Let's analyze the given algebraic expression [tex]\(7x^3 - 4x^2 - \frac{45}{y} + 27\)[/tex] to determine which statements are true.
Step 1: Identify the terms in the expression.
The expression [tex]\(7x^3 - 4x^2 - \frac{45}{y} + 27\)[/tex] can be broken down into the following terms:
1. [tex]\(7x^3\)[/tex]
2. [tex]\(-4x^2\)[/tex]
3. [tex]\(-\frac{45}{y}\)[/tex]
4. [tex]\(27\)[/tex]
So, we see that there are indeed four separate terms in the expression.
Step 2: Examine Statement A.
"A. There are four terms."
From our analysis above, we see that the expression does have four terms. So, Statement A is true.
Step 3: Examine Statement B.
"B. The entire expression is a difference."
The entire expression involves both addition and subtraction, not just subtraction. It combines the terms using both operations, so the statement claiming it to be entirely a difference is not accurate. Therefore, Statement B is false.
Step 4: Examine Statement C.
"C. The term [tex]\(-\frac{45}{y}\)[/tex] is a ratio."
The term [tex]\(-\frac{45}{y}\)[/tex] is indeed a fraction, which is a type of ratio. Hence, Statement C is true.
Step 5: Examine Statement D.
"D. There are three terms."
We already determined that the expression contains four terms, so Statement D is false.
Conclusion:
The true statements are:
- Statement A: "There are four terms."
- Statement C: "The term [tex]\(-\frac{45}{y}\)[/tex] is a ratio."
Therefore, the correct choices are:
A. There are four terms.
C. The term [tex]\(-\frac{45}{y}\)[/tex] is a ratio.
