June 19 geo

On the set of axes below, triangle ABC is graphed. Triangles A'B'C' and A"B"C", the images of triangle ABC, are graphed after a sequence of rigid motions. Identify which sequence of rigid motions maps △ABC onto △A'B'C' and then maps △A'B'C' onto △A"B"C".

• a rotation followed by another rotation

• a translation followed by a reflection

• a reflection followed by a translation

• a reflection followed by a rotation

The table below shows the population and land area, in square miles, of four counties in New York State at the turn of the century. Which county had the greatest population density?

• Broome

• Dutchess

• Niagara

• Saratoga

If a rectangle is continuously rotated around one of its sides, what is the three-dimensional figure formed?

• rectangular prism

• cylinder

• sphere

• cone

Which transformation carries the parallelogram below onto itself?

• a reflection over y = x

• a reflection over y = -x

• a rotation of 90° counterclockwise about the origin

• a rotation of 180° counterclockwise about the origin

After a dilation centered at the origin, the image of CD is C'D'. If the coordinates of the endpoints of these segments are C(6,-4), D(2,-8), C'(9,-6), and D'(3,-12), the scale factor of the dilation is

• 3/2

• 2/3

• 3

• 1/3

A tent is in the shape of a right pyramid with a square floor. The square floor has side lengths of 8 feet. If the height of the tent at its center is 6 feet, what is the volume of the tent, in cubic feet?

• 48

• 128

• 192

• 384

The line -3x + 4y = 8 is transformed by a dilation centered at the origin. Which linear equation could represent its image?

• y = 4/3 x + 8

• y = 3/4 x + 8

• y = -3/4 x - 8

• y = -4/3 x - 8

In the diagram below, AC and BD intersect at E. Which information is always sufficient to prove ΔABE ≅ ΔCDE?

• AB || CD

• AB ≅ CD and BE ≅ DE

• E is the midpoint of AC.

• BD and AC bisect each other.

The expression sin 57° is equal to

• tan 33°

• cos 33°

• tan 57°

• cos 57°

What is the volume of a hemisphere that has a diameter of 12.6 cm, to the nearest tenth of a cubic centimeter?

• 523.7

• 1047.4

• 4189.6

• 8379.2