Let's solve the given expression step-by-step:
Given the expression:
[tex]\[
\left|m^2 - 7\right| + n^2
\][/tex]
and the values [tex]\( m = -2 \)[/tex] and [tex]\( n = 5 \)[/tex].
1. Calculate [tex]\( m^2 \)[/tex]:
[tex]\[
m^2 = (-2)^2 = 4
\][/tex]
2. Subtract 7 from [tex]\( m^2 \)[/tex]:
[tex]\[
m^2 - 7 = 4 - 7 = -3
\][/tex]
3. Take the absolute value:
[tex]\[
\left| -3 \right| = 3
\][/tex]
4. Calculate [tex]\( n^2 \)[/tex]:
[tex]\[
n^2 = 5^2 = 25
\][/tex]
5. Add the absolute value to [tex]\( n^2 \)[/tex]:
[tex]\[
3 + 25 = 28
\][/tex]
Thus, the value of the expression when [tex]\( m = -2 \)[/tex] and [tex]\( n = 5 \)[/tex] is [tex]\( 28 \)[/tex].
