Cumulative Exam Answers

Triangle A B C is shown. Angle A B C is a right angle. Angle B C A is 22 degrees and angle C A B is 68 degrees.

An oblique cylinder has a radius of 10 units and slant length of 26 units.

Quadrilateral FGHJ is dilated according to the ruleDO,(x,y) to create the image quadrilateral F'G'H'J', which is not shown.

Circle R is shown. Tangents F G and H G intersect at point G outside of the circle to form an angle with a measure of 50 degrees. Point E is on the second arc. Arc F H has a measure of x degrees.

Triangles A B C and X Y Z are shown. Angles A B C and X Y Z are right angles. Angles B A C and Y X Z are congruent. The length of A B is 5, the length of A C is 13, and the length of B C is 12.

A regular hexagon is shown.

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.

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

Parallelogram A B C D is shown. Diagonals are drawn from point A to point C and from point D to point B and intersect at point E.

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.

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?

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.

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

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.

Circle O has a circumference of approximately 28.3 cm.

Point O is the center of dilation. Triangle D E F is dilated to create smaller triangle D prime E prime F prime. The length of O F prime is 3. The length of F prime F is 7.

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?

The statements below can be used to prove that the triangles are similar. ? △ABC ~ △XYZ by the SSS similarity theorem.Which mathematical statement is missing?

The equation  can be used to find the length of .

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 .

Which angle measures are correct? Select three options.

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

Complete the steps, which describe how to find the area of the shaded portion of the circle.

On a coordinate plane, parallelogram P Q R S is shown. Point P is at (5, 1), point Q is at (6, 4), point R is at (3, 10), and point S is at (2, 7).

Angle G is a circumscribed angle of circle E.

Rhombus LMNO is shown with its diagonals.

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

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.

An oblique cone has a radius of 5 units and a height of 9 units.

Consider circle N with radius 30 cm and radians.

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.

The hypotenuse of a 45°-45°-90° triangle measures  in.

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.

Triangle MRN is created when an equilateral triangle is folded in half.

In the diagram, .

On a coordinate plane, rhombus W X Y Z has points (negative 3, 1), (1, 4), (5, 1), and (1, negative 2).

Given: ABCD is a kite.Prove: BD bisects AC.

Triangle QRS is to be dilated using the rule .

is tangent to circle P at point Q.

Kite ABCD represents a softball field that is being built.

Figure ABCD is a square. Prove BD ≅ AC. Statements Reasons1.ABCD is a square1.given2.∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles2.definition of a square3.∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA3.right angles are congruent4.AB ≅ BC ≅ CD ≅ DA4.?5.△BAD ≅ △ABC5.SAS6.BD ≅ AC6.CPCTCWhat is the missing reason in the proof?

Circle Y is shown. Line segments X Y and Z Y are radii. The length of X Y is 16. Sector X Y Z of the minor angle is shaded.

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

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

The owner of a minigolf course is replacing the artificial grass on a portion of the course. The area to be replaced is shown in the diagram.

Two circles are concentric if they have the same center.

Triangle X Y Z is reflected over its hypotenuse to form kite X Y Z Y prime. Hypotenuse X Z has a length of 13, X Y is 5, and Y Z is 12.

What is the location of point G, which partitions the directed line segment from D to F into a 5:4 ratio?

Which statements about the clock are accurate? Select three options.

Parallelogram A B C D is shown. Line segment X Y goes from point X on side A B to point Y on side C D to form 2 trapezoids. The length of X Y is 11 and the length of Y C is 4. Sides X B and C Y are congruent.

Line segment JL is an altitude in triangle JKM.

On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (0, negative 1), point W is at (4, 0), point Y is at (3, negative 2), and point Z is at (negative 1, negative 3).

Read the proof.Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°Prove: △HKJ ~ △LNP

Triangle A B C is shown. The length of A B is 12, the length of B C is 24, and the length of C A is 12 StartRoot 3 EndRoot

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.

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.

Figure ABCD is a parallelogram.

An oblique prism has a square base and height of 3 centimeters.

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.

An oblique square prism is shown.