The spending limit on John's credit card is given by the function f(t) = 15,000 + 1.57, where x is his monthly income. 1-13) $60,000, his monthly income is The variable x represents in the inverse function. If John's spending limit is​

Answers

Answer 1
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

Related Questions

Help ASAP pls im giving away all of my points!!
Do you think you would have liked to have been a participant in Biosphere 2? Why or why not?

Answers

Answer:

NO. It sounds terrifying, and nearly deadly with the lack of oxygen..all the pollution from things like cars and factories, the littering, the deforestation, the animals that are either endangered or extinct.

Step-by-step explanation:

Consider the following graph.
The x y coordinate plane is given. The curve begins at (0, 5) goes down and right becoming less steep, changes direction at (1, 2) goes up and right becoming more steep, goes through the approximate point (2, 3.1), goes up and right becoming less steep, changes directions at (3, 4), goes down and right becoming more steep, sharply changes direction at (4, 1), goes up and right becoming less steep passing through the approximate point (5, 4.2) and ends at (6, 6).
(a) Find the interval(s) on which f is increasing. (Enter your answer using interval notation.)
(b) Find the interval(s) on which f is decreasing. (Enter your answer using interval notation.)
(c) Find the open interval(s) on which f is concave upward. (Enter your answer using interval notation.)
(d) Find the interval(s) on which f is concave downward. (Enter your answer using interval notation.)
(e) Find the coordinates of the point(s) of inflection.
(x, y) = ( )

Answers

a)Function is increasing in intervals (1,3) and (4,6).

b)Function is decreasing in intervals (0,1) and (3,4).

c)Graph is concave upward in the interval (0,2) and (3,5).

d)Graph is concave downward in the interval (3,4).

e)Points of inflection are x=3 and x=5.

Let us make the graph of the given function. In the graph, We have connected points linearly, please consider it as a curve.

What is the point of inflection?

The point of inflection or inflection point is a point in which the concavity of the function changes.

Therefore, From the attached graph, we can see that:

a)Function is increasing in intervals (1,3) and (4,6).

b)Function is decreasing in intervals (0,1) and (3,4).

c)Graph is concave upward in the interval (0,2) and (3,5).

d)Graph is concave downward in the interval (3,4).

e)Points of inflection are x=3 and x=5.

To get more about graphs visit:

https://brainly.com/question/1869945

Answer:

a.(1,3)U(4,6)

b.(0,1)U(3,4)

c.(0,2)

d.2,6

e. 2,3

Step-by-step explanation:

Looking at graph and finding intervals.

Will give brainiest if right

Two trains started moving at the same time, train A from Boston to
New York, and train B from New York to Boston. The distance
between the train stations in New York and Boston is 240 miles. The
average speed of train A is 60 mph, which is 3/4 of the average
speed of train B.
How soon will the trains meet?

Answers

Your answer would be after 1.7 hours

Which figures below have at least one acute angle? Mark all that appley ​

Answers

C and D

An acute angle is an angle less than 90 degrees.  

Answer

triangle and trapezium

Kim bought a lawn chair that had a ticket price of $25.00. She ended up paying $26.50 after tax. If she were to buy a $40.00 patio table, how much would she have to pay after tax?

Answers

Answer:

41.50

Step-by-step explanation:

you would have to minus the 26.50 and 25.00 and then you would get 1.5 so that's how much the tax is. you would still keep the zero tho bc if there is nothing after the 5 u add zero.

Can someone plz help. Will mark brainliest

Answers

Answer:

3. 73

4. 1500

Step-by-step explanation:

3. 7*9 = 63, 2*5 = 10, 63+10 = 73

4. 40*30 = 1200, 20*30 = 600 divided by 2 = 300, 1200+300 = 1500

Good afternoon or morning! Need some help with geometry.

Please only answer if you know the answer, the comment section is right below. Please don't waste my points!

Also, please show all of your work, you are trying to help me better understand the concept, not just give me the answer.

The image is down below. Show work! Thanks!

Answers

Answer:

x = 20.2

Step-by-step explanation:

sin = opposite / hypotenuse

sin 63° = 18/xx = 18 / sin 63°x = 20.2

What is the median of the data set?



9
8.5
8
10

Answers

Answer:

8.5

Step-by-step explanation:

When you write out the data set, it looks like this:

5, 8, 8, 8, 8, 9, 9, 9, 10, 10

The median means the exact middle of the data set. In this case, it falls between the 8 and the 9, so the middle would be 8.5, so that's the median of the set. I hope this helps :)

Answer:

The median is 8.5

Step-by-step explanation:

The median is the middle number in a data set. For example, if you had a data set:

2, 2, 3, 4, 4

You would go forwards and backwards in the set until you found the middle number, which is 3. 3 would be the median.

