Let's start by simplifying the original expression \( 12(9 - 70) + (-29)0 \).
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Calculate \( 9 - 70 \): \[ 9 - 70 = -61 \]
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Multiply that by 12: \[ 12 \times (-61) = -732 \]
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Calculate \( (-29)0 \): \[ (-29) \times 0 = 0 \]
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Add the two results: \[ -732 + 0 = -732 \]
Now, we need to determine which of the provided expressions also equals \(-732\):
A) \( 12(9 - 1) - 1 \):
- Simplify \( 9 - 1 = 8 \)
- Then, \( 12 \times 8 = 96 \)
- Finally, \( 96 - 1 = 95\)
B) \( \frac{1}{2}(9 - 1) - 1 \):
- Simplify \( 9 - 1 = 8 \)
- Then, \( \frac{1}{2} \times 8 = 4 \)
- Finally, \( 4 - 1 = 3 \)
C) \( 12(9 - 1) + 1 \):
- As calculated before, \( 12 \times 8 = 96 \)
- Finally, \( 96 + 1 = 97\)
D) \( 12(9 - 0) + 0 \):
- Simplify \( 9 - 0 = 9 \)
- Thus, \( 12 \times 9 = 108 \)
- Finally, \( 108 + 0 = 108\)
E) \( 12(2) + 1 \):
- \( 12 \times 2 = 24 \)
- Finally, \( 24 + 1 = 25 \)
None of these expressions equal \(-732\). Thus, the answer appears to not be present in the provided options. If the goal was to identify one of these as the equivalent expression, it seems there may have been an oversight in listing the options.