Question

Which of the following shows the correct process of solving −30+4.5
?(1 point)
Responses

−30+4.5=(−3)0+4.5=1+4.5=5.5
negative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5

−30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5
negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5

−30+4.5=−3+4.5=1.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 plus 4.5 equals 1.5

−3 to the power of 0 + 4.5=−3⋅0+4.5=0+4.5=4.5

Answer 1

To solve the expression \(-30 + 4.5\), we can first clarify that \(-30\) means \(-3\) (to the power of \(0\)) times \(10\) (which is often represented as \(−30 = −3 \cdot 10\) rather than the exponent notation, which is incorrectly used here). Thus, let's evaluate each response for being mathematically accurate in the process and calculation:

1. **Response 1:**
\(-30 + 4.5 = (-3)^0 + 4.5 = 1 + 4.5 = 5.5\)
- Incorrect. \((-3)^0\) is equal to \(1\), but it doesn't reflect the operation of \(-30\).

2. **Response 2:**
\(-30 + 4.5 = -1 \cdot 30 + 4.5 = -1 \cdot 1 + 4.5 = -1 + 4.5 = 3.5\)
- Incorrect. The calculation does not accurately reflect \(-30\) being added to \(4.5\).

3. **Response 3:**
\(-30 + 4.5 = -3 + 4.5 = 1.5\)
- Incorrect interpretation of \(-30\). \(-30\) cannot simply become \(-3\).

4. **Response 4:**
\(-3^0 + 4.5 = -3 \cdot 0 + 4.5 = 0 + 4.5 = 4.5\)
- This is incorrect as well since \(-3^0 = 1\) and this setup ignores the original context.

None of the responses show the correct process or logic for calculating \(-30 + 4.5\).

The correct calculation should be:
\[
-30 + 4.5 = -30 + 4.5 = -25.5
\]

None of the provided responses reach this conclusion. So, all of them are incorrect.