Question

Given the square root function, y=1/2x+3−−−−√−9 , what is the y-value when x=13 ?(1 point) Responses −5 negative 5 2 2 −7 negative 7 −1

Answer 1

To find the y-value for the function \( y = \sqrt{\frac{1}{2}x + 3} - 9 \) when \( x = 13 \), we will substitute \( x = 13 \) into the equation and simplify.

1. Substitute \( x = 13 \):

\[
y = \sqrt{\frac{1}{2}(13) + 3} - 9
\]

2. Calculate \( \frac{1}{2}(13) \):

\[
\frac{1}{2}(13) = 6.5
\]

3. Add 3 to \( 6.5 \):

\[
6.5 + 3 = 9.5
\]

4. Now, take the square root of \( 9.5 \):

\[
\sqrt{9.5}
\]

5. Substitute back into the equation:

\[
y = \sqrt{9.5} - 9
\]

6. Since \( \sqrt{9.5} \) is approximately \( 3.08 \):

\[
y \approx 3.08 - 9
\]

7. Calculate the final value:

\[
y \approx 3.08 - 9 \approx -5.92
\]

Which is approximately \(-6\).

However, let's look at the choices given:

- −5
- 2
- −7
- −1

The closest value to \(-6\) is \(-5\), which is rounded up from about \(-5.92\).

Thus, the y-value when \( x = 13 \) is approximately **−5**.