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Solve for r:
1/(r^3 + 7) - 7 = -r^3/(r^3 + 7)

Multiply both sides by r^3 + 7:
1 - 7 (r^3 + 7) = -r^3

Expand out terms of the left hand side:
-7 r^3 - 48 = -r^3

Add r^3 + 48 to both sides:
-6 r^3 = 48

Divide both sides by -6:
r^3 = -8

Taking cube roots gives 2 (-1)^(1/3) times the third roots of unity:

 r = -2     or     r = 2 (-1)^(1/3)     or     r = -2 (-1)^(2/3)

Here is agraphical solution (I used to check my answer above):
 

https://www.desmos.com/calculator/gdlnsk708d

Painting the room = 1    whole job

Morgan rate =   1/10

Sophia rate  =  1/4

Rate x time = 1    job

1/10 x   + 1/4 y  = 1/2      and

1/10 y  +  1/4 x  = 1          solve for x,y

Multiply top equation by - 2.5

(-2.5)/10 x   - (2.5/4) y = -1.25   

-1/4 x  - 5/8 y =  -1 .25

  and add to the second equation to get

1/10 y  - 5/8 y = -.25    solve for y

4/40 y - 25/40 y = -.25

-21/40 y = - .25

y =  10/21  hr                           Substitute this into one of the origianl equations to find 'x'

1/10  (10/21) + 1/4 x = 1

1/21 + 1/4 x = 1

1/4 x = 20/21

x = 80/21                                         x,y =  ( 3 17/21  ,  10/21) 

Hi Rudram, I can't really understand your question. May you use the latex thanks

-Evan

Rom, do you have the ability to contact Melody or anybody who has the permission to delete that post?

I have an email prepared to be sent to my teacher, but its best if that post is removed.

Face it.. you're doomed.

DOOOOOOOMED

I don't want to get in trouble for something I didn't do, PLEASE I am begging with my life!

Thank you guys, although I couldn't tell what grammar edits you made though...

C and D

Thank you so much ^_^

And you'll wind up with this....sooooN would be?

Start with the 18  14 column and build from there

18-4 = 14

14-4 = 10

10 - 4 = 6 .....

Thank you so much 

The sequences with the following terms are:
First term = 1
nth term    = 91
All term must be integers.
Common difference          91 as a term
1                                          91st. term
2                                          46th term
3                                          31st term
5                                           19th term
6                                           16th term
9                                            11th term
10                                          10th term
15                                           7th term
18                                            6th term
30                                            4th term
45                                            3rd term
90                                            2nd term
As you can see, there are 12 sequences which start at 1 and have 91 as one of terms and are all integers.

1. Triangles ABD and triangle CBD are congruent by SSS congruence. So, we know that x = Angle DCB = 30 Degrees

THANK YOU - wolf

The "generating function" appears to be:
a(n) =n * 3 + 1. So:
First term =1 * 3 + 1 = 4
2nd term   =2 * 3 + 1 = 7
3rd term    =3 * 3 + 1 = 10......and so on. 
.
.
. 
250th term =250 * 3 + 1 = 751 toothpicks.

I AM SOO SRRy, I forgot the digram, here it is,

If I understand your question correctly, the "generating function" is as follows:

a(n) =[a(n - 1) * a(n - 2)] - 1. So, in order to get 3,000 for the 3rd term, you have the following:

x * 2,000 - 1 = 3,000

x =3,001 / 2,000

x =1.5005 - This is the only positive real number that will give 3,000 as the 3rd term. After that the sequence "blows up"!, in the sense that the 4th term will be : 2,000 x 3,000 - 1 =5,999,999......and so on.

No diagram?

If each stage takes 3 toothpicks,  250 x 3 = 750

Thank you SO Much !!!

I think that would be more helpful   

xxxxxxxxxx

2+3(n-1)  = 2 + 3(25-1) = 74

I also can write the program that reverses the given number but my main target was to write the number reverser using math.