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.

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.

Answer 1

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.

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

0.4 and 3

0.4 and 3

0.4
0.4

3
3

−7

Answer 3

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.

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

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)

Answer 5

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)

Answer 6

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

Answer 7

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