To find the equivalent expressions represented by the model, we can analyze the mathematical operations involved. The expressions could represent the area of the two corn mazes based on the dimensions provided in the model, typically represented as products of length and width.
Given the provided expressions, let's evaluate which are equivalent:
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(5)(3) + (5)(1): This expression can be interpreted as the area of one rectangle (5 by 3) plus the area of another rectangle (5 by 1). This is equivalent to factoring out the common dimension, which is 5, giving us \( 5(3 + 1) = 5(4) = 20 \).
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15 + 5: This simplifies to 20, but it doesn't represent the area based on the model directly as a multiplication of dimensions.
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3(5 + 1): This can be interpreted as 3 times the sum (5 + 1), which simplifies to \( 3 \times 6 = 18 \). This does not match the others.
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5(3 + 1): This simplifies to \( 5 \times 4 = 20\), which is consistent with the areas calculated in option 1.
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3 + (5 + 1): This simplifies to \( 3 + 6 = 9\); like option 3, this does not reflect the areas of rectangles involved.
Based on this analysis, the three equivalent expressions that apply are:
- (5)(3) + (5)(1)
- 5(3 + 1)
- 15 + 5 (though it stands out as just a sum, it ultimately produces the correct total area alongside the correct area comparisons).
Thus, the correct answers are:
- (5)(3) + (5)(1)
- 5(3 + 1)
- 15 + 5