1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
____ [38]
3 years ago
8

Let $f(x) = 2x + 7$ and $g(x) = 3x + c$. find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

Mathematics
1 answer:
boyakko [2]3 years ago
5 0
Let me just rewrite the details in a more understandable manner

f(x) = 2x + 7
g(x) = 3x + c
f( g(x) ) = g( f(x) )

Proceeding to the problem, we have to find the value of c by making use of the relationship written by the third equation. The notation f( g(x) ) means that you have to replace x with g(x). So, you would have incorporate one equation to the other, and vice versa. By equating them, we can determine x. Let us start with f( g(x) ) .

f( g(x) ) = 2(3x + c) + 7
f( g(x) ) = 6x + 2c + 7

Next, we do the similar thing to g( f(x) ).
g( f(x) ) = 3(2x+7) + c
g( f(x) ) = 6x + 21 + c

Then, we equate both simplified equations
6x + 2c + 7 = 6x + 21 + c

Let's simplify further by placing c on one side, and the rest on the other side:
2c - c = 6x - 6x + 21 - 7
c = 14
You might be interested in
Alexandra has 78 emails in her box. she deletes 47 emails. How many emails are left in her box? Draw jumps and label the number
labwork [276]
There are 31 emails left in her box. Hope this helps!! :)
7 0
3 years ago
Read 2 more answers
Which fraction is equal to 1/5.<br> Can someone please answer this question
NeX [460]

Answer:

2/10

20/100

5/25

Step-by-step explanation:

I hope this helps you

4 0
2 years ago
Read 2 more answers
$9000 is 60% of what number?
yawa3891 [41]

Answer:

15000

Step-by-step explanation:

We have, 60% × x = 900 or,  

60

100

× x = 9000

Multiplying both sides by 100 and dividing both sides by 60,

we have x = 9000 ×  

100

60

x = 15000

If you are using a calculator, simply enter 9000×100÷60, which will give you the answer.

3 0
3 years ago
Elise drinks 2 cups of water per hour on Friday. At a certain time, she has already had 4 cups of water. On Friday, Jacob drinks
ziro4ka [17]

By finding and solving a system of equations, we will see that after 2 hours they will drink the same amount of water.

<h3></h3><h3>How to write and solve the system of equations?</h3>

For Elise, the number of cups consumed after the 10:00 am is:

y = 2*x + 4

Where x is the number of hours after 10:00 am.

For Jacob, the number is:

J = 3*x + 2

Then the system of equations is:

y = 2x + 4

y = 3x + 2

To solve it, we use the fact that the variable y is already isolated in both equations, so we can write:

2x + 4 = y = 3x + 2

2x + 4 = 3x + 2

Solving for x we get:

4 - 2 = 3x - 2x

2 = x

After 2 hours, Elise and Jacob drink the same amount of water.

If you want to learn more about systems of equations, you can read:

brainly.com/question/13729904

5 0
2 years ago
What is pythagoras thoerem​
tankabanditka [31]

Answer:

The Pythagorean theorem is a form of equation when dealing with the 3 sides of a right triangle. The formula is a^2 + b^2 = c^2. c^2 would be the side that equals the same amount of the other sides combined. Or a hypotenuse.

Note:

Hope this helps! Good Luck!

<em>-kiniwih426</em>

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is the slope of a line that is perpendicular to a line whose equation is 3y=−4x+2 ?
    12·1 answer
  • Entrance to a state park costs $6 per vehicle plus $2 per person in the vehicle how much would it cost for a car with 2 people t
    6·1 answer
  • Math help mee plzzzzzz THERE IS A ATTACHMENT SO WAIT AT LEAST 30 SECONDS PLZZZZ
    5·1 answer
  • A graph with a ? slip deceases from left to right
    6·1 answer
  • What is the equation of the line that passes through the point (3,6) and has a slope of 4/3
    14·1 answer
  • Don Walsh and Jacques Piccard:
    9·1 answer
  • You work in a furniture repair shop and are taking apart an old table to refinish it. You are trying to remove a bolt with a wre
    10·1 answer
  • Girl what the hell is this someone help
    8·1 answer
  • You are a contractor who is installing a new kitchen floor with square tiles. The dimensions of the rectangular kitchen floor ar
    11·1 answer
  • REVIEW HELP PLS
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!