To find the value of the expression [tex]\(\left|m^2 - 7\right| + n^2\)[/tex] when [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex], follow these steps:
1. Calculate [tex]\(m^2\)[/tex]:
[tex]\[
m = -2 \implies m^2 = (-2)^2 = 4
\][/tex]
2. Calculate [tex]\(|m^2 - 7|\)[/tex]:
[tex]\[
m^2 = 4 \implies m^2 - 7 = 4 - 7 = -3
\][/tex]
Taking the absolute value:
[tex]\[
|m^2 - 7| = |-3| = 3
\][/tex]
3. Calculate [tex]\(n^2\)[/tex]:
[tex]\[
n = 5 \implies n^2 = 5^2 = 25
\][/tex]
4. Add the results of the absolute value and [tex]\(n^2\)[/tex]:
[tex]\[
\left|m^2 - 7\right| + n^2 = 3 + 25 = 28
\][/tex]
Therefore, the value of the expression [tex]\(\left|m^2 - 7\right| + n^2\)[/tex] when [tex]\(m = -2\)[/tex] and [tex]\(n = 5\)[/tex] is [tex]\(28\)[/tex].
