Choose two statements that are true for this expression.
[tex]$5 x^3-6 x^2-\frac{25}{y}+18$[/tex]
A. There are three terms.
B. The term [tex]$-\frac{25}{y}$[/tex] is a ratio.
C. There are four terms.
D. The entire expression is a difference.
Answer (2)
Count the terms in the expression: 5 x 3 , − 6 x 2 , − y 25 , and 18 . There are four terms.
Determine if − y 25 is a ratio: Yes, it's a ratio of -25 to y.
Check if the entire expression is a difference: No, it includes both subtraction and addition.
The true statements are B and C: B , C
Explanation
Analyzing the Expression Let's analyze the given expression: 5 x 3 − 6 x 2 − y 25 + 18 . We need to identify true statements about it.
Counting the Terms First, let's count the terms. A term is a single number or variable, or numbers and variables multiplied together, separated by + or - signs. In the expression 5 x 3 − 6 x 2 − y 25 + 18 , we have 5 x 3 , − 6 x 2 , − y 25 , and 18 . So, there are four terms. This means statement A is false and statement C is true.
Identifying the Ratio Now, let's consider statement B: 'The term − y 25 is a ratio.' A ratio is a comparison of two quantities by division. The term − y 25 can be seen as the ratio of -25 to y. So, statement B is true.
Checking for Difference Finally, let's analyze statement D: 'The entire expression is a difference.' While the expression involves subtraction, it also includes addition (the +18 term). Therefore, it's more accurately described as a combination of sums and differences, not just a difference. So, statement D is false.
Final Answer Therefore, the two true statements are B and C.
Examples
Understanding expressions and their terms is fundamental in algebra. For instance, if you're calculating the total cost of items where each item has a base price and a variable tax depending on quantity, you'd use an expression. If the base price for an item is 5 x 3 , the discount is 6 x 2 , a shipping cost of − y 25 (where y is related to distance), and a fixed fee of $18, the total cost is represented by the expression 5 x 3 − 6 x 2 − y 25 + 18 . Identifying the terms helps in understanding each component's contribution to the total cost.
The two true statements about the expression are B (the term − y 25 is a ratio) and C (there are four terms). Statement A is false as there are four terms, and statement D is false since the expression is not purely a difference. Therefore, the correct answers are B and C.
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