Let's solve each question step by step.
Question 1: Temperature of refrigerator and oven
Let \( t \) be the time in hours after the power goes out.
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Temperature of refrigerator after \( t \) hours: \[ T_r = 40 + 5t \]
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Temperature of oven after \( t \) hours: \[ T_o = 340 - 45t \]
We want to find when \( T_r = T_o \): \[ 40 + 5t = 340 - 45t \]
Combining like terms: \[ 5t + 45t = 340 - 40 \] \[ 50t = 300 \rightarrow t = 6 \text{ hours} \]
Substituting \( t \) back to find the temperature: \[ T_r = 40 + 5(6) = 70 \text{ degrees} \] \[ T_o = 340 - 45(6) = 70 \text{ degrees} \]
Answer for Question 1: 6 hours, 70 degrees
Question 2: Container A and B
Let \( m \) be the time in minutes.
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Amount of water in Container A after \( m \) minutes: \[ A = 200 + 6m \]
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Amount of water in Container B after \( m \) minutes: \[ B = 500 - 6m \]
Setting them equal: \[ 200 + 6m = 500 - 6m \] Combining like terms: \[ 12m = 300 \rightarrow m = 25 \text{ minutes} \]
Answer for Question 2: 25 minutes
Question 3: Angles in a quadrilateral
Let the four angles be \( x \) degrees. Since they sum to 360 degrees: \[ x + x + x + x = 360 \] \[ 4x = 360 \rightarrow x = 90 \text{ degrees} \]
None of the options match \( 90 \) degrees. Assuming they mean to provide degrees sizes that validate. However, since the options given are 72, 24, 12, 110, the question lacks clarity.
Given common angles compliance, only \( x \) options indicate they might mess the question.
Answer for Question 3: No clear choice, assuming angle independents within given values.
Question 4: Gym costs
Let \( x \) be the number of months.
Cost for Gym A: \[ C_A = 30 + 25x \]
Cost for Gym B: \[ C_B = 24 + 26x \]
Setting them equal: \[ 30 + 25x = 24 + 26x \] Combining: \[ 30 - 24 = 26x - 25x \rightarrow 6 = x \]
Finding total cost: \[ C_A = 30 + 25(6) = 180 \]
Answer for Question 4: 6 months, $180
Question 5: Perimeter of the shapes
Assuming specific dimensions weren't provided; thus the method focuses on correlations between configurations (Triangle or Rectangle), let's assume \( x \) or given parameters define equality ratio for lengths.
To find:
Let \( P \) be the perimeter. If \( P_{Triangle} = P_{Rectangle} \), given standard cannot be evaluated without explicit measures. However:
The typical equilateral triangle's perimeter is \( 3x \) and rectangle as \( 2(l+w) \) must tie together some equation per hint, hence starting solves:
Assuming hypotenuse configurations by segment essentially.
Problem continued: Dominant calculations per triangle imply equality of base measures across parameters but specific numbers weren’t enumerated.
Answer for Question 5: Ambiguous without defined parameters, require stated values.
Hope this clarifies each step! If specific angle constraints/configurations fitted some standard measures, please check back with similar configurations.
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