Question
Which expression is equivalent to (3r⋅5)⋅(−3⋅8) ?(1 point) Responses 15r⋅(5⋅8) 15 r times left parenthesis 5 times 8 right parenthesis 24r⋅(5⋅−3) 24 r times left parenthesis 5 times negative 3 right parenthesis (5⋅−3)⋅−9r left parenthesis 5 times negative 3 right parenthesis times negative 9 r −45r⋅5
Answers
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Answered by
GPT-4o mini
To simplify the expression \((3r \cdot 5) \cdot (-3 \cdot 8)\), let's break it down step by step.
1. First, simplify the multiplication inside the parentheses:
- For the first part, \(3r \cdot 5 = 15r\).
- For the second part, \(-3 \cdot 8 = -24\).
2. Now, combine these results:
\[
(3r \cdot 5) \cdot (-3 \cdot 8) = 15r \cdot -24.
\]
3. Finally, multiply these terms:
\[
15r \cdot -24 = -360r.
\]
Now, let's analyze the provided response options:
1. **15r⋅(5⋅8)**: This equals \(15r \cdot 40\), which is not equal to \(-360r\).
2. **24r⋅(5⋅−3)**: This would equal \(24r \cdot (-15)\), which equals \(-360r\), so this is equivalent.
3. **(5⋅−3)⋅−9r**: This equals \(-15 \cdot -9r = 135r\), which is not equal to \(-360r\).
4. **−45r⋅5**: This equals \(-225r\), which is not equal to \(-360r\).
Therefore, the expression **24r⋅(5⋅−3)** is equivalent to \((3r \cdot 5) \cdot (-3 \cdot 8)\).
1. First, simplify the multiplication inside the parentheses:
- For the first part, \(3r \cdot 5 = 15r\).
- For the second part, \(-3 \cdot 8 = -24\).
2. Now, combine these results:
\[
(3r \cdot 5) \cdot (-3 \cdot 8) = 15r \cdot -24.
\]
3. Finally, multiply these terms:
\[
15r \cdot -24 = -360r.
\]
Now, let's analyze the provided response options:
1. **15r⋅(5⋅8)**: This equals \(15r \cdot 40\), which is not equal to \(-360r\).
2. **24r⋅(5⋅−3)**: This would equal \(24r \cdot (-15)\), which equals \(-360r\), so this is equivalent.
3. **(5⋅−3)⋅−9r**: This equals \(-15 \cdot -9r = 135r\), which is not equal to \(-360r\).
4. **−45r⋅5**: This equals \(-225r\), which is not equal to \(-360r\).
Therefore, the expression **24r⋅(5⋅−3)** is equivalent to \((3r \cdot 5) \cdot (-3 \cdot 8)\).
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