Given the equation 8x−3y=2x+9y , which of the following statements is correct?(1 point)

Question

Responses

8, −3, 2, and 9 are coefficients.
8, negative 3 , 2, and 9 are coefficients.

There are four variables.
There are four variables.

8, −3, 2, and 9 are constants.
8, negative 3 , 2, and 9 are constants.

8 is the only factor of 8x.

Answer 1

To analyze the equation \( 8x - 3y = 2x + 9y \):

1. Coefficients: In the terms \( 8x \), \( -3y \), \( 2x \), and \( 9y \), the numbers that stand in front of the variables (\( x \) and \( y \)) are called coefficients. So both statements "8, −3, 2, and 9 are coefficients." and "8, negative 3, 2, and 9 are coefficients." are correct.

2. Variables: The equation has two variables, \( x \) and \( y \). Therefore, the statements "There are four variables." is incorrect.

3. Constants: In this equation, the numbers 8, -3, 2, and 9 are not constants but are coefficients of the variables. So the statements "8, −3, 2, and 9 are constants." and "8, negative 3, 2, and 9 are constants." are incorrect.

4. Factors: The term "8 is the only factor of 8x" is misleading as it suggests that 8 is the only contributing number in the factorization. However, when factoring, we also consider the variable \( x \).

In conclusion, the correct statements are:

• "8, −3, 2, and 9 are coefficients."
• "8, negative 3, 2, and 9 are coefficients."

Both statements about coefficients are technically correct.

Answer 2

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

−7
negative 7

0.4 and 3

0.4 and 3

3
3

0.4

Answer 3

In the equation \( 0.4 - 7x = 3 \):

• Constants are the fixed values that do not change. In this equation, both \( 0.4 \) (which is the numerical term on the left side) and \( 3 \) (which is the constant on the right side) fit that definition.

• The term \( -7x \) involves a variable (\( x \)) and its coefficient (\( -7 \)), which is not a constant.

Therefore, the constants in the equation are \( 0.4 \) and \( 3 \).

The correct response is: 0.4 and 3.

Answer 4

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

2
2

x8
Start Fraction x over 8 End Fraction

3(x+4)
3 left parenthesis x plus 4 right parenthesis

3(x+4)2

Answer 5

To interpret the equation \( x^8 = 3(x+4)^2 \) and identify which expression represents a product, let's analyze the options:

1. 2: This is simply a number, not a product of terms.

2. \( x^8 \): This represents \( x \) raised to the power of 8, which indicates an exponent but does not describe a product in terms of multiplication of factors.

3. \( 3(x+4) \): This expression indicates a multiplication of 3 and the entire quantity \( (x + 4) \), which can be considered a product.

4. \( 3(x+4)^2 \): This expression involves multiplication as well. It represents the product of 3 and the quantity \( (x + 4) \) squared, which can also be considered a product.

Among these options, both \( 3(x+4) \) and \( 3(x+4)^2 \) represent products. However, since you are asked to pick one:

The best choice that clearly represents a product is: 3(x+4)2 (as it contains multiplication represented in a more complex form).

So the correct response is: 3(x+4)2.

Answer 6

Consider the expression [3(42+32÷4−5)] . Which quotient must be found to simplify the expression?(1 point)
Responses

32÷4
32 divided by 4

96÷4
96 divided by 4

48÷4
48 divided by 4

144÷4

Answer 7

To simplify the expression \( [3(42 + 32 \div 4 - 5)] \), we need to analyze which quotient is relevant to the expression.

Let's break down the expression inside the brackets step by step:

1. Start with the expression inside the parentheses: \( 42 + 32 \div 4 - 5 \).
2. According to the order of operations (PEMDAS/BODMAS), we first perform the division: \( 32 \div 4 \).
3. After this division is calculated, we can proceed with addition and subtraction.

Thus, the quotient that must be calculated to simplify the expression is:

• \( 32 \div 4 \) or 32 divided by 4.

The correct response is: 32 ÷ 4.