To solve the expression [tex]\(\frac{x^2 - 4y}{2}\)[/tex] given [tex]\(x = 4\)[/tex] and [tex]\(y = -3\)[/tex], follow these steps:
1. Substitute the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the expression:
[tex]\[
\frac{4^2 - 4(-3)}{2}
\][/tex]
2. Calculate [tex]\(x^2\)[/tex]:
[tex]\[
4^2 = 16
\][/tex]
3. Multiply [tex]\(-4\)[/tex] by [tex]\(y\)[/tex]:
[tex]\[
-4 \times (-3) = 12
\][/tex]
4. Add the results from steps 2 and 3 to get the numerator:
[tex]\[
16 + 12 = 28
\][/tex]
5. Divide the numerator by 2:
[tex]\[
\frac{28}{2} = 14
\][/tex]
So, the numerator of the expression [tex]\(x^2 - 4y\)[/tex] is [tex]\(28\)[/tex] and the final result of the entire expression [tex]\(\frac{x^2 - 4y}{2}\)[/tex] is [tex]\(14\)[/tex].
Thus, the detailed steps lead us to the answers:
- The numerator: [tex]\(28\)[/tex]
- The result of the expression: [tex]\(14\)[/tex]
