Sure! To evaluate the expression [tex]\(10m + \frac{n^2}{4}\)[/tex] when [tex]\(m = 5\)[/tex] and [tex]\(n = 4\)[/tex], follow these steps:
1. Substitute the values of [tex]\(m\)[/tex] and [tex]\(n\)[/tex] into the expression:
[tex]\[
10m + \frac{n^2}{4}
\][/tex]
becomes
[tex]\[
10 \cdot 5 + \frac{4^2}{4}
\][/tex]
2. Calculate [tex]\(10 \cdot 5\)[/tex]:
[tex]\[
10 \cdot 5 = 50
\][/tex]
3. Calculate [tex]\(n^2\)[/tex], which is [tex]\(4^2\)[/tex] in our case:
[tex]\[
4^2 = 16
\][/tex]
4. Divide [tex]\(16\)[/tex] by [tex]\(4\)[/tex]:
[tex]\[
\frac{16}{4} = 4
\][/tex]
5. Add the results from step 2 and step 4 together:
[tex]\[
50 + 4 = 54
\][/tex]
So, the value of the expression [tex]\(10m + \frac{n^2}{4}\)[/tex] when [tex]\(m = 5\)[/tex] and [tex]\(n = 4\)[/tex] is [tex]\(54.0\)[/tex].
