CPhill

Thanks, Knockout.....!!!

"Reduce" means  "subtract from"....so....

43  - l -8 + 6  l

Thanks, tertre   !!!!!

Correct, hoiuu  !!!

C (182, 180)  =

 182!

_________________  =

(182 - 180)! (180 ) !

182 * 181

__________  =

     2!

91 * 181  =

16,741

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  !!!

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  !!!!