CPhill

Here's one more way using polynomial division

(n + 1)^2                n^2 + 2n  + 1

_______   =          ___________

  n  +  23                 n  +  23

                  n    -   21

n + 23    [   n^2   +   2n     +   1   ]

                  n^2   +  23n

                 __________________

                             -21n   +    1

                             -21n   -  483

                            ___________

                                          484

n -  21    +        484

                     ________

                       n  + 23         

And note that, as GYanggg found, the largest n that makes the last fraction an integer is when n = 461

Very nice, GYanggg  !!!!!

This is a permutation

Out of 11 students....we want all the possible orders  in choosing  any 4 of them....this is given by :

P(11,4)   =  7920  different sequences in a week

5x * p  = x/5       divide both sides by 5x

p  =   x / [ 5*5x]       simplify

p  = 1/ 25    =  4/100   =   4%  

See this very nice answer that was  provided by Melody a while back....

https://web2.0calc.com/questions/circles-and-angles

See the graph here : https://www.desmos.com/calculator/jixmlpt6fz

The easiest way to do this is to find the area bounded by   y  = -2x + 6,  x  = 0   and y = 0    ....and from this subtract the area bounded by x + y  = 2, x = 0 and y  =0

For the first area....we have a triangle with a height of 6  and a base  of 3....so....the area  is  (1/2)(3)(6)  = 9 units^2

For the second area....we have atiangle with  a  height of 2 and a base of 2.....so....the are   is (1/2)(2)(2)  = 2 units^2

So....the area of the polygon is just    [ 9 - 2 ]  =   7 units^2

The largest denomination in US circulation is the $100 bill

A $100 bill is .0043 inches thick (.10922 mm), 6 inches wide (152.4 mm) and 2.5 inches tall (63.5 mm)

So the volume of one bill is  (.0043) (6) (2.5)  =  .0645 in^3

And we need  10000 of these to  make a million dollars

So....the volume of 10000 of these is of these is  (10^4)(.0645)  = 645 in^3

And the volume of your briefcase is  (17)(12)(3.5)  = 714 in^3

So.....you could (theoretically) fit all the money in your case

I leave the layout to you....!!!!!

If the last  function is supposed to  be  -³√x,  then  the  3rd graph is correct

We have

C(59, 5)  * C(35, 1)    = 175,223,510  possibilities

I think we have this  :

(x - 4)  ( x + 9)                (x - 4)  ( x + 9)

___________      =        ___________

   x^2  - 1                        (x - 1) ( x + 1)

The numerator has no effect upon the vertical  asymptotes

We will have a vertical  asymptote when the denominator   = 0

Note that when  x  = 1    or  x  = -1......one of the factors in the denominator will =  0.......so  ....these are the vertical asymptotes