Can you form a right triangle with the three lengths given? why or why not?
5 cm, 12 cm, 13 cm

no; 5^2 + 12^2 =/ 13^2

no; 5 + 12 =/ 13

yes; 5 + 12 = 13

yes; 5^2 + 12^2 = 13^2

A) If we assume the service charges are a one-time charge, we can let x represent the number of days of rental and a(x) and b(x) the charges for company A and company B, respectively. We are given the initial value and the rate per day in each case, so we can simply write down the equations:

... a(x) = 15 + 35x

... b(x) = 10 + 42x

B) Company A charges less for any rental lasting 1 day or longer. The total for the 1st day (50 vs 52) is less, and the rate per day is less for company A.

C) The difference in cost is ...

... b(x) - a(x) = (10 +42x) -(15 +35x) = 7x -5

so for 10 days, company A costs 7·10 -5 = 65 dollars less