However, if there is no middle number (there are an even number of points in the set), you add the two remaining numbers and divide it by two.

For example, if the final two numbers were:

2, 6

You would add 2 and 6 to get 8, and divide by 2, and you get the median 4.

In this set, we have

5, 8, 8, 8, 8, 9, 9, 9, 10, 10.

The final two numbers are 8 and 9, so you add 8+9=17, divided by 2 = 8.5.

Find the quotient of the following:
(12x^4- 3x^4+ 15x^2)
and ( - 3x)

Answers

Answer:

-4x³+x²-5x

Step-by-step explanation:

-4x³+x²-5x

Tom and Kim are playing a game in which they use a spinner with 10 sectors. One of the sectors says, "$0," four
say, "S100," three say, "$200," and two say, "$500." Use a table to show the probability distribution.

Answers

Answer:

It's C.

Step-by-step explanation:

The figure shows the dimensions of a rectangular storage room. Darnell
has boxes that are cubes with edges 1 1/2 ft long. What is the maximum
number of boxes that Darnell can fit in the storage room? Explain.
10 ft
6 ft
8 ft

Answers

The answer is 8I had dis
Its 8 i hope i responded in time

Impossible question please help

Answers

Answer:

x axis comes first before the y

Answer:

???? :( Its really impossible question for me

Answer asp

__% of 75 is 25

Answers

33% of 75 is 25... Hope that helps!!

What is the total surface area of the rectangular prism?

Answers

Answer:

286.5

Step-by-step explanation:

(3 x 7.5) x 2 = 45

(11.5 x 3) x 2 = 69

(11.5 x 7.5) x 2 = 172.5

45 + 69 + 172.5 = 286.5

Part A

Monica estimates the recipe makes about 5 cups of fruit salad,

Which explanation describes whether Monica's estimate is reasonable?

Not reasonable. Four fractions cannot equal more than 4 cups.

Not reasonable. The whole numbers add up to 3 so the total sum

cannot be 5 cups

Reasonable. The grapes and apples is about 2 cups and pears and

oranges is exactly 3 cups.

Reasonable. The pears and apples is about 3 cups and the grapes

and oranges is exactly 2 cups.

PLAY

(0)

Part B

What is the exact amount of fruit salad in cups?

cups

o

Enter your answer as a fraction or a mixed number.

Answers

Answer:

Part A: Choice 3) Reasonable. The grapes and apples is about 2 cups and pears and oranges is exactly 3 cups.

Part B: Exactly 4 11/12 cups

almost equal to 5 cups

Step-by-step explanation:

The missing part of the question is :

2 1/2 cups of pears. 2/3 cup of grapes 1 1/4 cups of apples 1/2 of orange slices .

Pears + apples

2 1/2+1 1/4 =

5/2 + 5/4

= 10+5/4

= 15/4

= 3 3/4 cups

Reasonable. The pears and apples is about 3 cups and the grapes

and oranges is exactly 2 cups. This statement is wrong.

Grapes and oranges

2/3 + 1/2

= 4+3/6

=7/6

=1 1/6 cups

grapes and apples

2/3 cup of grapes 1 1/4 cups of apples

2/3 + 5/4

= 8+15/12

= 23/12

= 1 11/12 cups

pears and oranges

2 1/2 cups +1/2 of orange slices

3 cups

Reasonable. The grapes and apples is about 2 cups and pears and

oranges is exactly 3 cups. this statement is true as shown above.

N.B the answer may vary due to the different measurements given in the missing part of the question.

Part B:

grapes and apples + pears and oranges

1 11/12 cups +3 cups

= 23/12+ 36/12

= 59/12

= 4 11/12 cups

What percent is equivalent to 0.25%

Answers

Answer:

the percent is 25% lol

Step-by-step explanation:

Decimal .25

percent 25%

fraction 1/4

Answer:

0.25

Step-by-step explanation:

Order the sides of each triangle from shortest to longest.

Answers

Answer:

FG, GH, FH

Step-by-step explanation:

H=180-100-50=30°

Since H is the smallest degree, the side opposite it (FG) is the shortest length.

Since F is the middle degree, the side opposite it (GH) would be the middle length.

Since G is the highest degree, the side opposite it (FH) would be the longest.

FG, GH, FH

Which statement correctly compares the spreads of the distribution

Answers

Answer:

From what I remember A is the answer but im  not sure.

