CPhill

Simplify as

-mn - 3m  + 15n  +   ____

- m ( n + 3)   +  15 (n  + 3)  =

( 15 - m) ( n + 3)

-mn - 3m  + 15n  +  45

[a + 2 ]  / [ a + 1]  = b / 3

3[a + 2] = b[a + 1]

3a + 6  = ab  + b

ab - 3a + b  =  6      multiply  the coefficients on a,b = (-3)(1)  = -3   and add to  both sides

ab - 3a + b - 3  =  6 - 3      factor the left side, simplify the right

(a + 1) (b - 3)  =  3

   a            b

  -4           2

  -2           0

   0           6

   2           4

s10  =   10a1  + (10 * 9)d / 2

s20   =   20a1  + (20 * 19)d / 2

So

0  =  10a1  + 45d    →  0  = -20a1 - 90d       (1)

1/5  = 20a1  +190d      (2)

add (1) , (2)

1/5  = 100d

d = 1/500

And

0  = 10a1 + 45(1/500)

10a1  =  -45/500

a1  = -45/5000  =  -9/1000

s70  =  70(-9/1000)  + (70 * 69)/2 * (1/500) =    -630/1000 +  2415 / 500  = 21 / 5 

\(2 + \frac{6}{7} +\frac {18}{49} + \frac{54}{343} + 1 + \frac{2}{14} + \frac{3}{98} \)

Rearrange as

1 + 2 + 6/7 + 2/14 + 18/49 + 54/343 + 3/98   = 

1 + 2 + (6/7 + 1/7)  +  18/49 + 54/343 + 3/98   = 

1 + 2 + 1  +   (126 + 54) / 343  +   (1.5) / 49   =

4  + 180/343  +  7(1.5) / 343   = 

4 + (180 / 343) + (10.5) /343  =

4 + (1800 + 105)  / 3430  

4 + 1905 /3430

4 + 381/686  =

3125 / 686

.036 / .4  = 9/100

,0000324 / .036  = 9 /10000

Not geometric !!!!

BC = 1

AC = sqrt 3

AB = 2

Construct a circle at B = (1,0)  with a radius of sqrt 2

The equation of the circle  is   (x -1)^2 + y^2  = 2

To find the intersection of BD and AC  let  x = 0

Then y  = 1

So D =  (x ,y)  = (0, 1)

BD  =  radius of the circle  = sqrt 2

DC  =1

The probability that BD < sqrt 2      is       DC / AC   =  1 / sqrt 3 ≈  57.7 %

https://web2.0calc.com/questions/algebra_19078

Sum =  [first term + last term ] * [number of terms / 2]

Nuimber of terms =   [6021 - 21 ]  / 6   +  1    =  1001

Sum =   [ 21 + 6021 ] *  [ 1001 / 2 ] =   3,024,021

https://web2.0calc.com/questions/coordinates_60311

https://web2.0calc.com/questions/help-meee_22#r1