Mary has gone into a department store with two coupons. one coupon is good for 20% off of the total not including tax. the other coupon will take $15 off of her pre-tax total. if f(x) = 0.8x calculates the total after the 20% off coupon and g(x) = x – 15 calculates the total after the $15 dollar off coupon, determine g(f( then describe what g(f(100)) represents in the context of this problem.

The value of g(f(100)) is 65.

Step-by-step explanation:

It is given that one coupon is good for 20% off of the total not including tax. The other coupon will take $15 off of her pre-tax total.

The given functions are

where, f(x) calculates the total after the 20% off coupon and g(x) calculates the total after the $15 dollar off coupon.

We need to find the value of g(f(100)).

Substitute x=100 in the above function.

Substitute x=80 in function g(x) to find the value of g(f(100)).

Therefore, the value of g(f(100)) is 65.

g(f(x)) represents the value goods after applying both coupons consecutively.

Therefore, g(f(100)) represents the value of $100 goods after applying both coupons consecutive is 65.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet