Answer :
Let's evaluate each statement one by one for the expression [tex]\( 5x^3 - 6x^2 - \frac{25}{y} + 18 \)[/tex]:
[tex]\[ 5x^3 - 6x^2 - \frac{25}{y} + 18 \][/tex]
### Statement A: The entire expression is a difference.
- A difference in an algebraic expression occurs when one term is subtracted from another. However, the given expression includes both additions and subtractions.
- It starts with [tex]\( 5x^3 \)[/tex] (positive), subtracts [tex]\( 6x^2 \)[/tex], subtracts [tex]\( \frac{25}{y} \)[/tex], and then adds 18.
- Therefore, this expression is not purely a difference; it is a combination of sums and differences.
Conclusion: Statement A is not true.
### Statement B: The term [tex]\( -\frac{25}{y} \)[/tex] is a ratio.
- A ratio can be defined as a quotient of two quantities. Here, [tex]\( -\frac{25}{y} \)[/tex] explicitly represents a ratio where 25 is divided by [tex]\( y \)[/tex].
- Despite the negative sign, it still involves a division.
Conclusion: Statement B is true.
### Statement C: There are four terms.
- To identify the number of terms in the expression, we look at the distinct parts separated by addition or subtraction signs.
- The terms in the expression [tex]\( 5x^3 - 6x^2 - \frac{25}{y} + 18 \)[/tex] are:
1. [tex]\( 5x^3 \)[/tex]
2. [tex]\( -6x^2 \)[/tex]
3. [tex]\( -\frac{25}{y} \)[/tex]
4. [tex]\( +18 \)[/tex]
- Hence, the expression indeed has four distinct terms.
Conclusion: Statement C is true.
### Statement D: There are three terms.
- As we identified above, there are four terms in the expression, not three.
- Therefore, this statement is incorrect.
Conclusion: Statement D is not true.
So, the correct statements are:
[tex]\[ \boxed{B \text{ and } C} \][/tex]
This means the correct answer is statements B and C. Hence, the returned result of running the code would be (2, 3), representing B and C respectively.
[tex]\[ 5x^3 - 6x^2 - \frac{25}{y} + 18 \][/tex]
### Statement A: The entire expression is a difference.
- A difference in an algebraic expression occurs when one term is subtracted from another. However, the given expression includes both additions and subtractions.
- It starts with [tex]\( 5x^3 \)[/tex] (positive), subtracts [tex]\( 6x^2 \)[/tex], subtracts [tex]\( \frac{25}{y} \)[/tex], and then adds 18.
- Therefore, this expression is not purely a difference; it is a combination of sums and differences.
Conclusion: Statement A is not true.
### Statement B: The term [tex]\( -\frac{25}{y} \)[/tex] is a ratio.
- A ratio can be defined as a quotient of two quantities. Here, [tex]\( -\frac{25}{y} \)[/tex] explicitly represents a ratio where 25 is divided by [tex]\( y \)[/tex].
- Despite the negative sign, it still involves a division.
Conclusion: Statement B is true.
### Statement C: There are four terms.
- To identify the number of terms in the expression, we look at the distinct parts separated by addition or subtraction signs.
- The terms in the expression [tex]\( 5x^3 - 6x^2 - \frac{25}{y} + 18 \)[/tex] are:
1. [tex]\( 5x^3 \)[/tex]
2. [tex]\( -6x^2 \)[/tex]
3. [tex]\( -\frac{25}{y} \)[/tex]
4. [tex]\( +18 \)[/tex]
- Hence, the expression indeed has four distinct terms.
Conclusion: Statement C is true.
### Statement D: There are three terms.
- As we identified above, there are four terms in the expression, not three.
- Therefore, this statement is incorrect.
Conclusion: Statement D is not true.
So, the correct statements are:
[tex]\[ \boxed{B \text{ and } C} \][/tex]
This means the correct answer is statements B and C. Hence, the returned result of running the code would be (2, 3), representing B and C respectively.
