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Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point)

Responses

−4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45

−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15

−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20

−4(3+120)+150=−4(15)+1=−60+1=−59
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 1 equals negative 60 plus 1 equals negative 59

5 answers

Let's analyze the expression \(-4(3 + 120) + 150\) step by step.

  1. Start by simplifying the inside of the parentheses: \[ 3 + 120 = 123 \]

  2. Now substitute that back into the expression: \[ -4(123) + 150 \]

  3. Next, multiply \(-4\) by \(123\): \[ -4 \times 123 = -492 \]

  4. Finally, add \(150\): \[ -492 + 150 = -342 \]

Now neither of the options provided seems to be solving this expression directly by using the Zero Power Rule or yielding the correct end value of \(-342\). The Zero Power Rule states that any non-zero number raised to the 0 power equals 1. However, it looks like the options presented involve incorrect interpretations of components of the original expression.

None of the provided options are correct, but if we had to clarify regarding the Zero Power Rule, we could consider if the expression was modified to interpret certain constants as ones with exponentiation, which appears to have been the intent in some options.

The answer should be \(−4(3 + 120) + 150 = -342\), thereby indicating all the responses are incorrect.

If you would like to focus on one of them particularly for clarification, please indicate which one I should elaborate on!

no pick one of theses −4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45

−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15

−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20

−4(3+120)+150=−4(15)+1=−60+1=−59

Let's analyze the options you've provided based on the original expression \(-4(3 + 120) + 150\):

  1. Option 1: \[ -4(3 + 120) + 150 = -4(15) + 15 = -60 + 15 = -45 \]

    • This option is incorrect. \(3 + 120\) equals \(123\), not \(15\).

  2. Option 2: \[ -4(3 + 120) + 150 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15 \]

    • This option is incorrect. The manipulation of \(3 + 120\) is incorrect, as it does not equal \(4\) (it equals \(123\)).

  3. Option 3: \[ -4(3 + 120) + 150 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -4 \cdot 5 = -20 \]

    • This option is also incorrect because \(3 + 120\) does not equal \(4\) and the multiplication doesn't correspond to the original problem.

  4. Option 4: \[ -4(3 + 120) + 150 = -4(15) + 1 = -60 + 1 = -59 \]

    • This is incorrect, too, for the same reason as the others; \(3 + 120\) is not equal to \(15\).

Selecting the Best Incorrect Answer:

None of the provided options result in \(-342\) or even align with the correct operations on the original expression. However, Option 1 at the very least provides a structure of operations that follows from manipulating parentheses, albeit incorrectly applied (as it used \(15\) instead of \(123\)).

Final Choice: If I must pick one based on how it follows an arithmetic structure, I would select the first option: \[ −4(3+120)+150 =−4(15)+15=−60+15=−45 \]

I emphasize that while it follows a format of operations, it is essential to clarify that the underlying arithmetic miscalculates because \(3 + 120\) doesn’t equal \(15\). Please do remember that the correct evaluation should yield \(-342\).

are you sure

I apologize for any confusion in my previous responses. Let's reevaluate the options carefully:

We're given the expression:

\[ -4(3 + 120) + 150 \]

Step-by-step evaluation:

  1. Combine inside the parentheses: \[ 3 + 120 = 123 \]

  2. Substitute back: \[ -4(123) + 150 \]

  3. Calculate \(-4 \times 123\): \[ -4 \times 123 = -492 \]

  4. Add \(150\): \[ -492 + 150 = -342 \]

Now, let's examine the provided options:

  1. Option 1: \[ -4(3 + 120) + 150 = -4(15) + 15 = -60 + 15 = -45 \]

    • Incorrect, because \(3 + 120\) does not equal \(15\).

  2. Option 2: \[ -4(3 + 120) + 150 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -16 + 1 = -15 \]

    • Incorrect, as \(3 + 120\) does not equal \(4\).

  3. Option 3: \[ -4(3 + 120) + 150 = -4(3 + 1) + 1 = -4 \cdot 4 + 1 = -4 \cdot 5 = -20 \]

    • Incorrect, because \(3 + 120\) is not \(5\).

  4. Option 4: \[ -4(3 + 120) + 150 = -4(15) + 1 = -60 + 1 = -59 \]

    • Incorrect, as \(3 + 120\) is not \(15\).

Conclusion:

None of the options correctly followed the original expression's evaluation nor yielded the right answer. Each option contains fundamental arithmetic mistakes regarding the values calculated from \(3 + 120\).

If I must choose one to represent how simplifying might proceed (though it is still incorrect in the endpoint), Option 1 is the closest in following a structure of operations, even though it is fundamentally wrong.

Thank you for your patience, and I hope this clears up any confusion! The correct result of the original expression is \(-342\).