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
A pharmacist has 40% and 80% of iodine solutions on hand. How many liters of each iodine solution will be required to produce 4 liters of a 50% iodine mixture?
.
Let x = liters of 40% iodine
then
4-x = liters of 80% iodine
Using algebra:
.40x + .80(4-x) = .50(4)
.40x + 3.20-.80x = 2
3.20-.40x = 2
x = 4 liters (40% iodine)
80% iodine:
4-x = 4-4 = 0 liters needed (80% iodine)
Answer:
C. (x + 2, Y - 3)
Step-by-step explanation:
C. (x + 2, Y - 3)
The answer would be -84.
Here are the steps I did.
1. Simplify 4 + 8 to 12 ( -7 * 12 )
2. Now lastly simplify and u get -84.
