CPhill

8b + 2  = 10b    subtract 8b from both sides

2  =  2b            divide both sides by 2

1  = b

3 = √ x  -  1    add 1 to both sides

4  =  √x          square both sides

16  = x

5n + 34n  = 2

39n  = 2     divide both sides by 39

n  =  2 / 39

If the dilation is centerd at the origin, we have

(-4,3 ) → (0 + 3(-4) ,  0 + 3(3) ) →  (-12, 9 )

3375 / 225  = 15 theatres

14 choose any 8   = 3003 different groups

14 x 9 x 8  =  1008 in^3

I guess we have this  :

12 ( 5 + 1/2)  =

12(5)  + 12 (1/2)  =

60   +   6  =

66 km

Thanks, Synth......

This isn't as difficult as it seems.....the area of the larger square can be found by applying the Law of Cosines directly.to one of the non-equilateral  triangles  ........

Letting s be the side of the larger square....we have

s^2  = 1^2 + 1^2  - 2(1)(1)cos(150)   = [2 + √3 ] ≈  3.732 units^2

But...since s^2  is the area of the larger square.....this just kind of "falls out".......

Hope that helps.....