Solving Quadratic Equations with Square Roots: Mastery Test

The formula for the volume of a right square pyramid is given below, where a is the side length of the base and h is the height: v = 1/3⁢a ^2⁢ℎ. Rewrite the formula by solving for a.

a = sqrt 3v/h

What are the solutions to this equation? 16x2 + 9 = 25

x = -1 and x = 1

Select the correct answer. What are the solutions to this equation? 7x2 − 28 = 0

A: x = -2 and x = 2

The product of two integers is 112. One number is four more than three times the other. Which of the following equations could be used to find one of the numbers?

A:3x2 + 4x = 112

Select the correct answer. The product of two integers is 72. One number is two less than five times the other. Which of the following equations could be used to find one of the numbers?

B:5x2 − 2x = 72

Select the correct answer. A pizza parlor uses square prisms for their pizza boxes. Due to the crust rising, the height of their boxes is always 2 inches. Additionally, the volume of the pizza box must be 450 cubic inches to fit their standard-sized pizza. A worker determined that the equation 2x2 = 450 could be used to find the side length, x, of the box needed to reach that volume. Determine which statement is true about the solutions to the equation.

B:The solutions are -15 and 15, but only 15 is a reasonable side length.

Select the correct answer. Solve the quadratic equation given below. (12⁢x − 27)^2 = 256

D. x = 43/12 ; 11/12

Select the correct answer from each drop-down menu. Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width. The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height. Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.

3 x^2 + 15 x = 252 Is it possible for the width of the tray to be 7.5 centimeters? No it's to small

Select the correct answer from the drop-down menu. Find the solution set. The solution set for 5v2 - 125 = 0 is

-5, 5

Select the correct answer from each drop-down menu. Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five less than half its width. Complete the equation that can be used to determine the dimensions of the monitor in terms of its width, w.

384 = 3 w^2 - 30 w

Select the correct answer from each drop-down menu. Gabriel is designing equally sized horse stalls that are each in the shape of a rectangular prism. Each stall must be 9 feet high and have a volume of 1,080 cubic feet. The length of each stall should be 2 feet longer than its width. The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height. Complete the equation that represents the volume of a stall in terms of its width of x feet.

9 x^2 + 18 x = 1,080 Is it possible for the width of a stall to be 10 feet? yes

Select the correct answer. The height of a triangle is 2 less than 5 times its base. If the base of the triangle is x feet, and the area of the triangle is 12 square feet, which equation models this situation?

C:5x2 − 2x − 24 = 0

Select the correct answer. The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, which equation models this situation?

C:6x2 + x − 26 = 0