Question

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

Answer 1

To determine an equivalent expression to the given expression \(12(9 - 70) + (-29)0\), we can simplify it step by step.

1. First, recognize that anything multiplied by \(0\) is \(0\):
\[
(-29)0 = 0
\]
Thus, the expression simplifies to:
\[
12(9 - 70) + 0
\]

2. Now, we can further simplify \(12(9 - 70)\):
\[
9 - 70 = -61
\]
Therefore:
\[
12(-61) + 0 = -732 + 0 = -732
\]

Now, we will examine each response option:

1. **12(9−0)+0**:
- This evaluates to \(12(9) + 0 = 108 + 0 = 108\), which is not equivalent to \(-732\).

2. **Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0**:
- This evaluates to \(\frac{1}{2}(9) + 0 = \frac{9}{2} + 0 = 4.5\), which is not equivalent to \(-732\).

3. **12(9−1)−1**:
- This evaluates to \(12(8) - 1 = 96 - 1 = 95\), which is not equivalent to \(-732\).

4. **Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1**:
- This evaluates to \(\frac{1}{2}(8) - 1 = 4 - 1 = 3\), which is not equivalent to \(-732\).

5. **12(2)+1**:
- This evaluates to \(12(2) + 1 = 24 + 1 = 25\), which is not equivalent to \(-732\).

6. **12(9−1)+1**:
- This evaluates to \(12(8) + 1 = 96 + 1 = 97\), which is not equivalent to \(-732\).

None of the response options provided are equivalent to the expression \(12(9 - 70) + (-29)0\), which simplifies to \(-732\). Thus, none are correct.