10.4 Solve Applications Modeled by Quadratic Equations

Before you get started, take this readiness quiz.

The sum of two consecutive odd numbers is $−100$. Find the numbers.
If you missed this problem, review the reference.

The area of triangular mural is 64 square feet. The base is 16 feet. Find the height.
If you missed this problem, review the reference.

Find the length of the hypotenuse of a right triangle with legs 5 inches and 12 inches.
If you missed this problem, review the reference.

The product of two consecutive odd integers is 99. Find the integers.

The product of two consecutive even integers is 168. Find the integers.

Find the dimensions of a triangle whose width is four more than six times its height and has an area of 208 square inches.

If a triangle that has an area of 110 square feet has a height that is two feet less than twice the width, what are its dimensions?

The sun casts a shadow from a flag pole. The height of the flag pole is three times the length of its shadow. The distance between the end of the shadow and the top of the flag pole is 20 feet. Find the length of the shadow and the length of the flag pole. Round to the nearest tenth of a foot.

The distance between opposite corners of a rectangular field is four more than the width of the field. The length of the field is twice its width. Find the distance between the opposite corners. Round to the nearest tenth.

The length of a 200 square foot rectangular vegetable garden is four feet less than twice the width. Find the length and width of the garden. Round to the nearest tenth of a foot.

A rectangular tablecloth has an area of 80 square feet. The width is 5 feet shorter than the length. What are the length and width of the tablecloth? Round to the nearest tenth of a foot.

An arrow is shot from the ground into the air at an initial speed of 108 ft/sec. Use the formula $h = −16 t^{2} + v_{0} t$ to determine when the arrow will be 180 feet from the ground. Round the nearest tenth of a second.

A man throws a ball into the air with a velocity of 96 ft/sec. Use the formula $h = −16 t^{2} + v_{0} t$ to determine when the height of the ball will be 48 feet. Round to the nearest tenth of a second.

Solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The product of two consecutive odd numbers is 255. Find the numbers.

Solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The product of two consecutive even numbers is 624. Find the numbers.

Solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The product of two consecutive odd numbers is 483. Find the numbers.

Solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

A triangle with area 45 square inches has a height that is two less than four times the width. Find the height and width of the triangle.

Solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is three feet. Find the lengths of the three sides of the triangle. Round to the nearest tenth.

Solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

The length of a rectangular driveway is five feet more than three times the width. The area is 350 square feet. Find the length and width of the driveway.

Solve by using methods of factoring, the square root principle, or the Quadratic Formula. Round your answers to the nearest tenth.

A firework rocket is shot upward at a rate of 640 ft/sec. Use the projectile formula $h = −16 t^{2} + v_{0} t$ to determine when the height of the firework rocket will be 1200 feet.

A bullet is fired straight up from a BB gun with initial velocity 1120 feet per second at an initial height of 8 feet. Use the formula $h = −16 t^{2} + v_{0} t + 8$ to determine how many seconds it will take for the bullet to hit the ground. (That is, when will $h = 0$ ?)

Make up a problem involving the product of two consecutive odd integers. Start by choosing two consecutive odd integers. ⓐ What are your integers? ⓑ What is the product of your integers? ⓒ Solve the equation $n \left(n + 2\right) = p$, where $p$ is the product you found in part (b). ⓓ Did you get the numbers you started with?