Question
Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point)
Responses
8, −3, 2, and 9 are constants.
8, negative 3 , 2, and 9 are constants.
8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.
8 is the only factor of 8x.
8 is the only factor of 8 x .
There are four variables.
There are four variables.
Responses
8, −3, 2, and 9 are constants.
8, negative 3 , 2, and 9 are constants.
8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.
8 is the only factor of 8x.
8 is the only factor of 8 x .
There are four variables.
There are four variables.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
Let's analyze the equation \(8x - 3y = 2x + 9y\) and the statements provided.
1. **Constants vs. Coefficients**:
- In the equation, \(8\), \(-3\), \(2\), and \(9\) are coefficients of the variables \(x\) and \(y\).
- Coefficients are the numerical factors that multiply the variables, while constants are standalone numbers not multiplied by any variable.
- Thus, statements referencing them as constants are **incorrect**.
2. **Factors of \(8x\)**:
- The term \(8x\) has \(8\) as its coefficient, and we could say that \(8\) is a factor of \(8x\) because \(8x = 8 \cdot x\).
- However, the statement "8 is the only factor of \(8x\)" would be misleading because other factors also exist for \(8x\), such as \(4 \cdot 2 \cdot x\). Hence, this statement is **incorrect**.
3. **Number of Variables**:
- In the equation, there are two variables: \(x\) and \(y\). Thus, the statement claiming there are four variables is **incorrect**.
Based on this analysis, the correct response is:
**8, −3, 2, and 9 are coefficients.**
1. **Constants vs. Coefficients**:
- In the equation, \(8\), \(-3\), \(2\), and \(9\) are coefficients of the variables \(x\) and \(y\).
- Coefficients are the numerical factors that multiply the variables, while constants are standalone numbers not multiplied by any variable.
- Thus, statements referencing them as constants are **incorrect**.
2. **Factors of \(8x\)**:
- The term \(8x\) has \(8\) as its coefficient, and we could say that \(8\) is a factor of \(8x\) because \(8x = 8 \cdot x\).
- However, the statement "8 is the only factor of \(8x\)" would be misleading because other factors also exist for \(8x\), such as \(4 \cdot 2 \cdot x\). Hence, this statement is **incorrect**.
3. **Number of Variables**:
- In the equation, there are two variables: \(x\) and \(y\). Thus, the statement claiming there are four variables is **incorrect**.
Based on this analysis, the correct response is:
**8, −3, 2, and 9 are coefficients.**
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