Which of the following is an equivalent expression to 1/2(9−70)+(−29)0 ? (1 point)Responses1/2(9−1)+1Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis plus 1 1/2(9−0)+0Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0 1/2(2)+1Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1 1/2(9−1)−1

Answer 1

Let's simplify the original expression step by step:

The expression is: \[ \frac{1}{2}(9 - 70) + (-29)0 \]

First, calculate \( (-29)0 \): \[ (-29)0 = 0 \] So the expression simplifies to: \[ \frac{1}{2}(9 - 70) + 0 = \frac{1}{2}(9 - 70) \]

Next, calculate \( 9 - 70 \): \[ 9 - 70 = -61 \]

Now, substitute this back into the expression: \[ \frac{1}{2}(-61) \] This simplifies to: \[ -\frac{61}{2} \]

Now let's check which of the given options is equivalent to \(-\frac{61}{2}\):

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

2. Option 2: \(\frac{1}{2}(9 - 0) + 0 = \frac{1}{2}(9) + 0 = \frac{9}{2}\)

3. Option 3: \(\frac{1}{2}(2) + 1 = 1 + 1 = 2\)

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

None of the options given are equal to \(-\frac{61}{2}\).

Thus, there seems to be no equivalent expression among the choices provided.