Question

simplify the expression using the order of operations.\\(\frac{(9 - 7) + (sqrt{16})}{17 - 4^2}\\)\\(\\) (1 point)\\(\\) \\(\circ\\) 6\\(\\) \\(\circ\\) \\(\frac{1}{6}\\)\\(\\) \\(\circ\\) \\(\frac{2}{17}\\)\\(\\) \\(\circ\\) 0

Explanation:

Step1: Simplify numerator and denominator separately.

First, handle the numerator: \( (9 - 7) + (\sqrt{16}) \). Calculate \( 9 - 7 = 2 \) and \( \sqrt{16} = 4 \). Then add them: \( 2 + 4 = 6 \).

Next, handle the denominator: \( 17 - 4^2 \). Calculate \( 4^2 = 16 \), then subtract: \( 17 - 16 = 1 \). Wait, no, wait. Wait, \( 4^2 = 16 \), so \( 17 - 16 = 1 \)? Wait, no, wait the original expression is \( \frac{(9 - 7) + (\sqrt{16})}{17 - 4^2} \). Wait, let's recalculate denominator: \( 4^2 = 16 \), so \( 17 - 16 = 1 \)? Wait, no, that can't be. Wait, no, wait the numerator is \( (9 - 7) + \sqrt{16} = 2 + 4 = 6 \). Denominator: \( 17 - 4^2 = 17 - 16 = 1 \)? Wait, but that would make the fraction \( \frac{6}{1} = 6 \), but that's one of the options. Wait, let's check again.

Wait, \( 9 - 7 = 2 \), \( \sqrt{16} = 4 \), so numerator: \( 2 + 4 = 6 \). Denominator: \( 17 - 4^2 = 17 - 16 = 1 \). So the fraction is \( \frac{6}{1} = 6 \)? But let's check the options. One of the options is 6. Wait, but let me confirm the order of operations. Parentheses first, then exponents, then multiplication/division, then addition/subtraction. So in numerator: (9-7)=2, sqrt(16)=4, so 2+4=6. Denominator: 4^2=16, then 17-16=1. So 6/1=6.

Step2: Wait, but let me check again. Wait, is the denominator 17 - 4 squared? 4 squared is 16, 17-16=1. So numerator is 6, denominator is 1, so 6/1=6. So the answer is 6.

Answer:

6