Question

The function p(x)=−2(x−9)2+100 is used to determine the profit on t-shirts sold for x dollars. What would the profit from sales be if the price of the t-shirts were $15 each?(1 point)Responses$15$15$28$28$172$172$244

Answer 1

To determine the profit from sales if the price of the t-shirts is $15 each using the function \( p(x) = -2(x - 9)^2 + 100 \), we need to substitute \( x = 15 \) into the function.

1. Substitute \( x = 15 \) into the function:

\[
p(15) = -2(15 - 9)^2 + 100
\]

2. Calculate \( 15 - 9 \):

\[
15 - 9 = 6
\]

3. Now calculate \( (6)^2 \):

\[
6^2 = 36
\]

4. Substitute \( 36 \) back into the equation:

\[
p(15) = -2(36) + 100
\]

5. Calculate \( -2(36) \):

\[
-2(36) = -72
\]

6. Now add \( 100 \):

\[
p(15) = -72 + 100 = 28
\]

Thus, the profit from sales when the t-shirts are priced at $15 each is \( \boxed{28} \).