Which of the following is an equivalent expression to 12(9−70)+(−29)0

Question

? (1 point)
Responses

12(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0

12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1

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
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Answer 1

To find which expression is equivalent to \( 12(9 - 70) + (-29)(0) \), let's first simplify the original expression step by step.

1. Calculate \( (-29)(0) \): Any number multiplied by zero is zero, so: \[ (-29)(0) = 0. \]

2. Now simplify \( 12(9 - 70) \): \[ 9 - 70 = -61, \] so: \[ 12(9 - 70) = 12(-61) = -732. \]

3. Combine the results: \[ 12(9 - 70) + 0 = -732 + 0 = -732. \]

Now, let's evaluate the options provided to find any that are equivalent to \( -732 \).

1. Option 1: \( 12(9 - 0) + 0 \) \[ 12(9) + 0 = 108 + 0 = 108. \]

2. Option 2: \( \frac{1}{2}(9 - 0) + 0 \) \[ \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5. \]

3. Option 3: \( 12(9 - 1) - 1 \) \[ 12(8) - 1 = 96 - 1 = 95. \]

4. Option 4: \( \frac{1}{2}(9 - 1) + 1 \) \[ \frac{1}{2}(8) + 1 = 4 + 1 = 5. \]

5. Option 5: \( 12(2) + 1 \) \[ 12(2) + 1 = 24 + 1 = 25. \]

6. Option 6: \( 12(9 - 1) + 1 \) \[ 12(8) + 1 = 96 + 1 = 97. \]

None of the evaluated options are equivalent to \( -732 \).

Conclusion:

The expression \( 12(9 - 70) + (-29)(0) \) simplifies to \( -732 \), which does not match any provided options. Thus, none of the responses are correct.