Sure! Let's evaluate the expression [tex]\(\frac{4c + a^2}{c}\)[/tex] with the given values [tex]\(a = 4\)[/tex] and [tex]\(c = 2\)[/tex].
1. Substitute the given values into the expression:
[tex]\[
\frac{4 \cdot 2 + 4^2}{2}
\][/tex]
2. Calculate the exponent and multiplication:
- First, [tex]\(4^2 = 16\)[/tex].
- Second, [tex]\(4 \cdot 2 = 8\)[/tex].
So the expression now looks like this:
[tex]\[
\frac{8 + 16}{2}
\][/tex]
3. Add the numbers in the numerator:
[tex]\[
8 + 16 = 24
\][/tex]
Now, the expression is:
[tex]\[
\frac{24}{2}
\][/tex]
4. Divide the numerator by the denominator:
[tex]\[
\frac{24}{2} = 12
\][/tex]
So, the value of the expression when [tex]\(a = 4\)[/tex] and [tex]\(c = 2\)[/tex] is [tex]\(\boxed{12}\)[/tex].
