To solve the expression [tex]\( f(x) = 2x^2 + 5 \sqrt{x+2} \)[/tex] at [tex]\( x = 0 \)[/tex] and round the answer to the nearest hundredth, follow these steps:
1. Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(0) = 2(0)^2 + 5\sqrt{0 + 2}
\][/tex]
2. Simplify the terms inside the function:
[tex]\[
0^2 = 0
\][/tex]
[tex]\[
\sqrt{0 + 2} = \sqrt{2}
\][/tex]
3. Calculate the values:
[tex]\[
2(0)^2 = 2 \cdot 0 = 0
\][/tex]
[tex]\[
5 \cdot \sqrt{2} \approx 5 \cdot 1.414 = 7.07
\][/tex]
4. Add the simplified terms together:
[tex]\[
f(0) = 0 + 7.07 = 7.07
\][/tex]
5. Present the final answer, rounded to the nearest hundredth:
[tex]\[
7.07
\][/tex]
Therefore, the complete statement would be:
(A0) - [tex]\( \boxed{7.07} \)[/tex]
