Question

Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point) Responses 12(2)+1 Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1 12(9−1)+1 Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1 12(9−1)−1 Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1 12(9−0)+0

Answer 1

To simplify the expression \( 12(9−70)+(−29)0 \):

1. Calculate \( (−29)0 \): \[ (−29)0 = 0 \]

2. Now, the expression simplifies to: \[ 12(9−70) + 0 = 12(9−70) \]

3. Next, simplify \( 9-70 \): \[ 9 - 70 = -61 \]

4. Substitute back: \[ 12(9−70) = 12(-61) = -732 \]

Now, let's check which of the options is equivalent to \(-732\):

1. Option 1: \( 12(2)+1 = 24 + 1 = 25 \)
2. Option 2: \( \frac{1}{2}(2) + 1 = 1 + 1 = 2 \)
3. Option 3: \( 12(9−1) + \frac{1}{2}(9-1) + 1 \):
   • Calculate \( 9 - 1 = 8 \)
   • So, \( 12(8) + \frac{1}{2}(8) + 1 = 96 + 4 + 1 = 101 \)
4. Option 4: \( 12(9−0)+0 = 12(9) + 0 = 108 + 0 = 108 \)

None of the answers provided produce the value of \(-732\). If you're certain that these are the only options provided, then there might have been a misunderstanding in the question or provided options, as none of them are equivalent to the original expression.

Please double-check the original expression or the options provided.