Modeling with Quadratic Equations Answers

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.

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.

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

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 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.

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.

A computer company makes a rectangular screen with a diagonal of 20 inches. The width of the screen is 4 inches less than its length.

The product of two numbers is 450. The first number is half the second number. Which equation can be used to find x, the greater number?

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.

The projectile motion of an object can be modeled usings(t) = gt2 + v0t + s0, where g is the acceleration due to gravity, t is the time in seconds since launch, s(t) is the height after t seconds, v0 is the initial velocity, and s0 is the initial height. The acceleration due to gravity is –4.9 m/s2.

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.

The product of two consecutive integers is 342. Which quadratic equation can be used to find x, the greater number?

An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled using h(t)=144-16t2.How many seconds will it take the object to reach the ground?

The product of two numbers is 713. The first number is 9 more than the second number. Which equation can be used to find x, the greater number?

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.

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?