Modeling with Quadratic Equations Answers

The product of two positive numbers is 1,800. One number is twice the other number. The equation to determine the two numbers, with x representing the value of the lesser number, is x(2x) = 1,800.

Sergei buys a rectangular rug for his living room. He measures the diagonal of the rug to be 18 feet. The length of the rug is 3 feet longer than the width.

Aisha wants to make two quilts, each with the same area. The first quilt will be square with sides s feet long. The second quilt will be a rectangle with a width that is half the length of a side of the square quilt and a length that is 6 feet longer than a side length of the square quilt.

A rectangle’s width is one-fourth of its length. Its area is 9 square units. The equation l(l) = 9 can be used to find l, the length of the rectangle.

The product of two numbers is 240. The first number is 8 less than the second number. Which equation can be used to find x, the lesser number?

The product of two positive numbers is 750. The first number is 5 less than the second number. The equationx(x – 5) = 750 can be used to find x, the value of the greater number.

A rectangle’s length is 2 units more than twice its width. Its area is 40 square units. The equation w(2w + 2) = 40 can be used to find w, the width of the rectangle.

A rocket is launched into the air. The projectile motion of the rocket can be modeled using h(t) = 112t –16t2, where t is the time since launch in seconds and h(t) is the height of the rocket at time t.

The product of two consecutive positive integers is 812. What is the value of the lesser integer?

Kyla makes a triangular school pennant. The area of the triangle is 180 square inches. The base of the pennant is z inches long. The height is 6 inches longer than twice the base length.