Question

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.

Answer 1

It looks like you're trying to solve a quadratic equation of the form \( y = -\frac{25}{36}x^2 + \frac{50}{3}x \). To determine how far the firework will travel, you would typically set the equation equal to zero and solve for \( x \):

\[
-\frac{25}{36}x^2 + \frac{50}{3}x = 0
\]

Now we can factor out \( x \):

\[
x\left(-\frac{25}{36}x + \frac{50}{3}\right) = 0
\]

This gives us one solution:

\[
x = 0
\]

Now, let's solve the remaining equation:

\[
-\frac{25}{36}x + \frac{50}{3} = 0
\]

To isolate \( x \), we first move the term involving \( x \):

\[
-\frac{25}{36}x = -\frac{50}{3}
\]

Now, multiply both sides by \(-1\):

\[
\frac{25}{36}x = \frac{50}{3}
\]

To eliminate the fraction, multiply both sides by \( \frac{36}{25} \):

\[
x = \frac{50}{3} \cdot \frac{36}{25}
\]

Now perform the multiplication:

\[
x = \frac{50 \times 36}{3 \times 25} = \frac{1800}{75} = 24
\]

Thus, the solutions to the equation are \( x = 0 \) and \( x = 24 \). The firework will reach the ground at \( x = 24 \). So, from the values in your table, if \( 24 \) is provided, it is a solution to this equation.