Mastering Quadratics: Real-World Word Problems Unveiled

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. The height of the ball in meters after t seconds is given by the equation h(t) = -4.9t^2 + 10t + 1.5. How long will it take for the ball to hit the ground?

• 1.75 seconds

• 2.24 seconds

• 3.10 seconds

• 4.50 seconds

The path of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48, where h is the height in feet and t is the time in seconds. At what time will the projectile reach its maximum height?

• 0.5 seconds

• 2 seconds

• 1 second

• 3 seconds

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -5x^2 + 150x - 200. How many items should the company sell to maximize its profit?

• 25

• 20

• 15

• 10

The area of a triangular field is 120 square meters. If the base of the triangle is 4 meters longer than its height, find the dimensions of the triangle using a quadratic equation.

• Height: 15 meters, Base: 19 meters

• Height: 10 meters, Base: 14 meters

• Height: 12 meters, Base: 16 meters

• Height: 8 meters, Base: 12 meters

A car's value decreases according to the function V(t) = -2000t^2 + 12000t + 3000, where V is the value in dollars and t is the time in years. When will the car's value be $0?

• 12 years

• 10 years

• 8.5 years

• 5 years

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, what are the dimensions of the pool?

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 30 meters

• Width: 8 meters, Length: 16 meters

The height of a water fountain is modeled by the equation h(t) = -5t^2 + 20t + 10. How long will it take for the fountain to reach a height of 30 meters?

• 2 seconds

• 5 seconds

• 3 seconds

• 1 second

A farmer wants to create a rectangular pen for his sheep. He has 100 meters of fencing. If the length of the pen is 10 meters more than its width, what are the dimensions of the pen?

• Width: 15 meters, Length: 25 meters

• Width: 30 meters, Length: 40 meters

• Width: 20 meters, Length: 30 meters

• Width: 25 meters, Length: 35 meters

The revenue R (in dollars) from selling x units of a product is given by R(x) = -3x^2 + 60x. How many units should be sold to maximize revenue?

• 15

• 5

• 20

• 10