To simplify the expression \( 12(9−70)+(−29)0 \), let's analyze it step by step.
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First, evaluate the term \( (−29)0 \): \[ (−29)0 = 0 \] So the expression simplifies to: \[ 12(9 - 70) + 0 = 12(9 - 70) \]
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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 \(-732\):
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Response 1: \( 12(9−1)+1 \) \[ 12(9 - 1) + 1 = 12(8) + 1 = 96 + 1 = 97 \quad (\text{not } -732) \]
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Response 2: \( \frac{1}{2}(9 - 1) + 1 \) \[ \frac{1}{2}(9 - 1) + 1 = \frac{1}{2}(8) + 1 = 4 + 1 = 5 \quad (\text{not } -732) \]
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Response 3: \( 12(9−1)−1 \) \[ 12(9 - 1) - 1 = 12(8) - 1 = 96 - 1 = 95 \quad (\text{not } -732) \]
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Response 4: \( 12(9−0)+0 \) \[ 12(9 - 0) + 0 = 12(9) + 0 = 108 + 0 = 108 \quad (\text{not } -732) \]
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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.