Answer :
To find the value of the rational expression [tex]\(\frac{2x+1}{x^2}\)[/tex] when [tex]\(x=5\)[/tex], let's calculate it step-by-step.
1. Substitute [tex]\(x=5\)[/tex] into the expression.
[tex]\[
\text{Expression: } \frac{2 \cdot 5 + 1}{5^2}
\][/tex]
2. Calculate the numerator.
- Multiply 2 by 5, which gives [tex]\(10\)[/tex].
- Add 1 to [tex]\(10\)[/tex], resulting in [tex]\(11\)[/tex].
3. Calculate the denominator.
- Square 5, which gives [tex]\(25\)[/tex].
4. Divide the numerator by the denominator.
[tex]\[
\frac{11}{25} = 0.44
\][/tex]
The value of the rational expression [tex]\(\frac{2x+1}{x^2}\)[/tex] when [tex]\(x=5\)[/tex] is [tex]\(\frac{11}{25}\)[/tex], which is equivalent to [tex]\(0.44\)[/tex]. Among the given options, [tex]\(\frac{11}{25}\)[/tex] doesn't directly appear, but the decimal 0.44 confirms the value from our calculation.
1. Substitute [tex]\(x=5\)[/tex] into the expression.
[tex]\[
\text{Expression: } \frac{2 \cdot 5 + 1}{5^2}
\][/tex]
2. Calculate the numerator.
- Multiply 2 by 5, which gives [tex]\(10\)[/tex].
- Add 1 to [tex]\(10\)[/tex], resulting in [tex]\(11\)[/tex].
3. Calculate the denominator.
- Square 5, which gives [tex]\(25\)[/tex].
4. Divide the numerator by the denominator.
[tex]\[
\frac{11}{25} = 0.44
\][/tex]
The value of the rational expression [tex]\(\frac{2x+1}{x^2}\)[/tex] when [tex]\(x=5\)[/tex] is [tex]\(\frac{11}{25}\)[/tex], which is equivalent to [tex]\(0.44\)[/tex]. Among the given options, [tex]\(\frac{11}{25}\)[/tex] doesn't directly appear, but the decimal 0.44 confirms the value from our calculation.