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I don't think heureka's method will work on very large numbers such as: nC13=153,121,753,939,078,375

There is, however, a method that will work on any n and it goes as follows:

Take the above answer=153,121,753,939,078,375 x 13! =953,492,346,711,122,973,955,200,000

Now, take this huge last number and take the 13th root of it as follows:

953,492,346,711,122,973,955,200,000^(1/13) =118.941. round off this to 119. Then add 13 to it, or

119 + 13 = 132. Now take the average of [119 + 132] / 2 =125.5. Discard the fractional part and keep the integer part or 125, which is answer to n above.

Note: This method will work on ANY n, no matter the size.

jelly donuts

Ohhh I get it. It's d. Because the derivative of that is f'(x) = 5 so whatever value of x will always give us 5. Thanks for helping me through that :) 

Let's do a little detective work.....

x^2  - 16     factors as   ( x + 4)  ( x - 4)   so we have vertical asypmtotes at   x  = - 4  and x  = 4

This rules out the first graph

Note that when  x  = 0    the y intercept  =  -6/16  =  3/8   .....this rules out the third graph which has a negative y intercept

Now.....let's find the  zeroes of the function  (where the grpah  intercepts the x  axis ) by solving this

x^ 2  + 5x  - 6  =  0

(x - 1) ( x + 6)  = 0

Setting both of these to 0 and solving produces  x = 1  and x  = -6

Note that  the second graph meets all the criteria

1. Vertical asymptotes at  x  = -4  and x  = 4

2. Positive y intercept

3. Zeroes (roots)  at  x  = -6   and  x  = 1

Second one

https://es.symbolab.com/solver/functions-calculator/f%5Cleft(x%5Cright)%3D%5Cfrac%7Bx%5E%7B2%7D%2B5x-6%7D%7Bx%5E%7B2%7D-16%7D

14.

d^2 - 5d  + 6               d^2  - 4d  - 5

__________    +      _____________

d^2 + d  - 6                d^2  +  3d  + 2

(d - 3) (d - 2)               (d - 5) ( d + 1)

__________       +      ___________

(d + 3) ( d - 2)              (d + 2) ( d + 1)

d- 3                            d - 5

____      +               ______   

d + 3                         d  + 2

(d - 3)(d + 2)  +  ( d - 5) (d + 3)

________________________

     (d + 3)  ( d + 2)

[ d^2  - d - 6  +  d^2  - 2d -  15 ]

__________________________

     ( d + 3)  ( d + 2)

2d^2  - 3d  - 21

____________

 ( d + 2)  ( d + 3)       

thanks

11.

x^2 +7x  + 10               x^2  - 3x  - 18

___________      *     _____________

    x + 3                          x^2 + x  - 2

( x + 5) ( x + 2)  *  (x -6) ( x + 3)                 ( x + 5) ( x - 6)

_________________________        =      ____________            x cannot be  -3, -2  or 1

      (x + 3)   (x +  2)  ( x  - 1)                             ( x  - 1)

12.

  2x                   x + 7

  ___      -         _____

  x - 7                   x

(2x * x)   -  (x + 7) (x - 7)                      2x^2  - ( x ^2- 49)                        x^2  + 49

____________________     =             ______________    =                _________  

    x  ( x - 7)                                               x ( x - 7)                                  x ( x - 7 )

13.

n^2  +  3n + 2                       2n

___________   -                 ______

 n^2  + 5n + 6                      n + 3

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

____________          -             ____

 ( n + 3) ( n + 2)                       n + 3

( n + 1)                          2n

_______           -          ______

 ( n + 3)                        (n + 3)

( n + 1  -  2n )

___________

    n  + 3

 1 - n

_____

 n + 3

x^4  - 2x^2   - 8  = 0        factor

(x^2 - 4)  (x^2 + 2)   =0

(x - 2)  (x + 2)  (x^2  + 2)  = 0

Set the   factors   = 0    and solve

x  - 2 = 0      x +  2  =0                     x^2  + 2   = 0

x  = 2            x  = -2                         x^2   = -2        take both roots

                                                         x  = √-2        x  = - √2

                                                          x  = i√2        x  =    -i √2

I agree, Julius......none  = 5   when  x  = 2

If the third one were  x^2  +  x.....it would work.....

ok what do you want to talk about

Chord  = AC

Tangent  =  {Purple line at top }

Radius  = {Orange line from the center }

Secant  = {Light Blue-Green Line }

Diameter  = BD

Minor arc  = ABC

Major arc  = ACD

8.   We have       

same  degree polynomial

____________________

same degree  polynomial

In these situationns, NSS....the horizontal asymptote is just the ratio of the coefficient on the highest power variable in the numerator/ the coefficient of the highest power variable in the denominator  =  -2 / 8    =  -1 / 4

10.

t^2  + 4t  - 12              (t -2) (t + 6)                  t  + 6

___________     =      _________      =      __________      and t cannot =  -2   or 2      (third answer )

      t^2  - 4                  (t - 2) (t + 2)                 t + 2

CPhill: Would heureka's method work on large numbers such as: nC4 =3,921,225, where n = 100 ???.

4.  Here's the first.....the asymptotes  are also shown

https://www.desmos.com/calculator/krknmtrhap

6.       

                 x - 8

        __________               factor the denominator

        x^2 + 5x  - 6

                x  - 8

            __________

            (x + 6) ( x - 1)

The two  values that  make the denominator  = 0  are    x  = -6   and  x  = 1

So.....these are the points of discontinuity  (last answer )

OK

We have that

y  = k wx  / z      and we know that  y  = 320   when  w  = 6, x = 20   and z  = 3

So   we need to  find  the proportionality constant, k......so we have.....

320  = k (6) (20)  / 3

320  = k *120 / 3

320  = k * 40       divide both sides by 40

8 = k

So......the correct answer is

y  = 8 wx /  z

Here's the second one

xy  + 16  = 0 

https://www.desmos.com/calculator/r8slfagryd

Thanks Arriane!! you too

Yes sir it does

Thank you sir

Remember, Manuel.....

Perimeter  =  2W + 2L        and Area   = LW

So  

40  =  2W + 2L         divide through by 2

20  = W + L     subtract W  from both sides

20 - W  = L         (1)  

And

96  = LW       sub in (1)   for    L.....and we have

96  = (20 - W) * W       simplify

96 = 20W  - W^2       add W^2 to both sides, subtract 20W from both sides

W^2 - 20W  +  96  = 0        factor.....-8 and  - 12  are what we need

(W  - 8) ( W - 12)   = 0

Set each factor to 0  and solve for W

W  = 8    or   W  = 12

So, Manuel....we can let  W  = 8....so

 L = 20 - 8  = 12

So....Width  = 8   and Length   = 12

Check  - perimeter =  2W  + 2L  =   2(8)  + 2(12)   =  16 + 24  = 40

area  = 8 * !2   =  96     

Hope that helped......!!!!

yeah ok