To solve for [tex]\(\left(\frac{f}{g}\right)(5)\)[/tex] given the functions [tex]\(f(x) = 7 + 4x\)[/tex] and [tex]\(g(x) = \frac{1}{2x}\)[/tex], we need to follow these steps:
1. Evaluate [tex]\(f(5)\)[/tex]:
[tex]\[
f(x) = 7 + 4x
\][/tex]
Substitute [tex]\(x = 5\)[/tex]:
[tex]\[
f(5) = 7 + 4 \cdot 5 = 7 + 20 = 27
\][/tex]
2. Evaluate [tex]\(g(5)\)[/tex]:
[tex]\[
g(x) = \frac{1}{2x}
\][/tex]
Substitute [tex]\(x = 5\)[/tex]:
[tex]\[
g(5) = \frac{1}{2 \cdot 5} = \frac{1}{10} = 0.1
\][/tex]
3. Compute [tex]\(\left(\frac{f}{g}\right)(5)\)[/tex]:
[tex]\[
\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)}
\][/tex]
Substitute [tex]\(x = 5\)[/tex]:
[tex]\[
\left(\frac{f}{g}\right)(5) = \frac{f(5)}{g(5)} = \frac{27}{0.1}
\][/tex]
To perform the division:
[tex]\[
\frac{27}{0.1} = 27 \times 10 = 270
\][/tex]
So, the value of [tex]\(\left(\frac{f}{g}\right)(5)\)[/tex] is 270.
Among the given options, the correct answer is:
[tex]\[
\boxed{270}
\][/tex]
