Asked by Glitchtrap
Given the equation 8x−3y=2x+9y, which of the following statements is correct?(1 point)
Responses
8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.
8, −3, 2, and 9 are constants.
8, negative 3 , 2, and 9 are constants.
8 is the only factor of 8x.
8 is the only factor of 8 x .
There are four variables.
Responses
8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.
8, −3, 2, and 9 are constants.
8, negative 3 , 2, and 9 are constants.
8 is the only factor of 8x.
8 is the only factor of 8 x .
There are four variables.
Answers
Answered by
Glitchtrap
An equation can be broken down into expressions, terms, variables, constants, and coefficients. In the equation 0.4−7x=3, what is/are the constant(s) in the equation?(1 point)
Responses
0.4 and 3
0.4 and 3
0.4
0.4
3
3
−7
Responses
0.4 and 3
0.4 and 3
0.4
0.4
3
3
−7
Answered by
Glitchtrap
Use the grouping symbols to interpret the following equation: x8=3(x+4)2. Which expression in the equation represents a product?(1 point)
Responses
x8
Start Fraction x over 8 End Fraction
2
2
3(x+4)2
Start Fraction 3 left parenthesis x plus 4 right parenthesis over 2 End Fraction
3(x+4)
Responses
x8
Start Fraction x over 8 End Fraction
2
2
3(x+4)2
Start Fraction 3 left parenthesis x plus 4 right parenthesis over 2 End Fraction
3(x+4)
Answered by
Glitchtrap
Consider the expression [3(42+32÷4−5)]. Which quotient must be found to simplify the expression?(1 point)
Responses
96÷4
96 divided by 4
32÷4
32 divided by 4
48÷4
48 divided by 4
144÷4
Responses
96÷4
96 divided by 4
32÷4
32 divided by 4
48÷4
48 divided by 4
144÷4
Answered by
GPT-4o mini
To analyze the equation \(8x - 3y = 2x + 9y\), we can identify the relevant components:
1. Coefficients are the numerical factors accompanying variables in an expression. In the equation:
- The coefficient of \(x\) on the left side is \(8\).
- The coefficient of \(y\) on the left side is \(-3\).
- The coefficient of \(x\) on the right side is \(2\).
- The coefficient of \(y\) on the right side is \(9\).
Thus, \(8, -3, 2,\) and \(9\) are indeed coefficients.
2. Constants are terms that do not have variables associated with them. In this equation, there are no standalone constant terms, so \(8, -3, 2,\) and \(9\) cannot be considered constants.
3. The statement "8 is the only factor of 8x" is misleading. While \(8\) is indeed a factor of \(8x\), it is not the only "factor" since any non-zero multiplicative representation of \(x\) retains \(8\) as a coefficient.
4. There are two variables, which are \(x\) and \(y\).
Given this analysis, the correct statement is:
**8, −3, 2, and 9 are coefficients.**
1. Coefficients are the numerical factors accompanying variables in an expression. In the equation:
- The coefficient of \(x\) on the left side is \(8\).
- The coefficient of \(y\) on the left side is \(-3\).
- The coefficient of \(x\) on the right side is \(2\).
- The coefficient of \(y\) on the right side is \(9\).
Thus, \(8, -3, 2,\) and \(9\) are indeed coefficients.
2. Constants are terms that do not have variables associated with them. In this equation, there are no standalone constant terms, so \(8, -3, 2,\) and \(9\) cannot be considered constants.
3. The statement "8 is the only factor of 8x" is misleading. While \(8\) is indeed a factor of \(8x\), it is not the only "factor" since any non-zero multiplicative representation of \(x\) retains \(8\) as a coefficient.
4. There are two variables, which are \(x\) and \(y\).
Given this analysis, the correct statement is:
**8, −3, 2, and 9 are coefficients.**
Answered by
GPT-4o mini
In the equation \(0.4 - 7x = 3\), we can identify the following components:
- **Constants** are terms that do not have a variable associated with them.
- **Variables** in this case include \(x\).
- **Coefficients** are the numerical factors attached to variables, like the \(-7\) in front of \(x\).
In this equation:
- \(0.4\) is a constant.
- \(3\) is also a constant.
- \(-7\) is a coefficient.
Therefore, the constants in the equation are \(0.4\) and \(3\).
The correct response is:
**0.4 and 3.**
- **Constants** are terms that do not have a variable associated with them.
- **Variables** in this case include \(x\).
- **Coefficients** are the numerical factors attached to variables, like the \(-7\) in front of \(x\).
In this equation:
- \(0.4\) is a constant.
- \(3\) is also a constant.
- \(-7\) is a coefficient.
Therefore, the constants in the equation are \(0.4\) and \(3\).
The correct response is:
**0.4 and 3.**
Answered by
GPT-4o mini
In the equation \( x^8 = 3(x + 4)^2 \), we are asked to identify which expression represents a product.
To evaluate the options:
1. **\(x^8\)**: This is a single term where \(x\) is raised to the 8th power. This is not a product of factors in the traditional sense, but rather \(x\) multiplied by itself eight times.
2. **\(2\)**: This is just a constant and does not represent a product.
3. **\(3(x + 4)^2\)**: This expression can be interpreted as \(3\) multiplied by \((x + 4)^2\). Inside the parentheses, \((x + 4)\) is also squared, which means it is multiplied by itself. So, while this expression as a whole represents a product of three and the square of \((x + 4)\), \((x + 4)\) itself is not a product.
4. **\(3(x + 4)\)**: This expression represents a product of \(3\) and \((x + 4)\), which is another instance of multiplication.
Given this analysis, the best answer to the question regarding which expression represents a product is:
**3(x + 4)**
To evaluate the options:
1. **\(x^8\)**: This is a single term where \(x\) is raised to the 8th power. This is not a product of factors in the traditional sense, but rather \(x\) multiplied by itself eight times.
2. **\(2\)**: This is just a constant and does not represent a product.
3. **\(3(x + 4)^2\)**: This expression can be interpreted as \(3\) multiplied by \((x + 4)^2\). Inside the parentheses, \((x + 4)\) is also squared, which means it is multiplied by itself. So, while this expression as a whole represents a product of three and the square of \((x + 4)\), \((x + 4)\) itself is not a product.
4. **\(3(x + 4)\)**: This expression represents a product of \(3\) and \((x + 4)\), which is another instance of multiplication.
Given this analysis, the best answer to the question regarding which expression represents a product is:
**3(x + 4)**
Answered by
GPT-4o mini
To simplify the expression \( 3(42 + 32 \div 4 - 5) \), we need to focus on the operations inside the parentheses. Let's break it down:
1. **Identify components in the parentheses**:
- \( 42 \)
- \( 32 \div 4 \) (this is the quotient we need to find)
- \( - 5 \)
2. **Perform the division**:
- We see that \( 32 \div 4 \) needs to be calculated as part of simplifying the expression.
Thus, the quotient that must be found in order to simplify the expression is:
**32 ÷ 4**
1. **Identify components in the parentheses**:
- \( 42 \)
- \( 32 \div 4 \) (this is the quotient we need to find)
- \( - 5 \)
2. **Perform the division**:
- We see that \( 32 \div 4 \) needs to be calculated as part of simplifying the expression.
Thus, the quotient that must be found in order to simplify the expression is:
**32 ÷ 4**
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