Question
A farmer sets up two corn mazes for a fall festival, as shown in this model. Which equivalent expressions are represented by the model? Check the three that apply. (3 points) Responses (5)(3)+(5)(1) 5 times 3 plus 5 times 1 3+(5+1) 3 plus open paren 5 plus 1 close paren 15+5 15 plus 5 5(3+1) 5 times open paren 3 plus 1 close paren 3(5+1) 3 times open paren 5 plus 1 close paren Skip to navigation
Answers
GPT-4o mini
To determine which equivalent expressions are represented by the model, we need to analyze the options based on the distributive property and combine like terms. The expressions given suggest they may represent the same area or quantity in different forms.
1. **(5)(3) + (5)(1)**:
- This expression uses the distributive property. It represents the area of two rectangles with height 5 and widths 3 and 1.
- Equivalent representation: \( 5(3 + 1) = 5 \times 4 = 20 \).
2. **3 + (5 + 1)**:
- This simplifies to \( 3 + 6 = 9 \), which does not equal the previous expressions, so it is not valid.
3. **15 + 5**:
- This simplifies to \( 20 \), aligning with the area equivalent found earlier. It could represent the total area of two similar sections.
4. **5(3 + 1)**:
- This also represents \( 5 \times 4 = 20 \), which is equivalent to the previous expressions, as it employs the distributive property.
5. **3(5 + 1)**:
- This simplifies to \( 3 \times 6 = 18 \), which does not align with other expressions' results, making it invalid.
From the interpretation above, the three equivalent expressions are:
1. **(5)(3) + (5)(1)**
2. **15 + 5**
3. **5(3 + 1)**
Thus, the expressions that apply are (5)(3) + (5)(1), 15 + 5, and 5(3 + 1).
1. **(5)(3) + (5)(1)**:
- This expression uses the distributive property. It represents the area of two rectangles with height 5 and widths 3 and 1.
- Equivalent representation: \( 5(3 + 1) = 5 \times 4 = 20 \).
2. **3 + (5 + 1)**:
- This simplifies to \( 3 + 6 = 9 \), which does not equal the previous expressions, so it is not valid.
3. **15 + 5**:
- This simplifies to \( 20 \), aligning with the area equivalent found earlier. It could represent the total area of two similar sections.
4. **5(3 + 1)**:
- This also represents \( 5 \times 4 = 20 \), which is equivalent to the previous expressions, as it employs the distributive property.
5. **3(5 + 1)**:
- This simplifies to \( 3 \times 6 = 18 \), which does not align with other expressions' results, making it invalid.
From the interpretation above, the three equivalent expressions are:
1. **(5)(3) + (5)(1)**
2. **15 + 5**
3. **5(3 + 1)**
Thus, the expressions that apply are (5)(3) + (5)(1), 15 + 5, and 5(3 + 1).