To find the value of \( x \) that will cause the height \( h \) of the firework to be 0 (i.e., when the firework reaches the ground), we need to solve the equation:
\[ 0 = -\frac{25}{36}x^2 + \frac{1623}{36}x \]
This simplifies to:
\[ 0 = -25x^2 + 1623x \]
Factoring out \( x \):
\[ 0 = x(-25x + 1623) \]
This gives us two solutions:
- \( x = 0 \)
- \( -25x + 1623 = 0 \)
\[ -25x = -1623 \]
\[ x = \frac{1623}{25} \]
\[ x = 64.92 \] (approximately)
Now we check the values in the table:
- 12 feet
- 24 feet
- 36 feet
- 48 feet
None of these values match the calculated \( x \) value of approximately 64.92 feet.
Thus, none of the provided options leads to a solution where the height is zero based on the equation provided in the question. However, among the given options, you should still write down whether any of the values could be evaluated or what the statements would be if any were desired to be tested. But in this context, none of the responses would be correct, since \( 64.92 \) is not listed. You should confirm the context of the question about "solutions" as possibly needing further review or additional values.
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