To solve the problem [tex]\(\left(\frac{f}{g}\right)(5)\)[/tex] where [tex]\(f(x) = 7 + 4x\)[/tex] and [tex]\(g(x) = \frac{1}{2x}\)[/tex], let's work through the steps to find the solution.
1. Evaluate [tex]\(f(5)\)[/tex]:
- Start with the function [tex]\(f(x) = 7 + 4x\)[/tex].
- Substitute [tex]\(x = 5\)[/tex] into the function:
[tex]\[
f(5) = 7 + 4 \cdot 5
\][/tex]
- Calculate the result:
[tex]\[
f(5) = 7 + 20 = 27
\][/tex]
2. Evaluate [tex]\(g(5)\)[/tex]:
- Start with the function [tex]\(g(x) = \frac{1}{2x}\)[/tex].
- Substitute [tex]\(x = 5\)[/tex] into the function:
[tex]\[
g(5) = \frac{1}{2 \cdot 5}
\][/tex]
- Calculate the result:
[tex]\[
g(5) = \frac{1}{10} = 0.1
\][/tex]
3. Calculate [tex]\(\left(\frac{f}{g}\right)(5)\)[/tex]:
- We need to find [tex]\(\left(\frac{f}{g}\right)(5)\)[/tex], which means [tex]\(\frac{f(5)}{g(5)}\)[/tex].
- Use the previously calculated values:
[tex]\[
\left(\frac{f}{g}\right)(5) = \frac{f(5)}{g(5)} = \frac{27}{0.1}
\][/tex]
- Calculate 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 [tex]\(270\)[/tex]. Hence, the correct answer is [tex]\( \boxed{270} \)[/tex].
