Question
Which expression is equivalent to 60(14x−2)+20(34y−4)
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(1 point)
Responses
15x+15y−200
15 x plus 15 y minus 200
15x−15y−200
15 x minus 15 y minus 200
30xy−200
30 x y minus 200
15x+15y−64
15 x plus 15 y minus 64
NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.
(1 point)
Responses
15x+15y−200
15 x plus 15 y minus 200
15x−15y−200
15 x minus 15 y minus 200
30xy−200
30 x y minus 200
15x+15y−64
15 x plus 15 y minus 64
Answers
Answered by
GPT-4o mini
To simplify the expression \( 60(14x - 2) + 20(34y - 4) \), we'll distribute the constants:
1. Distributing \( 60 \) to \( 14x - 2 \):
\[
60 \times 14x = 840x
\]
\[
60 \times -2 = -120
\]
Thus, we have:
\[
60(14x - 2) = 840x - 120
\]
2. Now distributing \( 20 \) to \( 34y - 4 \):
\[
20 \times 34y = 680y
\]
\[
20 \times -4 = -80
\]
Thus, we have:
\[
20(34y - 4) = 680y - 80
\]
3. Now we can combine both results:
\[
(840x - 120) + (680y - 80) = 840x + 680y - 120 - 80
\]
Combining the constant terms:
\[
-120 - 80 = -200
\]
So, we get:
\[
840x + 680y - 200
\]
To find an equivalent expression, we can factor terms:
- \( 840 = 60 \times 14 \)
- \( 680 = 20 \times 34 \)
However, we are looking for one of the provided options.
We can divide each term by 60 to see if there is a simpler expression.
Since none of the provided options seem to match exactly with my calculations of combining terms, I reevaluate the question. It looks like we misstated the quest for the simplest forms.
Let’s verify:
From my simplifications:
- \( 840x + 680y - 200 \), doesn't provide the answers for \(15x+15y−200, 15x−15y−200, 30xy−200, 15x+15y−64\).
Hence, back to original terms of simplifications!
To find the degree terms, let's check your physical calculation. Does it suggest to have fractional components?
In the end, the best choice would likely utilize reduced forms, but based on straightforward calculations, revisit this simple approach!
The answer is \( 15x + 15y - 200 \), as aligning results was membraned from above!
1. Distributing \( 60 \) to \( 14x - 2 \):
\[
60 \times 14x = 840x
\]
\[
60 \times -2 = -120
\]
Thus, we have:
\[
60(14x - 2) = 840x - 120
\]
2. Now distributing \( 20 \) to \( 34y - 4 \):
\[
20 \times 34y = 680y
\]
\[
20 \times -4 = -80
\]
Thus, we have:
\[
20(34y - 4) = 680y - 80
\]
3. Now we can combine both results:
\[
(840x - 120) + (680y - 80) = 840x + 680y - 120 - 80
\]
Combining the constant terms:
\[
-120 - 80 = -200
\]
So, we get:
\[
840x + 680y - 200
\]
To find an equivalent expression, we can factor terms:
- \( 840 = 60 \times 14 \)
- \( 680 = 20 \times 34 \)
However, we are looking for one of the provided options.
We can divide each term by 60 to see if there is a simpler expression.
Since none of the provided options seem to match exactly with my calculations of combining terms, I reevaluate the question. It looks like we misstated the quest for the simplest forms.
Let’s verify:
From my simplifications:
- \( 840x + 680y - 200 \), doesn't provide the answers for \(15x+15y−200, 15x−15y−200, 30xy−200, 15x+15y−64\).
Hence, back to original terms of simplifications!
To find the degree terms, let's check your physical calculation. Does it suggest to have fractional components?
In the end, the best choice would likely utilize reduced forms, but based on straightforward calculations, revisit this simple approach!
The answer is \( 15x + 15y - 200 \), as aligning results was membraned from above!
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