CPhill

HAHAHA!!!  Love those "trick pics," rosala!!!  .....especially the "BIG BIRD" and those bridesmaids sitting on the chairs......

We're glad that you're back, but your life seems pretty busy, at the moment .....  

P.S. ------  ALWAYS take the key WITH you!!!   LOL!!!!!

We can also do this with one variable.

Let x be the son's age 4 years ago,

Then his father's age 4 years ago  = 7x

And years later, - 4 years from now -  the father will be 3 times older than his son. So we have.....

3(x + 8)  = 7x + 8    simplify

3x+ 24  = 7x + 8

4x = 16

So the son's age 4 years ago was 4

And his father was 7(4)  = 28

And 4 yeara later the son is 8 and the father is 32.

If 10 students are taking algebra and drafting  and 24 are taking algebta, then 24 - 10 = 14 are taking algebra only.

So   11 + 14 = 25 are taking algebra and drafting, but not both.

South Africa.....look up "Apartheid"

Consider that Justin and Tim  comprise two of the players in a five player set where the other players are "A," "B" and "C"

Then, each possible set looks like this:

{A, B, C, Justin, Tim }

Then, we just want to choose any 3 of the 8 remaining players to comprise all these possible sets

So C(8,3) = 56

So....they played on the same team 56 times

2x + 3y  = 6

When we "solve for" something, we want that thing on one side of the equation and everything else on the other side.....so subtract 2x from both sides....this gives

3y = -2x + 6       now......divide both sides by 3

y = (-2/3)x + 2  

And that's it!!!  .....BTW.....this is just the equation of a line....

 (X+4)(x-9)-4x=0      simplify

x^2 -5x - 36 - 4x  = 0

x^2 - 9x - 39 = 0       factor

(x - 12)(x + 3)  = 0     set each factor to 0 and solve

So

x = 12   and x = -3

The product of x and y equals -340 and the sum of x and y equals -3

So we have

xy = -340     and

x + y  = -3  

We can transform the second equation to

y = -3 - x  

And putting this into the first equation, we have

x(-3 -x) = -340    simplify

-3x - x^2 = -340        multiply through by -1

x^2 + 3x  = 340         subtract 340 from each side

x^2 + 3x  - 340 = 0    facror, if possible

(x +20)(x - 17)  = 0     set each factor to 0

So

x = -20   and x =  17

And using y = -3 - x

When x = -20,    y = -3- (-20)  = 17

When x = 17  y = -3 - 17 = -20

So the solutions are   (-20, 17) and (17, -20)

√(2 / 9) =

√2 / √9 =

√2 / 3  = 

And since the √2 is irrational, any integer division of it is also irrational.