Question

Given the square root function, y=12x+3−−−−√−9 , what is the y-value when x=13 ?(1 point)
Responses

2
2

−1
negative 1

−5
negative 5

−7
negative 7

Answer 1

To find the y-value when \( x = 13 \) in the function \( y = \sqrt{12x + 3} - 9 \), we follow these steps:

1. Substitute \( x = 13 \) into the function:

\[
y = \sqrt{12(13) + 3} - 9
\]

2. Calculate \( 12(13) \):

\[
12(13) = 156
\]

3. Add 3:

\[
156 + 3 = 159
\]

4. Take the square root of 159:

\[
\sqrt{159}
\]

5. Subtract 9:

\[
y = \sqrt{159} - 9
\]

Now, we can calculate the approximated value of \( \sqrt{159} \). The square root of 159 is approximately 12.57.

6. Calculate \( 12.57 - 9 \):

\[
12.57 - 9 \approx 3.57
\]

The approximate y-value when \( x = 13 \) is \( 3.57 \), which does not match any of the given choices.

Looking at the options provided:

- 2
- -1
- -5
- -7

None of these correspond to the calculated result. Therefore, it seems there may either be a misinterpretation in the function or an error in the options. If strictly considering the options, none of them fit the y-value derived from the function given.