Simone paid $12 for an initial year's subscription to a magazine. The renewal rate is $7 per year. This situation can be represented by the equation y = 7x + 12, where x represents the number of years the subscription is renewed and y represents the total cost, in dollars.

Step-by-step explanation:

Step one:

Simone paid $12 initial subscription

The rate renewable = $7 per year

let the number of years be x

and the total amount be y

the linear function/expression for the total amount is represented using the equation of line

i.e y=mx+c

where

     m= gradient = $7

     x= independent variable

     c= constant, $12

this is also given as

y=7x+12

Step two:

let's assume the plan is for 3 years, that is x=3

then

y=7(3)+12

y=21+12

y=33

$33

For any number of years, just put x=the number of years and solve

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

  answer:

  write 548 as 500 + 40 + 8. multiply each addend by 5. then add the three products to get 2,740.