1) Find d in simplest radical form. Right square pyramid with equilateral triangular faces

has 8 on all sides

A) 4�ã2
B) 8�ã2
C) 4�ã3
D) 8�ã3

#2) Decide whether the statement is true or false. The sides of a regular polyhedron, although having to be the same polygon, do not have to be regular polygons.

A) True
B) False

#3) Write the answer to the problem as an algebraic expression. Bill is q years old. How old will he be in 10 years? How old was he 8 years ago?

A) q + 10; q - 8
B) 10 q; q - 8
C) q + 10; 8 - q;
D) q + 8; q - 10

#4) Determine whether the lines are Parallel, Perpendicular, or Neither.

A) y = 5( 4x + 9) and y = - 1/20x - 4
B) y = 9x + 9 and y = -9x + 9

1) To find the answer, we need to understand the relationship between the edge length of the equilateral triangular face and the height of the right square pyramid.

In an equilateral triangle, the height (h) can be expressed as h = sqrt(3)/2 * s, where s is the length of the side of the triangle.

Since all sides of the pyramid have a length of 8, the side length of the equilateral triangle is also 8.

Plugging this value into the equation for the height, we get h = sqrt(3)/2 * 8 = 4sqrt(3).

Since d represents the diagonal of the base of the pyramid, which is twice the height of the equilateral triangle, d = 2 * 4sqrt(3) = 8sqrt(3).

Therefore, the answer in the simplest radical form is D) 8�ã3.

2) A regular polyhedron is a solid that has congruent regular polygons as its faces, and every vertex of the polyhedron is surrounded by the same number of these faces.

For a regular polyhedron, all the faces are not only congruent regular polygons but also have the same number of sides. So the statement is false.

The answer is B) False.

3) To answer this question, we need to create algebraic expressions for Bill's age in 10 years and 8 years ago based on the given information.

Let's assume Bill's current age is q.

In 10 years, Bill will be q + 10 years old.

8 years ago, Bill was q - 8 years old.

Therefore, the answer is A) q + 10; q - 8.

4) To determine whether the lines are parallel, perpendicular, or neither, we need to examine their slopes.

A) For the first set of lines: y = 5(4x + 9) and y = -1/20x - 4.

The slope of the first line is 4 * 5 = 20, and the slope of the second line is -1/20. Since the slopes are negative reciprocals of each other, the lines are perpendicular.

The answer is Perpendicular.

B) For the second set of lines: y = 9x + 9 and y = -9x + 9.

The slope of both lines is 9, which indicates that the lines are parallel.

The answer is Parallel.