Let's analyze the given expression and determine which statements are true.
The expression given is:
[tex]\[ 6x^3 - 8x^2 - \frac{40}{y} + 21 \][/tex]
Step-by-Step Analysis:
1. Identify the number of terms:
- Terms in an algebraic expression are separated by addition or subtraction signs.
- The terms in the given expression are [tex]\( 6x^3 \)[/tex], [tex]\( -8x^2 \)[/tex], [tex]\( -\frac{40}{y} \)[/tex], and [tex]\( 21 \)[/tex].
Counting these, we have:
- [tex]\( 6x^3 \)[/tex]
- [tex]\( -8x^2 \)[/tex]
- [tex]\( -\frac{40}{y} \)[/tex]
- [tex]\( 21 \)[/tex]
Thus, there are four separate terms. (This validates Statement A).
2. Determine the nature of the expression:
- The entire expression contains both addition and subtraction operations, hence it cannot simply be described as a difference. (This disproves Statement B).
3. Consider if any term is a ratio:
- A ratio is typically a fraction or division form. The term [tex]\( -\frac{40}{y} \)[/tex] involves division and takes the form of a fraction.
Hence, [tex]\( -\frac{40}{y} \)[/tex] is indeed a ratio. (This validates Statement C).
4. Check the claim about the number of terms:
- We previously counted four terms, not three. (This disproves Statement D).
To summarize, after analyzing the expression, we conclude that:
- There are four terms in the expression.
- The term [tex]\( -\frac{40}{y} \)[/tex] is indeed a ratio.
Therefore, the two true statements are:
A. There are four terms.
C. The term [tex]\( -\frac{40}{y} \)[/tex] is a ratio.
