Mastering Quadratic Equations in Real-World Scenarios

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: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 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

• 3.10 seconds

• 4.50 seconds

• 2.24 seconds

The path of a projectile can be modeled by the equation h(t) = -5t^2 + 20t + 15, where h is the height in meters and t is the time in seconds. What is the maximum height reached by the projectile?

• 30 meters

• 25 meters

• 40 meters

• 35 meters

A company finds that the profit P (in dollars) from selling x items can be modeled by the equation P(x) = -2x^2 + 40x - 100. How many items should the company sell to maximize its profit?

• 5

• 15

• 10

• 20

A car's distance from a starting point can be modeled by the equation d(t) = 2t^2 + 3t, where d is in meters and t is in seconds. What is the distance traveled by the car after 5 seconds?

• 100 meters

• 80 meters

• 50 meters

• 65 meters

The area A of a triangle can be expressed as A = 1/2 * base * height. If the height is 2 meters more than the base, and the area is 30 square meters, what are the dimensions of the triangle?

• Base: 4 meters, Height: 6 meters

• Base: 5 meters, Height: 7 meters

• Base: 10 meters, Height: 12 meters

• Base: 6 meters, Height: 8 meters

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 longer than the width, what are the dimensions of the pen?

• Width: 20 meters, Length: 30 meters

• Width: 30 meters, Length: 40 meters

• Width: 15 meters, Length: 25 meters

• Width: 25 meters, Length: 35 meters

The height of a water fountain can be modeled by the equation h(t) = -3t^2 + 12t, where h is the height in meters and t is the time in seconds. At what time will the fountain reach its maximum height?

• 4 seconds

• 1 second

• 3 seconds

• 2 seconds

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: 8 meters, Length: 16 meters

• Width: 15 meters, Length: 30 meters

A toy rocket is launched from the ground with an initial velocity of 30 meters per second. The height of the rocket in meters after t seconds is given by the equation h(t) = -4.9t^2 + 30t. How long will it take for the rocket to reach its maximum height?

• 5.0 seconds

• 3.06 seconds

• 2.5 seconds

• 4.2 seconds