Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point)

A. 1/2 (9-1) - 1
B. 1/2 (9-0) + 0
C. 1/2 (9-1) +1
D. 1/2 (2) + 1

1 answer

Let's simplify the given expression \( 12(9 - 70) + (-29)0 \).

First, simplify \( (-29)0 \): \[ (-29)0 = 0 \]

Now, the expression becomes: \[ 12(9 - 70) + 0 \] We only need to calculate \( 12(9 - 70) \).

Calculating \( 9 - 70 \): \[ 9 - 70 = -61 \]

Now, multiply by 12: \[ 12 \times -61 = -732 \]

So, the entire expression simplifies to: \[ -732 + 0 = -732 \]

Now, we'll evaluate each of the provided options to see which one is equivalent to \(-732\).

Option A: \[ \frac{1}{2}(9 - 1) - 1 = \frac{1}{2}(8) - 1 = 4 - 1 = 3 \]

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

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

Option D: \[ \frac{1}{2}(2) + 1 = 1 + 1 = 2 \]

None of the options evaluate to \(-732\). Therefore, it appears that there may have been a misunderstanding or error in the options provided since all of them yield much smaller positive values. Please double-check the options or provide more context for further assistance!