ElectricPavlov

Re-arrange

x^2 -8x      +    y^2+5y      = 35            complete the square for x and y

(x-4)^2      +   (y+2.5)^2       =   35   + 16 + 6.25

x,y =   (4 , - 2.5)

1/89 = 0.0112359550561798       from this website calculator

Multiply first equation by 2     then add it to the 2nd equation...this will eliminate 'y'...you can then solve for 'x'

   use this value of 'x' in one of the equtions to solve for 'y'

Multiply thru by n^2 to get

.28 n^2 = n +2    re-arrange

.28n^2 - n -2 = 0    Quadratic formula (for the negative value)    n = - 1.42857

Use Pythagorean theorem

   the diagonal is the hypotenuse    one leg is 20       find the other leg (width)

         h^2 = l₁ ²  + l₂ ²

         25²  = 20²  +  w^{2       Solve for w}

Acid of ingredients added together = acid in final solution

.10a      +    .20 ( f-a)   = .16 f               a = amount of X      f-a = amount of Y    f = final amount

.10a + .20f-.20a = .16f

-.1 a = - .04 f

a = .4 f        ( this is the amount of X)

then      Y = f - a = f - .4f = .6 f

then X:Y =    .4  :  .6 =   2 :3                         

Bike store

 1.30 x = 125     solve for 'x' the wholesale price of the bike

1.87 / 22 = .085 = 8.5% tax

66 * .085 = $ 5.61 tax

Another way:   66 dollars is 3 times 22, so the  tax will be 3 times the 22meal tax    1.87 * 3 = $ 5.61

Please post multiple questions seperately....you are more likely to get a response....

   I answered ONE of your questions.....people will see there is a response and not look at your post to realize there are more questions!

I should have included units to make things clearer perhaps, but often the units can clutter the equation and lead to confusion:

6200 N  * 95000 m = ......... j

(Hint: 1 kN= 1000 N)    as given in the Q