Question

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

−1
negative 1

2
2

−5
negative 5

−7

Answer 1

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

1. Substitute \( x = 13 \) into the equation:
\[
y = \sqrt{12(13) + 3} - 9
\]

2. Calculate \( 12(13) + 3 \):
\[
12(13) = 156
\]
\[
156 + 3 = 159
\]

3. Now, take the square root of \( 159 \) and then subtract \( 9 \):
\[
y = \sqrt{159} - 9
\]

4. Calculate \( \sqrt{159} \):
\[
\sqrt{159} \approx 12.enericity \text{ (exact value wouldn't be a clean integer)}
\]
Assuming a calculator gives the value approximately \( 12.61 \) (but you can keep it as \( \sqrt{159} \) for the exact calculation).

5. Now subtract \( 9 \):
\[
y \approx 12.61 - 9 \approx 3.61
\]

Since none of the options provided matches this value, let’s see if we simplify a bit differently:

Calculating generally, the function tends to yield \( y = \sqrt{159} - 9 \). If this value is around \( 3.61 \), then it doesn’t match any given options. Thus, y-value calculations may ideally use:

- \( \sqrt{159} \approx 12.61 \) giving \( y \approx 3.61 \) (confirmed).
- Yet options were \( -1, 2, -5, -7 \).

However, numbers provided suggest potential invalidation in setup/options or calculation not aligning.

Final approximation leads \( y \) clearly indicating an error in potential answers available to underlying expressions. Therefore:

The best answer based on calculation yields an approximate \( y \approx 3.61 \) which didn’t exist in given options.

Clarification would be possibly reexamining underlying function set to confirm spectrum against general outputs or expectation construct.