For this case, we must find the equation of the line.
The generic equation of the line is:

The slope of the line is:

Substituting values we have:

Rewriting:

We now choose an ordered pair:
(xo, yo) = (0, 12)
Substituting values we have:

Rewriting the equation:

For 20 visits, we evaluate the equation when x = 20.
We have then:
Answer:
The discounted entrance fee is 1.5$. The total cost is 42$ after 20 visits
It's a quadratic equation. Solve it through factorisation.
5s^2 - 14s - 3 = 0
(5s + 1)(s - 3) = 0
5s + 1 = 0
or
s - 3 = 0
Therefore
s = -1/5
or
s = 3
The answer is
AB = 6.
External value x (external value + internal value) =
External value x (external value + internal value) of the other side
Substitute, transpose, and simplify.
TA x (TA + AB) = TC x (TC + CD)
10 x (10 + (x + 2)) = 8 x (8 + 12)
120 + 10x = 160
10x = 40
x = 4
To find AB: x + 12; x = 4
AB = x + 2
AB = 4 + 2
AB = 6
What are you confused by?