Use the table to answer the question.

Question

x Substituted Evaluate True Statement?
12
24
36
48
When set off, a certain firework follows the path of the quadratic function h=−2536x2+1623x
ℎ
=
−
25
36
𝑥
2
+
16
2
3
𝑥
, where:

h=
ℎ
=
the height of the firework in feet.
x=
𝑥
=
the horizontal distance it travels in feet.
To determine how far the firework will travel before reaching the ground, determine which value of x in table is a solution to the equation 0=−2536x2+1623x
0
=
−
25
36
𝑥
2
+
16
2
3
𝑥
.

(1 point)
Responses

48 feet
48 feet

24 feet
24 feet

36 feet
36 feet

12 feet

Answer 1

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:

1. $x=0$
2. $-25x+1623=0$
   $$-25x=-1623$$
   $$x=\frac{1623}{25}$$
   $$x=64.92$$ (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.