Answer:b

Step-by-step explanation:t

Please help solve!
g(x) = 4x + 3
f(x) = 3x-4
Find (g o f)(5)

Answers

Answer:

(g o f)(5) = 47

Step-by-step explanation:

We are given a composite function:

g(x) = 4x + 3

f(x) = 3x - 4

We are supposed to find (g o f)(5), which really means g( f(x) ). So, we put the function of f(x) for every x in g(x), like this:

g(x) = 4x + 3

g( f(x) ) = 4(3x - 4) + 3

g( f(x) ) = 12x - 16 + 3

g( f(x) ) = 12x - 13

Now, we also need to evaluate for x = 5, like this:

g( f(5) ) = 12(5) - 13

g( f(5) ) = 47

Which expression shows 50 4 30 written as a product of two factors
10(5 + 3)
6(10 + 7)
6(1043)
10(5 + 2)

Answers

Answer:

The answers is 10(5 + 3)

I need help and NO LINKS

Answers

second graph, the other three are all the same(reflection) while number two is different and shows a translation

The county fair charges $1.00 per rode and an additional $3.00 to get in the fair. Write an equation to represent the total cost of attending the fair.

First identify the independent and dependent variables.​

Answers

Answer:

Step-by-step explanation:

It's independent

PLEASE HELP ME KSDAKJDSAJDJKS

Answers

Answer: x = 16

Step-by-step explanation:

60x - 60 = 900

60x = 960

60x / 60 = 960 / 60

x = 16

Please help fast....

Answers

Answer:

Step-by-step explanation:

Answer:

Volume = 1.25

Step-by-step explanation:

Length = 5 * 1/2 = 2.5

Width = 1 * 1/2 = .5

Height = 2 * 1/2 = 1

[tex]2.5 * .5 * 1 = 1.25[/tex]

help meee plss it’s timed !!

Answers

Answer:

i did it to its C

Step-by-step explanation:

mark me pls

Answer:

D

Step-by-step explanation:

use Pythagoreans theorem to solve (a^2+b^2=c)

Investigate the patern “13/1 family” of fractions. Use plenty of space to show what you find.

Answers

Answer:

2/1 of a family

Step-by-step explanation:



A roller coaster is being designed that starts at (0,22) and ends at (19,2),

Along the ride there is a relative minimum at (5,6) and a relative

maximum at (10,18). The roller coaster is almost finished but one

section is missing. Find the correct function that completes the roller

coaster so that the ride is smooth and continuous.

Answers

Answer:

The function is, f(x) = 6·sin((π/5)(x + 3π/2)) + 12

Step-by-step explanation:

The general form of equation of a roller coaster is given as follows;

y = A·sin(B(x - C)) + D

Where;

A = The amplitude = (18 - 6)/2 = 6

D = The vertical shift = 12

One revolution = 10 unit

∴2·π = 10 unit

Therefore, 10 = 2·π/B

B = 2·π/10

The phase shift = 3·π/2

Therefore, we have the function as follows;

f(x) = 6·sin(2·π/10(x + 3π/2)) + 12 = 6·sin((π/5)(x + 3π/2)) + 12

A classroom is 32 1/2 feet long, 30 feet wide, and 7 1/2 feet high what is the volume

Answers

Answer:

6000

Step-by-step explanation:

The answer options is is and is not

Answers

Answer:

Question 1 is a statistical question

Question 2 is not

Step-by-step explanation:

A statistical question is a question that can be answered by collecting data that vary

The Chemistry Club is experimenting with different mixtures of water with a

certain chemical to make fake snow.

To make each mixture, the students start with some amount of water, and then add

1/7 of that amount of the chemical, and then 9 more grams of the chemical. The

chemical is expensive, so there can't be more than a certain number of grams of the

chemical in any one mixture. How much water can you start with so that you don't

use up too much of the chemical?

a. 1/7x + 9 < 26.25

b. 9x + 1/7 s 26.25

26.25x + 9 = 1/7

C.

d. 1/7x + 26.25 39

Answers

Answer:

Suppose we have with x, the amount of water we use (in grams).

1/7 of this will be the chemical, then we have (1/7)*x grams of chemical.

Then we add another 9g of the chemical, then we have in total:

(1/7)*x + 9g of the chemical.

And we know that the chemical is expensive, so there can't be more than a given number of grams of the chemical, because of the phrase:

"...There can't be more than..."

We will have a relation like:

(1/7)*x + 9g ≤ something.

By looking at the options, we can see that "something" = 26.25 grams

then we will have the inequality:

(1/7)*x + 9g ≤ 26.25 g

Now we can solve this for x, the amount of water used:

(1/7)*x ≤ 26.25 g - 9g

x ≤ (26.25 g - 9g)*7

x ≤ 120.75 grams

This means that the maximum amount of water we can use is 120.75 grams of water.

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