To find the y-value when \( x = 13 \) for the function \( y = \sqrt{12x + 3} - 9 \), we first substitute \( x = 13 \) into the equation:
\[ y = \sqrt{12(13) + 3} - 9 \]
Calculating inside the square root:
\[ 12(13) = 156 \]
Now, adding 3:
\[ 156 + 3 = 159 \]
Now taking the square root:
\[ \sqrt{159} \]
Finally, subtracting 9:
\[ y = \sqrt{159} - 9 \]
Now let's approximate \( \sqrt{159} \): Since \( 12^2 = 144 \) and \( 13^2 = 169 \), we know that \( \sqrt{159} \) is between 12 and 13.
Approximating further, we'll use 12.5 for simplicity, which gives us:
\[ y \approx 12.5 - 9 = 3.5 \]
None of the options provided exactly match this approximate outcome. However, if we consider the choices:
- \(-1\)
- \(2\)
- \(-5\)
- \(-7\)
None of these seem to be an accurate answer based on our approximation. Just to confirm the calculation:
- We established: \[ y = \sqrt{159} - 9 \] and since \( \sqrt{159} \) is between 12 and 13, \( \sqrt{159} - 9 \) indeed falls somewhere between \( 3 \) and \( 4 \).
But approximating \( \sqrt{159} \) as \( 12.6 \) (not exact):
- So \( \sqrt{159} \approx 12.6 \)
- \( y \approx 12.6 - 9 \approx 3.6 \)
Final conclusion:
The most likely case is that none of the options provided is correct; however, if you must choose the closest option, you should choose those that fall nearest to \( 0.6 \), which still leads us nowhere in current options.
Given the function and calculations, it's best to say that the options provided do not include a correct answer based on the specified function and x-value.
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