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What is the value of this expression when [tex]$x = -6$[/tex] and [tex]$y = -\frac{1}{2}$[/tex]?

[tex]4(x^2 + 3) - 2y[/tex]

A. -131
B. -35
C. [tex]\quad 57 \frac{1}{2}[/tex]
D. 157


Sagot :

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