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Yes, https://snag.gy/3AP2wT.jpg

Before you say anything, yes I did try. I still can't do it. My answers never seem to look correct. I only tried the first one.

Is there a graph?

Thank you!!

Performing some polynomial division

                 4x^2  + 3x  - 2

2x +  1    [ 8x^2  + 10x^2  - x  - 2  ]

                 8x^2  +   4x^2

                ___________________

                               6x^2 - x

                               6x^2 + 3x

                               ____________

                                         -4x - 2

                                         4x -  2

                                       ________

The length is in red

Maybe another slight sign error.....???

Slope

[ -1 - 2 ]  / [ 2 - - 3 ]  =  -3/ 5

Using  (2, -1)  we have

y  = (-3/5) ( x - 2)  - 1        multiply through by the denominator of the fraction ⇒  5

5y = -3(x - 2) - 5     implify

5y  = -3x + 6 - 5

5y  =   -3x + 1     add 3x to  both sides

3x + 5y   =  1

Note that we can check to see if this is true...plugging in the original points should both make sense

3(2) + 5(-1)  =  1 

6  - 5  = 1         is true     and

3(-3) + 5(2)  =  1   

-9 + 10  =  1         is also true

OK....but be careful with this method..it isn't foolproof in all cases

For instance

y  = 3x       and y   = (1/4)x

Putting  0   into the first returns 0  

So  (0,0)  is on the first graph

So....putting the "returned" value of 0  into the second graph gives us back the original value of 0

So...these would appear to be inverses....but they are not

Using the foolproof method

3 [ (1/4)x ]  =    (3/4) x

This isn't   "x"......so....we can stop here....they are NOT inverses  !!!

I think I prefer the first method but its nice seeing 2 different ways . I will make notes of these! Thank you for showing me both. 

OK...we can use either point....using  ( -2. 6)  we have

( y - 6)   = -2 ( x -  -2 )

( y - 6) =  -2 (x + 2) ⇒   last choice

They were just trying to trick you......!!!!!

Here's the foolproof method :

Using 

(1/3)x  -  5      and    3x + 15

Put the second function into the first for each x and we have

(1/3) (3x + 15)  - 5 

x +  5  -  5

x

Now...put the first function  nto the second for each x  and we have

3 [ (1/3)x -  5 ]  + 15

x - 15  +  15

x

If we get an x in each case.....the functions are inverses  !!!!

Yes, but these were the options i have  

y−2=−2(x+6)

y−2=2(x+2)

y−2=−2(x+2)

y−6=−2(x+2)

I believe you made a slight sign error, hoiuu.....check this out

Slope =   [ -2 - 6 ]  / [  2 - - 2 ]   =   -8/4    = -2

So......using  ( 2, -2)  we have

( y - [-2 ] )  =  -2 ( x -  2 )  =

( y + 2) =  -2 ( x -  2)

I am most definitely going to use your feedback for any future problems and make sure to always check my problems afterward! I appreciate the tips and tricks, it has and will help me. Also, yes I really do enjoy learning and I do want to make sure I fully understand everything just so for my own knowledge as well as to just learn new things. I really appreciate you helping me on this, you explained everything clearly that made me understand so it was super easy , and now I can use this knowledge you gave me for any other problems! Thank you.

I would like to learn the foolproof method if you dont mind explaining,I think it would really help me.

We have    7 + 5 + 9   =   21 equal parts

And B's donation was  5 of these

So

(5/21) * 42000   =  $10000 

Slope  =  [ -1 - 5 ] /    [  -2 - 6 ]  =  -6/-8 =  3/4

Using   (6,5)  we have

( y - 5)  =  (3/4) ( x - 6) 

P. S.   ....I'm glad to see that you are trying to work toward the answers instead of just  accepting them blindly...!!!

Put 15  into the original function and we get 0  back

So

(15, 0)  is on the original function

So....0  should return 15 in your proposed inverse....so

3(0)  +  15  =  15  ....correct  !!!

Note...this isn't foolproof....but if given a list of proposed inverses...it should test out 

There is a "foolproof" method  [ if you are interested.... ]

Thank You! I have another question , same like this one if I could check with you ?

What is the inverse of the function?

f(x)=1/3x−5

f−1(x)=3x+15

f−1(x)=−1/3x+5/3

f−1(x)=−1/3x+5

f−1(x)=−3x+5/3

I think the answer would be A , f−1(x)=3x+15 ?

Yes thank you!

Correct  !!!!

Note....here's how you can check your solution

Put  a value  in the first equation...I'll choose  3...  and we get - (4/3) * 3  + 2  =  -4+ 2  =  -2

So...the point ( 3, -2)  is on the graph

The inverse "reverses" the   coordinates....so the point (-2, 3) should be on the inverse graph

So...putting -2 into your inverse and we get

-(3/4) (-2)  +  3/2  =

6/4 + 3/2  =

3/2 + 3/2  =

3  !!!!!

So   ( -2, 3)  shows that your inverse solution is correct  !!!!

Good Job  !!!!

We have two  equations, here

x - 500  = 8           and                       - ( x - 500)  =  8

Add 500 to both sides                          Simplify

x  =  508                                              -x + 500  = 8

                                          Add x to both sides. subtract 8 from both sides

                                                                   492  = x

So   [ min. max ]   =   [ 492, 508 ]  ⇒  "C"

We don't need much math here, hoiuu

Total cost  =   Variable Cost  + Fixed Cost

The Variable Cost  =  25 times "x" number of days  rented   = 25x

The Fixed Cost  = 50    [ this amount is paid no matter what ]

So.letting the Total Cost  = y

y  = 25x + 50

Does this make sense  ???

based off your steps the second one would be -3/4x+3/2 ? Am I correct?

Slope  =   [ 40 - 55 ] / [ 3 - 0 ]  =    -15 /  3  = - 5

Equation of line using  (0 , 55)

y =  -5x + 55     add 5x to both sides

5x + y  =  55

Correct. hoiuu  !!!!!!