Solving Real-World Quadratics: Apply & Analyze Solutions

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. How long will it take for the ball to hit the ground?

• 3.00 seconds

• 4.50 seconds

• 2.12 seconds

• 1.75 seconds

The path of a projectile can be modeled by the equation h(t) = -4.9t^2 + 20t + 1.5, where h is the height in meters and t is the time in seconds. When will the projectile reach its maximum height?

• 4.2 seconds

• 1.5 seconds

• 3.0 seconds

• 2.04 seconds

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

• 15

• 20

• 5

• 10

A car's height above the ground can be modeled by the equation h(t) = -5t^2 + 20t + 2, where t is the time in seconds. At what time will the car reach the ground?

• 4.1 seconds

• 5.0 seconds

• 2.8 seconds

• 3.5 seconds

The area of a triangular plot of land is 150 square meters. If the base is 5 meters longer than the height, find the dimensions of the plot using a quadratic equation.

• Height: 12 meters, Base: 17 meters

• Height: 15 meters, Base: 20 meters

• Height: 10 meters, Base: 15 meters

• Height: 20 meters, Base: 25 meters

A swimming pool is being filled with water. The volume V (in cubic meters) of water in the pool after t hours is given by V(t) = -2t^2 + 12t + 5. When will the pool be full if its capacity is 50 cubic meters?

• Approximately 15.75 hours

• Approximately 5.25 hours

• Approximately 10.35 hours

• Approximately 8.50 hours

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

• Width: 20 meters, Length: 30 meters

• Width: 30 meters, Length: 40 meters

• Width: 25 meters, Length: 35 meters

• Width: 15 meters, Length: 25 meters

A projectile is launched from the ground with an initial velocity of 30 meters per second. The height of the projectile can be modeled by the equation h(t) = -4.9t^2 + 30t. How long will it take for the projectile to reach a height of 45 meters?

• 2.50 seconds and 5.00 seconds

• 1.41 seconds and 6.36 seconds

• 3.00 seconds and 4.00 seconds

• 1.00 seconds and 7.00 seconds

A rectangular box has a volume of 1200 cubic centimeters. If the length is twice the width and the height is 5 centimeters less than the width, find the dimensions of the box.

• Width: 15 cm, Length: 30 cm, Height: 10 cm

• Width: 12 cm, Length: 24 cm, Height: 7 cm

• Width: 20 cm, Length: 40 cm, Height: 15 cm

• Width: 10 cm, Length: 20 cm, Height: 5 cm