ElectricPavlov

from 9 to -84   is  27 more of the common diference , d , of the sequence

(-84 - 9 )/27 =  -93/27 = -31 / 9

from 5 th tem to 23 is addition of 18  d's

  9 + 18 ( -31/9) = -53

I think only n =1    and  n= 2   and n = 4 , 8 , 12    ...multiples of 4

Here is HOW:

2/5  =  x / 800      multiply both sides by 800

2/5  * 800 = x = 320

2x^2 - 12x     + 2y^2 + 4y      =   20       arrange this into standard circle form  ( (x-h)^2  + (y-k)^2   = r^2 

                                                                     by completing the square for  x   and y      the    radius * 2 = square side length....the area = s * s

divide by 2

  x^2 - 6x        +   y^2 + 2y      = 10         now complete the square for x and y        Can you take it from here? 

6   10    16   26    30  36   40 

Vertex form of parabola

y = a ( x- 2)^2 + 4        sub in point to calulate  a

-11 = a(-1)^2 + 4

 a = -15

y = -15 (x-2)^2 + 4

  = -15x^2 + 60x-56

n = 150

150 ( 301+ 599)/2 = 450*150 = 67500

Smallest interior angle     136       exterior angle = 180 - 136 = 44 degrees

Largest interior angle       144       exterior angle = 180 -144 = 36 degrees

the exterior angles sum to 360

36      +     36 + d      +   36 +2d     +   36 + 3d      +    36+4d     +    36 + 5d    +    36 + 6d    +    36 + 7d    +   44   = 360

8(36) + 28d + 44 = 360

d =1

 k = 9

Interior angle sum:

(n-2)(180) = 7(180) =1260                 1260 / 9 = 140  (the average)            Check!

t = track length

5/6 * t =   40      multiply both sides by 6/5

t = 40 * 6/5 = 48 meters

x + 3y = -5               re arrange to y = mx+b from:

y = -1/3 x - 5/3         slope = -1/3     ( parallel slope is the same)

y = -1/3 x -  b           sub in the given point to calculate 'b'

2 = -1/3 (-7) + b       shows b = - 1/3

y = -1/3 x - 1/3         multiply by 3 to get rid of fraction

3y = 3x - 3

3x -3y = 3                 then   B - A =  -3 - 3 = - 6