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

Question

Responses:

1 over 2(2) + 1

1 over 2(9 − 1) − 1

1 over 2(9 − 0) + 0

1 over 2(9 − 1) + 1

Answer 1

Let's simplify the expression $\frac{1}{2}(9-7^0)+(-29{)}^0$ step by step.

1. Calculate $7^0$: $$7^0=1$$

2. Next, calculate $(-29{)}^0$: $$(-29{)}^0=1$$

3. Now substitute these values back into the expression: $$\frac{1}{2}(9-1)+1$$

4. Simplify inside the parentheses: $$9-1=8$$

5. Now, plug it back in: $$\frac{1}{2}\times 8+1$$

6. Calculate $\frac{1}{2}\times 8$: $$\frac{1}{2}\times 8=4$$

7. Finally, add: $$4+1=5$$

Now, let's compare it to the choices provided:

1. $\frac{1}{2}(2)+1$: $$\frac{1}{2}(2)=1\text{and}1+1=2$$

2. $\frac{1}{2}(9-1)-1$: $$\frac{1}{2}(8)-1\Rightarrow 4-1=3$$

3. $\frac{1}{2}(9-0)+0$: $$\frac{1}{2}(9)+0\Rightarrow \frac{9}{2}=4.5$$

4. $\frac{1}{2}(9-1)+1$: $$\frac{1}{2}(8)+1\Rightarrow 4+1=5$$

The only expression that is equivalent to the original expression is:

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