1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
y=15,000+1.5x
1.5x = y-15,000
X=y-15,000/1.5
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
X=g(y) y-15000/1.5
since we generally use the letter x for the variable of a function, we write g again as:
G (x) x-15000/1.5
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
G(600,000)=60,000-15,000/ 1.5=45,000/1.5 =30,000
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation
(10+2x)(8+2x) = 120
4x^2 + 36x + 80 = 120
x^2 + 9x + 20 = 30
x^2 + 9x - 10 = 0
(x+10)(x-1) = 0
x = 1 inch dimension
The weight is proportional to the price. So if 10lb cost $18.24, quarter as much (2.5lb) would cost four times less($18.24÷4=$4.56).
Answer:
z = -166
Step-by-step explanation:
1. Subtract 3 from both sides to get z/2 = -83
2. Multiply 2 by both sides to get z = -166
z = -166
