Let's solve the inequality [tex]\( x^2 > 100 \)[/tex] step-by-step to determine which values satisfy it. We are given four values to check: 12, -11, 9, and -9.
1. Given inequality:
[tex]\[
x^2 > 100
\][/tex]
2. Test each value individually:
- Value [tex]\( A: x = 12 \)[/tex]
[tex]\[
12^2 = 144
\][/tex]
[tex]\[
144 > 100 \quad \text{(True)}
\][/tex]
Therefore, 12 satisfies the inequality [tex]\( x^2 > 100 \)[/tex].
- Value [tex]\( B: x = -11 \)[/tex]
[tex]\[
(-11)^2 = 121
\][/tex]
[tex]\[
121 > 100 \quad \text{(True)}
\][/tex]
Therefore, -11 satisfies the inequality [tex]\( x^2 > 100 \)[/tex].
- Value [tex]\( C: x = 9 \)[/tex]
[tex]\[
9^2 = 81
\][/tex]
[tex]\[
81 > 100 \quad \text{(False)}
\][/tex]
Therefore, 9 does not satisfy the inequality [tex]\( x^2 > 100 \)[/tex].
- Value [tex]\( D: x = -9 \)[/tex]
[tex]\[
(-9)^2 = 81
\][/tex]
[tex]\[
81 > 100 \quad \text{(False)}
\][/tex]
Therefore, -9 does not satisfy the inequality [tex]\( x^2 > 100 \)[/tex].
3. Summary:
The values that satisfy the inequality [tex]\( x^2 > 100 \)[/tex] are:
[tex]\[
\text{A. 12 and B. -11}
\][/tex]
4. Final Answer:
- A. 12
- B. -11
