Question

writing an algebraic expression in exercises 13–22, write an algebraic expression for the verbal description. 13. the product of two consecutive odd integers, the first of which is 2n - 1 14. the sum of the squares of two consecutive even integers, the first of which is 2n 15. the distance a car travels in t hours at a rate of 55 miles per hour 16. the travel time for a plane traveling at a rate of r kilometers per hour for 900 kilometers 17. the amount of acid in x liters of a 20% acid solution 18. the sale price of an item with a 33% discount on its list price l 19. the perimeter of a rectangle with a width x and a length that is twice the width 20. the area of a triangle with a base that is 16 inches and a height that is h inches 21. the total cost of producing x units for which the fixed costs are $2500 and the cost per unit is $40 22. the total revenue obtained by selling x units at $12.99 per unit

Explanation:

Problem 13

Step1: Identify the second odd integer

Consecutive odd integers differ by 2. If the first is \(2n - 1\), the next is \((2n - 1)+2 = 2n + 1\).

Step2: Find the product

Multiply the two integers: \((2n - 1)(2n + 1)\).

Step1: Identify the second even integer

Consecutive even integers differ by 2. If the first is \(2n\), the next is \(2n + 2\).

Step2: Find the sum of squares

Square each and add: \((2n)^2+(2n + 2)^2\).

Step1: Recall distance formula

Distance \(d=\text{rate}\times\text{time}\).

Step2: Substitute values

Rate is 55 mph, time is \(t\) hours. So \(d = 55t\).

Answer:

\((2n - 1)(2n + 1)\)

Problem 14