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Real Numbers
Identifying parts in an algebraic expression
Consider the following expression.

3y+7x+4
Select all of the true statements below.

3y is a factor.
4 is a constant.

3y is a coefficient.

3y and 4 are like terms.

3y+7x+4 is written as a sum of three tern
None of these are true.

Real Numbers $\newline$ Identifying parts in an algebraic expression $\newline$ Consider the following expression. $\newline$ $3 y+7 x+4$ $\newline$ Select all of the true statements below. $\newline$ $3 y$ is a factor. $\newline$ $4$ is a constant. $\newline$ $3 y$ is a coefficient. $\newline$ $3 y$ and $4$ are like terms. $\newline$ $3 y+7 x+4$ is written as a sum of three tern $\newline$ None of these are true.

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Identify independent and dependent variables

Full solution

Q. Real Numbers

\newline

Identifying parts in an algebraic expression

\newline

Consider the following expression.

\newline

3 y+7 x+4

\newline

Select all of the true statements below.

\newline

3 y

is a factor.

\newline

4

is a constant.

\newline

3 y

is a coefficient.

\newline

3 y

and

4

are like terms.

\newline

3 y+7 x+4

is written as a sum of three tern

\newline

None of these are true.

Identify Factors: To determine which statements are true, we need to understand the components of the algebraic expression $3y+7x+4$ .
Evaluate Constant: First, let's consider the statement ＂ $3y$ is a factor.＂ In the context of algebraic expressions, a factor is a quantity that is multiplied by another quantity. However, in the expression $3y+7x+4$ , ＂ $3y$ ＂ is not being multiplied by another expression; it is a term that is being added to others. Therefore, this statement is false.
Assess Coefficient: Next, let's look at the statement ＂ $4$ is a constant.＂ A constant is a value that does not change and is not multiplied by a variable. In the expression $3y+7x+4$ , ＂ $4$ ＂ is indeed a constant because it is a standalone number without a variable. Therefore, this statement is true.
Compare Like Terms: Now, let's evaluate the statement ＂ $3y$ is a coefficient.＂ A coefficient is a numerical or constant factor in front of a variable in an algebraic expression. In the term ＂ $3y$ ,＂＂ $3$ ＂ is the coefficient of the variable ＂ $y$ .＂ Therefore, this statement is false because ＂ $3y$ ＂ is a term, not a coefficient; ＂ $3$ ＂ is the coefficient.
Verify Sum of Terms: Considering the statement ＂ $3y$ and $4$ are like terms.＂ Like terms are terms that have the same variables raised to the same powers. Since ＂ $3y$ ＂ contains a variable and ＂ $4$ ＂ is a constant without a variable, they are not like terms. Therefore, this statement is false.
Verify Sum of Terms: Considering the statement ＂ $3y$ and $4$ are like terms.＂ Like terms are terms that have the same variables raised to the same powers. Since ＂ $3y$ ＂ contains a variable and ＂ $4$ ＂ is a constant without a variable, they are not like terms. Therefore, this statement is false.Finally, let's assess the statement ＂ $3y+7x+4$ is written as a sum of three terms.＂ The expression is indeed written as a sum of three terms: ＂ $3y$ ,＂＂ $7x$ ,＂ and ＂ $4$ .＂ Therefore, this statement is true.

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