which of the dollowing is an equivalent expression to 1/2(9 - 7^0) + (-29)^0

Question

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

Answer 1

Let's simplify the original expression step by step:

1. Evaluate \( 7^0 \): \[ 7^0 = 1 \]

2. Evaluate \( (-29)^0 \): \[ (-29)^0 = 1 \]

Now, plug these values back into the expression:

\[ \frac{1}{2}(9 - 1) + 1 \]

This simplifies to:

\[ \frac{1}{2}(8) + 1 = 4 + 1 = 5 \]

Now, let's analyze the answer choices:

A. \( \frac{1}{2}(9 - 0) + 0 \)

Simplifying: \[ \frac{1}{2}(9) + 0 = \frac{9}{2} + 0 = 4.5 \quad \text{(not equal to 5)} \]

B. \( \frac{1}{2}(9 - 1) + 1 \)

Simplifying: \[ \frac{1}{2}(8) + 1 = 4 + 1 = 5 \quad \text{(equal to 5)} \]

C. \( \frac{1}{2}(9 - 1) - 1 \)

Simplifying: \[ \frac{1}{2}(8) - 1 = 4 - 1 = 3 \quad \text{(not equal to 5)} \]

D. \( \frac{1}{2}(2) + 1 \)

Simplifying: \[ 1 + 1 = 2 \quad \text{(not equal to 5)} \]

Therefore, the equivalent expression to the original expression is B: \( \frac{1}{2}(9 - 1) + 1 \).