ElectricPavlov

630 divided by 42 = 15     the other two integers, when multiplied = 15    so  either they are   3 and 5   or   1 and 15 

(d-7) = 9 (g-7)     Given

(d-4) = 6 (g-4)      Given       <==== solve for   g= (d+20)/6     <==== use THIS in the first equation 

d-7 = 9 ( (d+20)/6   - 7)       Solve for   d

d-7 = (9d+180)/6 - 63 

d+56 = (9d+180)/6 

6d + 336 = 9d + 180 

156 = 3d 

d = 52 y/o  now

Slope intercept form is   y = mx + b    so you just need to solve the given equation for 'y'

-4x + 6y = 16 

6y = 4x + 16 

y = 4/6 x + 16/6

y = 2/3 x + 2 2/3     Done. 

(x-2)(x+2)  =0     expands to 

x^2 -4  = 0                 divide by -4 

-1/4 x^2  + 0x  +1    = 0             shows A = -1/4  and B = 0      so  A+B = -1/4 

Hey Bader....   when I do the calculation of your expresion between step 4 and step 5  I get a  negative square root......

Here is what I find:

If you use your calculator to do all of the math calculations you will wind up with 

arc cos ( .9359059268) 

   which is ~  .36  R    or    9/25 R 

20 members * 30 minutes = 600 member minutes required

600 member minutes / 1500 ft^2 = .4 member minutes / ft^2 

.4 member minutes / ft^2  * 1200 ft^2   /  15 members =  32 minutes required 

The disciminant   b^2 - 4ac   must = 0 for this to be true 

Simplify to   x^2 + 15x + k      then comute the discriminant

                           15^2 - 4 (1)(k) = 0 

                                           4k = 225 

                                             k = 56.25 

Find slope between the two points   m = (y1-y2) / (x1-x2) 

                                                          m = (8-17) / ( 5 - -4)  = -9/9 = - 1 

Point slope form is then (pick either point) 

        y-8 = -1 (x-5) 

          re-arrange 

           y-8 = - x + 5 

           x + y = 13     Divide by 13 

         1/13 x   + 1/13 y = 1                 then a = 13      Done. 

Let sides be  h and w 

2h + 2w = 40      <=== Given     so:   h = 20 - w 

Pythagorean theorem: 

h^2 + w^2 =  (10 sqrt2) ^2 

(20-w)^2 + w^2 = 200 

2w^2 -40w + 200 = 0           Use Quadratic Formula with a = 2 b = -40 c = 200    to find   w = 10     then    h = 20 -w  shows     h = 10    too.

    area = w * h = 10 * 10 = 100 units^2