To determine the value of the expression [tex]\(4\left(x^2 + 3\right) - 2y\)[/tex] when [tex]\(x = -6\)[/tex] and [tex]\(y = -\frac{1}{2}\)[/tex], we follow these detailed steps:
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
- Given [tex]\(x = -6\)[/tex]
- Given [tex]\(y = -\frac{1}{2}\)[/tex]
2. Calculate [tex]\(x^2\)[/tex]:
[tex]\[
x^2 = (-6)^2 = 36
\][/tex]
3. Add 3 to [tex]\(x^2\)[/tex]:
[tex]\[
x^2 + 3 = 36 + 3 = 39
\][/tex]
4. Multiply the result by 4:
[tex]\[
4(x^2 + 3) = 4 \times 39 = 156
\][/tex]
5. Multiply [tex]\(y\)[/tex] by -2:
[tex]\[
-2y = -2 \times \left(-\frac{1}{2}\right) = 1
\][/tex]
6. Combine the results from steps 4 and 5:
[tex]\[
4(x^2 + 3) - 2y = 156 + 1 = 157
\][/tex]
Thus, the value of the expression when [tex]\(x = -6\)[/tex] and [tex]\(y = -\frac{1}{2}\)[/tex] is [tex]\(157\)[/tex].
The correct answer is:
D. 157
