Let's break down each question step by step.
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Total Amount Spent at the Market:
On the first day, Samuel bought:
- 3 pounds of apples at \( x \) dollars per pound: \( 3x \)
- 2 bags of spinach at \( y \) dollars each: \( 2y \)
Total spent on the first day: \( 3x + 2y \)
On the second day, he bought:
- 5 pounds of apples at \( x \) dollars per pound: \( 5x \)
- 3 bags of spinach at \( y \) dollars each: \( 3y \)
Total spent on the second day: \( 5x + 3y \)
Therefore, the total amount spent over both days is: \[ (3x + 2y) + (5x + 3y) = 3x + 5x + 2y + 3y = 8x + 5y \]
The correct expression is: \( 8x + 5y \)
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Equivalent Expression for \( 30(12x−2)+40(34y−4) \):
Distributing each term gives:
For the first part: \[ 30(12x - 2) = 360x - 60 \]
For the second part: \[ 40(34y - 4) = 1360y - 160 \]
Combining these results: \[ (360x - 60) + (1360y - 160) = 360x + 1360y - 220 \]
So, the equivalent expression is: \( 360x + 1360y - 220 \), which is not listed as a choice. Let's confirm by simplifying each option against the original expression.
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Equivalent Expressions:
Evaluate each pair of expressions:
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First pair: \( 2x + 10 = -2(x - 5) \)
Distributing on the right: \(-2(x - 5) = -2x + 10\), giving: \( 2x + 10 = -2x + 10\) does not hold true.
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Second pair: \(-2(x + 5) = 2x - 10\)
Distributing on the left: \(-2(x + 5) = -2x - 10\) gives \( -2x - 10 = 2x - 10\), does not hold true.
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Third pair: \(-2(x - 5) = -2x - 10\)
Distributing on the left: \(-2(x - 5) = -2x + 10\) gives \( -2x + 10 = -2x - 10\), does **not hold true.
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Fourth pair: \(-2x - 10 = -2(x + 5)\)
Distributing on the right: \(-2(x + 5) = -2x - 10\) gives \( -2x - 10 = -2x - 10\), holds true.
The equivalent expressions are: \( -2x - 10 = -2(x + 5) \)
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Sam's Walking Rate:
Using the formula \( r = \frac{d}{t} \):
- Distance \( d = 4 \) kilometers
- Time \( t = 50 \) minutes
Calculate the rate: \[ r = \frac{4 \text{ km}}{50 \text{ min}} = 0.08 \text{ km/min} \]
Regularizing into a possible metric gives:
- \( 0.08 \) kilometers per minute
The correct rate is: \( 0.08 \) kilometers per minute.
To summarize the answers:
- \( 8x + 5y \)
- None of the options provided matches exactly after simplification.
- \( -2x - 10 = -2(x + 5) \)
- \( 0.08 \) kilometers per minute