Identify the variables that are contained in the expression.

[tex]\[ 4x^2 - 9y + w \][/tex]

A. [tex]\( x \)[/tex]

B. [tex]\( y \)[/tex]

C. [tex]\( w \)[/tex]

D. [tex]\( z \)[/tex]



Answer :

Certainly! Let's analyze the given expression:
[tex]\[ 4x^2 - 9y + w \][/tex]

To identify the variables contained within the expression, let's go through each term systematically.

### Step-by-Step Analysis:

1. First Term: [tex]\(4x^2\)[/tex]
- The first term consists of a coefficient [tex]\(4\)[/tex] and the variable [tex]\(x\)[/tex] raised to the power of [tex]\(2\)[/tex].
- Therefore, the variable [tex]\(x\)[/tex] is present in this term.

2. Second Term: [tex]\(-9y\)[/tex]
- The second term consists of a coefficient [tex]\(-9\)[/tex] and the variable [tex]\(y\)[/tex].
- Hence, [tex]\(y\)[/tex] is a variable in this term.

3. Third Term: [tex]\(w\)[/tex]
- The third term is simply the variable [tex]\(w\)[/tex].
- Thus, [tex]\(w\)[/tex] is present in this term.

### Variables in the Expression:

From the above examination, we can see that the variables present in the expression [tex]\( 4x^2 - 9y + w \)[/tex] are:
- [tex]\(x\)[/tex]
- [tex]\(y\)[/tex]
- [tex]\(w\)[/tex]

### Checking for Missing Variables:

4. Variable [tex]\(z\)[/tex]
- We need to check for the presence of any other variables, such as [tex]\(z\)[/tex].
- In the expression [tex]\( 4x^2 - 9y + w \)[/tex], the variable [tex]\(z\)[/tex] does not appear at all.

### Conclusion:

Based on our detailed analysis, the variables contained in the expression are [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(w\)[/tex]. The variable [tex]\(z\)[/tex] is not present in the expression.

Answer:
- [tex]\(x\)[/tex]: Present
- [tex]\(y\)[/tex]: Present
- [tex]\(w\)[/tex]: Present
- [tex]\(z\)[/tex]: Not Present

So, the correct identification of variables is:
- [tex]\(x\)[/tex] is present.
- [tex]\(y\)[/tex] is present.
- [tex]\(w\)[/tex] is present.
- [tex]\(z\)[/tex] is not present.