Question

Question
Which of the following is an equivalent expression to 1?2(9−7^0)+(−29)^0
? (1 point)
Responses

1?2(9−0)+0

1/2(9−1)−1

1/2(9−1)+1

1/2(2)+1

Answer 1

Let's simplify the expression \(1?2(9−7^0)+(−29)^0\) step by step.

1. First, calculate \(7^0\) and \((-29)^0\):
- Any non-zero number raised to the power of 0 is 1, so \(7^0 = 1\) and \((-29)^0 = 1\).

2. Substitute these values back into the expression:
\[
1?2(9 - 1) + 1
\]

3. Now simplify \(9 - 1\):
\[
9 - 1 = 8
\]

4. Substitute this value back into the expression:
\[
1?2 \cdot 8 + 1
\]
- Here, the notation "?" is unclear and might be a typo. Assuming it means multiplication, we interpret it as:
\[
1 \cdot 2 \cdot 8 + 1
\]
Simplifying further,
\[
16 + 1 = 17
\]

Since \(1?2(9−7^0)+(−29)^0 = 17\), we need to check which of the responses is equivalent to 1.

Let's evaluate each option:

1. **1?2(9−0)+0**: Assuming "?" means multiplication, this simplifies to:
\[
1 \cdot 2(9 - 0) + 0 = 2 \cdot 9 + 0 = 18 \quad (\text{not 1})
\]

2. **1/2(9−1)−1**:
\[
\frac{1}{2}(8) - 1 = 4 - 1 = 3 \quad (\text{not 1})
\]

3. **1/2(9−1)+1**:
\[
\frac{1}{2}(8) + 1 = 4 + 1 = 5 \quad (\text{not 1})
\]

4. **1/2(2)+1**:
\[
\frac{1}{2}(2) + 1 = 1 + 1 = 2 \quad (\text{not 1})
\]

None of the options provided seem to simplify to 1.

If there was any misunderstanding in the interpretation of "?", you may need to clarify or correct, as the expression itself does not evaluate to 1, and neither do the options listed. The expression as initially interpreted simplifies to 17.