An internet company charges a one-time setup fee of $44.99 and a monthly fee of $29.99 for internet service. the company is offering a 25% discount on the monthly fee for the first year. part a: write an expression to determine the cost, after the discount and before tax, of m months of service during the first year. (remember that an expression is just like an inequality except there is equal sign than a less than or greater than sign and plz show work) part b: an 8% sales tax is added to the total cost. rewrite the expression in part a to include the sales tax. part c: what is the total amount a customer will pay, to the nearest cent, including tax, for the first 4 months of internet service with the internet company? (try to explain a little for these questions if u can)

PART A :

let cost, after the discount and before tax, of m months = x

The cost will have two parts

1) a one-time setup fee of $44.99

2) monthly fee for m months including discount

monthly fee  = $29.99

for m months , fee = 29.99 × m = 29.99m

from the given statement "m months of service during the first year" we can say that discount of 25% will be applicable  for m months.

for m months , fee after pplying discount = 29.99m - 25% of 29.99m

                                                                    = 22.4925m

so total cost = a one-time setup fee + monthly fee for m months including discount

hence required expression is as follows

⇒ x = 44.99 + 22.4925m       expression 1

where x  is cost in $ and m is number of months kess than or equal to 12

PART B :

let total cost including sales tax =  y

so y = x + 8% of x       [ where x is cost calculated in part A ]

⇒ y = x + 8x/100  

⇒ y = 108x/100 = 1.08x

⇒ y = 1.08 ( 44.99 + 22.4925m )         [ substituting value of x from expression 1 ]

⇒y = 48.5892 + 24.2919m  

so cost after including sales tax will be given by following expression

y = 48.5892 + 24.2919m             expression 2

where y is cost in $ and m in number of months less than or equal to 12.

Part C :

As total cost including sales tax is represented by expression 2 that is

y = 48.5892 + 24.2919m

when m = 4 months

y = 48.5892 + (24.2919 ×  4)

y = 48.5892 + 97.1676

 = 145.7568.

so the total amount a customer will pay including tax, for the first 4 months of Internet service  will be $ 145 and 76 cents.

the above all equations will only hold true for first years , after that discount will not be in place.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.