their overall satisfaction with the company. the two way table shows his data... select three statements
thee majority of the part time employees were not satisfied the full time employees were twice as likely to say they were satisfied than the part time employees over fifty percent of the employees were satisfied with their job
AG, BF, and CE are all parallel, as are BH, CG, and DF. The designer wants to prove that triangle ABJ - triangle BCK - triangle CDL - triangle HGJ - triangle GFk - triangle FEL. What additional information, by itself, would be enough to prove the similarity of the triangles? Evaluate each answer choice separately. Choose all that are correct,
triangle ACG - triangle GEC triangle ABH =/~ triangle HGA <BAH =/~ <GHA and <BCE =/~ <GFD
The diagram below shows the first steps in copying a triangle using a compass and straightedge. Which is the next step in the construction?
triangle YWX with line W-X with a line on x and above W and Z. Check study guide! its a picture answer so... description doesn't help much
In the circle o, BD is a diameter. Which states are true about the circle. Select all the apply
x = 50 degrees m(cd) = 130 degrees m<BCD = 25 degrees
NOPQ is a rhombus, Use coordinate geometry to find the length of side ON
√a^2 + d^2