Question

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

Answer 1

To simplify the expression \( 12(9−70)+(−29)0 \), let's analyze it step by step.

1. First, evaluate the term \( (−29)0 \):
\[
(−29)0 = 0
\]
So the expression simplifies to:
\[
12(9 - 70) + 0 = 12(9 - 70)
\]

2. Now evaluate \( 9 - 70 \):
\[
9 - 70 = -61
\]
Therefore, the expression becomes:
\[
12(-61) = -732
\]

Now we need to determine which of the provided responses simplifies to \(-732\):

1. **Response 1**: \( 12(9−1)+1 \)
\[
12(9 - 1) + 1 = 12(8) + 1 = 96 + 1 = 97 \quad (\text{not } -732)
\]

2. **Response 2**: \( \frac{1}{2}(9 - 1) + 1 \)
\[
\frac{1}{2}(9 - 1) + 1 = \frac{1}{2}(8) + 1 = 4 + 1 = 5 \quad (\text{not } -732)
\]

3. **Response 3**: \( 12(9−1)−1 \)
\[
12(9 - 1) - 1 = 12(8) - 1 = 96 - 1 = 95 \quad (\text{not } -732)
\]

4. **Response 4**: \( 12(9−0)+0 \)
\[
12(9 - 0) + 0 = 12(9) + 0 = 108 + 0 = 108 \quad (\text{not } -732)
\]

5. **Response 5**: \( 12(2)+1 \)
\[
12(2) + 1 = 24 + 1 = 25 \quad (\text{not } -732)
\]

After checking all the responses, none of them simplify to \(-732\) or provide an equivalent expression. It seems there might be a miscommunication with the options, as none are equivalent to the simplified expression from the initial computation. Please recheck the options provided.