Given the equation 8x−3y=2x+9y, which of the following statements is correct?(1 point)
Responses
There are four variables.
There are four variables.
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, −3, 2, and 9 are coefficients.
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)
The constant in the equation 0.4 - 7x = 3 is 0.4 and 3.
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
48÷4
48 divided by 4
32÷4
32 divided by 4
144÷4
The quotient that must be found to simplify the expression [3(42+32÷4−5)] is 32÷4
The correct statement is:
"8, −3, 2, and 9 are coefficients."
In the equation 8x−3y=2x+9y, 8, −3, 2, and 9 are coefficients because they are the numbers multiplying the variables x and y.
To determine which statement is correct, we need to understand the terms in the equation.
The given equation is 8x - 3y = 2x + 9y.
In this equation, the variables are x and y. Variables are letters used to represent unknown values.
The constants in the equation are 8, -3, 2, and 9. Constants are known values that do not change.
The coefficients in the equation are the numbers multiplied by the variables. In this equation, the coefficients are 8 and 2 for x, and -3 and 9 for y. Coefficients determine the scale or magnitude of the variables.
Now let's evaluate each statement:
1. "There are four variables" - This statement is incorrect. There are only two variables in the equation, x and y.
2. "8, -3, 2, and 9 are constants" - This statement is correct. 8, -3, 2, and 9 are constants since they are known values that do not change.
3. "8, -3, 2, and 9 are coefficients" - This statement is also correct. 8 and 2 are the coefficients for x, while -3 and 9 are the coefficients for y. Coefficients determine the scale or magnitude of the variables.
4. "8 is the only factor of 8x" - This statement is incorrect. In the equation 8x - 3y = 2x + 9y, 8x represents a term where x is being multiplied by 8. In this case, x and 8 are multiplied together, making 8 a coefficient, not a factor.
Therefore, the correct statement is "8, -3, 2, and 9 are coefficients."