Question

Use the table to answer the question.

This table is set up to evaluate a statement for different values of x by showing the substituted value, the evaluated result, and whether the statement is true.
x Substituted Evaluate True Statement?
12
24
36
48
When set off, a certain firework follows the path of the quadratic function h=−25/36 x^2+ 16 2/3x
, where:

h=
the height of the firework in feet.
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=-25/36 x^2+ 16 2/3x
.

(1 point)

12 feet

36 feet

48 feet

24 feet
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Answer 1

Convert 16 2/3 to an improper fraction: 16 2/3 = 50/3. The equation is

0 = −(25/36)x^2 + (50/3)x.

Multiply both sides by 36: 0 = −25x^2 + 600x = x(−25x + 600).

So x = 0 or x = 600/25 = 24. Therefore 24 feet.