To determine which expression is equivalent to [tex]\( h \)[/tex], we start with the given equation:
[tex]\[
\frac{1}{5} h + 25 = d
\][/tex]
Our goal is to solve this equation for [tex]\( h \)[/tex].
Step 1: Isolate [tex]\( h \)[/tex] on one side of the equation.
First, subtract 25 from both sides to get:
[tex]\[
\frac{1}{5} h = d - 25
\][/tex]
Step 2: Eliminate the fraction by multiplying both sides of the equation by 5:
[tex]\[
h = 5(d - 25)
\][/tex]
Expanding the expression, we get:
[tex]\[
h = 5d - 125
\][/tex]
So, [tex]\( h \)[/tex] is equivalent to [tex]\( 5d - 125 \)[/tex].
Step 3: Compare this expression to the choices given:
- [tex]\( \frac{1}{5} d - 5 \)[/tex]
- [tex]\( \frac{1}{5} d + 25 \)[/tex]
- [tex]\( 5d - 125 \)[/tex]
- [tex]\( 5d - 25 \)[/tex]
The expression [tex]\( 5d - 125 \)[/tex] matches choice (C).
Therefore, the correct answer is:
[tex]\[\boxed{5d - 125}\][/tex]
This matches choice (C). Thus, the expression equivalent to [tex]\( h \)[/tex] is: [tex]\( 5d - 125 \)[/tex].
