Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
During a water balloon fight, Louisa uses a slingshot to fire a water balloon over the fortified wall of the opponent. When fir...Question
During a water balloon fight, Louisa uses a slingshot to fire a water balloon over the fortified wall of the opponent. When fired from the slingshot, the balloon will follow the path h(x)=−x^2+12x
, where h(x)
is the height of the balloon in feet, and x is the horizontal distance it will travel. To determine how far the balloon will travel before it reaches the ground, Louisa sets the height equal to zero and solves the quadratic equation 0=−x^2+12x
. How far will the balloon travel before it reaches the ground?(1 point)
The balloon will travel
feet before it reaches the ground.
Remaining Attempts : 3
Skip to navigation
page 15 of 16
, where h(x)
is the height of the balloon in feet, and x is the horizontal distance it will travel. To determine how far the balloon will travel before it reaches the ground, Louisa sets the height equal to zero and solves the quadratic equation 0=−x^2+12x
. How far will the balloon travel before it reaches the ground?(1 point)
The balloon will travel
feet before it reaches the ground.
Remaining Attempts : 3
Skip to navigation
page 15 of 16
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine how far the water balloon will travel before it reaches the ground, we need to solve the quadratic equation given by:
\[ 0 = -x^2 + 12x \]
We can rearrange this equation:
\[ -x^2 + 12x = 0 \]
Factoring out the common term \( x \):
\[ x(-x + 12) = 0 \]
This gives us two potential solutions:
1. \( x = 0 \)
2. \( -x + 12 = 0 \) which simplifies to \( x = 12 \)
The first solution, \( x = 0 \), represents the point where the balloon is released (initial position). The second solution, \( x = 12 \), represents the distance at which the balloon hits the ground.
Therefore, the balloon will travel **12 feet** before it reaches the ground.
\[ 0 = -x^2 + 12x \]
We can rearrange this equation:
\[ -x^2 + 12x = 0 \]
Factoring out the common term \( x \):
\[ x(-x + 12) = 0 \]
This gives us two potential solutions:
1. \( x = 0 \)
2. \( -x + 12 = 0 \) which simplifies to \( x = 12 \)
The first solution, \( x = 0 \), represents the point where the balloon is released (initial position). The second solution, \( x = 12 \), represents the distance at which the balloon hits the ground.
Therefore, the balloon will travel **12 feet** before it reaches the ground.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.