Let's analyze the given mathematical expression step by step:
[tex]\[ 6x^3 - 8x^2 - \frac{40}{y} + 21 \][/tex]
1. Identify the number of terms:
- The terms in the expression are separated by plus (+) and minus (-) signs.
- Decomposing the expression, we get:
- [tex]\(6x^3\)[/tex] (first term)
- [tex]\(-8x^2\)[/tex] (second term)
- [tex]\(-\frac{40}{y}\)[/tex] (third term)
- [tex]\(+21\)[/tex] (fourth term)
Therefore, there are four terms in the expression.
2. Analyze the term [tex]\(-\frac{40}{y}\)[/tex]:
- This term represents a division, where 40 is divided by [tex]\(y\)[/tex]. In mathematical terminology, this kind of expression can be referred to as a ratio.
Given this detailed analysis, we can determine which statements are true:
- Statement A: There are three terms.
- This statement is false because there are four terms in the expression.
- Statement B: The term [tex]\(-\frac{40}{y}\)[/tex] is a ratio.
- This statement is true because [tex]\(-\frac{40}{y}\)[/tex] represents the division of 40 by [tex]\(y\)[/tex], which is a ratio.
- Statement C: There are four terms.
- This statement is true because the expression has four distinct terms.
- Statement D: The entire expression is a difference.
- This statement is false because the entire expression involves both addition and subtraction, not just subtraction.
Therefore, the two true statements for the given expression are:
B. The term [tex]\(-\frac{40}{y}\)[/tex] is a ratio.
C. There are four terms.
