A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x)=−125x(x−45) , where h(x) is the height of the golf ball and x is the horizontal distance it has traveled. Solve the equation to determine how far the ball will have traveled when it hits the ground. How far will the ball need to roll to make it to the hole? 0=−125x(x−45) (1 point) Responses The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole. The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole. The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole. The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole. The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole. The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole. The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.

Question

A golfer hits a golf ball toward the hole 55 yards away. The ball follows a parabolic path given by the function h(x)=−125x(x−45) , where h(x) is the height of the golf ball and x is the horizontal distance it has traveled. Solve the equation to determine how far the ball will have traveled when it hits the ground. How far will the ball need to roll to make it to the hole? 0=−125x(x−45) (1 point) Responses The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole. The ball will hit the ground after it has traveled 10 yards. It will need to roll an additional 45 yards to reach the hole. The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole. The ball will hit the ground after it has traveled 25 yards. It will need to roll an additional 30 yards to reach the hole. The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole. The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole. The ball will hit the ground after it has traveled 30 yards. It will need to roll an additional 25 yards to reach the hole.

Answer 1

To determine how far the ball will have traveled when it hits the ground, we need to solve the equation 0=−125x(x−45).

We can solve this equation by setting each term equal to zero.

First, we set -125x equal to zero:
-125x = 0

Dividing both sides by -125, we find that x = 0.

Next, we set (x-45) equal to zero:
x-45 = 0

Adding 45 to both sides, we find that x = 45.

Therefore, the ball will hit the ground when it has traveled 45 yards.

To determine how far the ball will need to roll to make it to the hole, we need to subtract the distance the ball has traveled from the total distance to the hole.

Total distance to the hole = 55 yards.

Distance traveled by the ball when it hits the ground = 45 yards.

Therefore, the ball will need to roll an additional 55 - 45 = 10 yards to reach the hole.

The correct answer is:

The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.

Answer 2

To determine how far the ball will have traveled when it hits the ground, we need to solve the equation 0 = -125x(x-45).

First, let's set each factor to zero:

-125x = 0 or x - 45 = 0

Solving these equations separately, we find:

x = 0 or x = 45

Since the distance cannot be negative, we can disregard x = 0.

Therefore, the ball will hit the ground after it has traveled 45 yards.

To determine how far the ball will need to roll to make it to the hole, we can subtract the distance already traveled from the distance to the hole:

Distance remaining = 55 yards - 45 yards = 10 yards

Therefore, the ball will need to roll an additional 10 yards to reach the hole.

So, the correct answer is: The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.

Answer 3

To find out how far the golf ball will travel when it hits the ground, we need to solve the equation for h(x) = 0.

The equation given is h(x) = -125x(x - 45)

So, we set h(x) = 0 and solve for x:

0 = -125x(x - 45)

Expanding and rearranging the equation, we get:

-125x^2 + 5625x = 0

Factor out x from both terms:

x(-125x + 5625) = 0

This equation will be true if either x = 0 or -125x + 5625 = 0.

Solving -125x + 5625 = 0:

-125x = -5625

Dividing by -125:

x = 45

Now we have two solutions: x = 0 and x = 45. However, we are interested in the distance the ball travels before hitting the ground, so the answer is x = 45.

Therefore, the ball will hit the ground after it has traveled 45 yards.

To determine how far the ball needs to roll to make it to the hole, we need to subtract the distance the ball has traveled when it hits the ground from the distance to the hole, which is given as 55 yards.

So the ball needs to roll an additional 55 - 45 = 10 yards to reach the hole.

Therefore, the correct answer is: The ball will hit the ground after it has traveled 45 yards. It will need to roll an additional 10 yards to reach the hole.