To determine how far the golf ball will travel before it hits the ground, we need to solve the equation:
\[ 0 = -125x(x - 45) \]
This equation can be factored as follows:
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Set the equation to zero: \[ -125x(x - 45) = 0 \]
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This gives us two solutions:
- \( x = 0 \) (when the ball is at the starting point)
- \( x = 45 \) (the other factor)
Thus, the ball will hit the ground after it has traveled 45 yards.
Next, we need to calculate how far the ball will need to roll to reach the hole, which is 55 yards away. The distance the ball will need to roll is:
\[ \text{Distance to the hole} - \text{Distance the ball travels} = 55 \text{ yards} - 45 \text{ yards} = 10 \text{ yards} \]
Therefore, the correct response 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.