Let's analyze the given expression step-by-step:
[tex]\[ 5 x^3 - 6 x^2 - \frac{25}{y} + 18 \][/tex]
### Step 1: Identify the terms in the expression
A term in an algebraic expression is a part of the expression that is separated by plus [tex]\( (+) \)[/tex] or minus [tex]\( (-) \)[/tex] signs.
- [tex]\( 5x^3 \)[/tex]: This is the first term.
- [tex]\( -6x^2 \)[/tex]: This is the second term. (Notice the negative sign is part of the term)
- [tex]\( -\frac{25}{y} \)[/tex]: This is the third term. (Again, the negative sign is part of the term)
- [tex]\( +18 \)[/tex]: This is the fourth term.
So, we have four terms in this expression.
### Step 2: Determine if any term represents a ratio
To check if any term represents a ratio, we look for fractions of the form [tex]\( \frac{a}{b} \)[/tex].
- [tex]\( -\frac{25}{y} \)[/tex] is indeed a ratio because it represents the quotient of [tex]\(-25\)[/tex] and [tex]\( y \)[/tex].
### Step 3: Check if the entire expression is a difference
A difference implies the entire expression is in the form of one term subtracted from another.
- The given expression has both additions and subtractions and is not exclusively a difference. There are terms being added as well.
### Summary
Based on the analysis above:
- A. There are four terms in the expression: [tex]\( 5x^3 \)[/tex], [tex]\(-6x^2\)[/tex], [tex]\(-\frac{25}{y}\)[/tex], and [tex]\( 18 \)[/tex].
- B. The term [tex]\( -\frac{25}{y} \)[/tex] is a ratio, as it represents the quotient of [tex]\(-25\)[/tex] and [tex]\( y \)[/tex].
- C. The statement about there being three terms is incorrect as the expression has four terms, not three.
- D. The entire expression is not a difference; it contains both sums and differences.
### Conclusion
The two true statements are:
- A. There are four terms.
- B. The term [tex]\( -\frac{25}{y} \)[/tex] is a ratio.
