CPhill

-5x+4y=19   

 4x- 5y= -8          multiply the top equation by 4   and the bottom one by 5

-20x + 16y  =  76

 20x  -25y =   -40        add the equations

-9y   =  36        divide both sides by  -9

y  = - 4        and using either equation, we can find x

4x - 5(-4)  = -8

4x  + 20  = -8      subtract 20 from both sides 

4x  = -28        divide both sides by  4

x  = -7

So   { x , y}   = {-7, -4 }

9-3x-(8y)+9x-y   =

9 - 3x - 8y  +  9x   - y     =

9 - 3x + 9x - 8y  - y  =

9 + 6x - 9y

No, unfortunately, there's not much you can do......it is tempting to want to get rid of the logs  and solve  a * b  = c.......however.....we can quicly see that this will not work.......consider this....  [I'm using 10 as the base]

log(100) * log(1000)  =  log (1,000,000)      which is true

But

100 * 1000  ≠  1,000,000

So.....in general, for

log(a)*log(b) = log(c)

a * b ≠  c

3x+3y= -6        the object here is to get y by itself.......first, divide through by 3

x + y  = -2        subtract x from both sides

y =   -x  - 2     

This is slope/intercept form.....the slope = -1    and the y intercept is at -2

Using the Law of Cosines.......we can determine the distance, d, between his starting point and his ending point........so we have

d^2  = 4^2 + 8^2 - 2(4*8)cos(140)

d^2  =  about 129.03 mi

d = √129.03  = about 11.359 miles

And we can use the Law of Sines  to find the included angle, A, between the first leg of the journey and his last leg of the journey.........so we have

sin140/ 11.359  = sinA/8

8*sin140/11.359  = sinA

So

A = arcsin [ 8*sin140/11.359]  = about  26.92°

Subtract 25 from this  = 1.92°

Add this angle to the bearing of 270 =   271.92

So the yacht is about 11.359 miles from its starting position

And the bearing of the yacht to its starting position  is 271.92°

Of what ???

36x^2-65x+25=0

This factors as

(9x - 5) (4x -5)  = 0

Set both factors to 0    and we get that

9x - 5  = 0                                        and                  4x - 5  =  0

                                           add 5 to both sides

9x = 5                                                                     4x  = 5

divide both sides by 9                                          divide both sides by 4

x = 5/9                                    or                             x =  5/4

The sequence  is given by :    3(2)^n-1

Here's a good resource that explains it........http://www.purplemath.com/modules/percents2.htm#Decimal_to_Fraction

16x^2 - 25   =  a difference of two squares =

(4x - 5) (4x + 5)