To determine which of the given expressions is equivalent to \( \frac{1}{2}(9 - 7^0) + (-29)^0 \), we first need to simplify the original expression.
-
Calculate \( 7^0 \): \[ 7^0 = 1 \]
-
Substitute \( 7^0 \) in the expression: \[ \frac{1}{2}(9 - 1) + (-29)^0 \]
-
Calculate \( (-29)^0 \): \[ (-29)^0 = 1 \]
-
Now substitute this back in: \[ \frac{1}{2}(9 - 1) + 1 \]
-
Simplify \( 9 - 1 \): \[ 9 - 1 = 8 \]
-
Now, calculate \( \frac{1}{2}(8) + 1 \): \[ \frac{1}{2}(8) = 4 \] \[ 4 + 1 = 5 \]
So, the original expression simplifies to \( 5 \).
Now let's check each response to see which one also equals \( 5 \):
-
Response 1: \( \frac{1}{2}(9 - 1) + 1 \) \[ = \frac{1}{2}(8) + 1 = 4 + 1 = 5 \quad \text{(This is equivalent)} \]
-
Response 2: \( \frac{1}{2}(2) + 1 \) \[ = 1 + 1 = 2 \quad \text{(Not equivalent)} \]
-
Response 3: \( \frac{1}{2}(9 - 0) + 0 \) \[ = \frac{1}{2}(9) + 0 = 4.5 + 0 = 4.5 \quad \text{(Not equivalent)} \]
-
Response 4: \( \frac{1}{2}(9 - 1) - 1 \) \[ = \frac{1}{2}(8) - 1 = 4 - 1 = 3 \quad \text{(Not equivalent)} \]
Thus, the only equivalent expression is:
\[ \frac{1}{2}(9 - 1) + 1 \quad \text{(Response 1)} \]