CPhill

(x+y+z)(xy+xz+yz)=25,  x^2(y+z)+y^2(x+z)+z^2(x+y)=7 

Expand the first equation 

yx^2 + zx^2 + xyz  + xy^2 + xyz + zy^2  + xyz + xz^2 + yz^2   =  25  simplify

yx^2 + zx^2 + xy^2 + zy^2 + xz^2 + yz^2 + 3xyz = 7     (1) 

Expand the second equation

yx^2 + zx^2 + xy^2 + zy^2 + xz^2 + yz^2  = 7      (2)

Substitute  (2) into (1)

7 + 3xyz  =   25       subtract 7 from 25

3xyz   = 18            divide both sides by 3

xyz  = 6

190+7x=170+9x     subtract 170, 7x from both sides

20  = 2x                  divide both sides by 2

10  = x

Call the points scored by one player, x

Call the points scored by another player, 2x

Call the points scored by the third player, x - 10

So we have

x + 2x + x - 10   = 70    simplify

4x - 10  = 70     add 10 to both sides

4x = 80       divide both sides by 4

x = 20   

2x = 2(20) = 40

x - 10  =   20 - 10  =  10

So the three players scored 10, 20 and 40 points, respectively

Example :

log ₁₂₅ 5     input as     log (5, 125)

3 8/9 + 1 5/12

3 + 8/9  =   35/9

1 + 5/12  =    17/12

So

35/9 +  17/12        get a common denomonator of 36

140/36 +  51/36 = 

191/36   =  5 + 11/36

28+(9*6-23)*4^0  =      evaluate within the parentheses, first

28 + (54 - 23)*4^0  =  

28 + ( 31)*4^0      =         exponentiation is done next...remember that a^0  = 1   as long as  "a" ≠  0

28 + (31)* 1  =

28 + 31   = 

59

You can travel  12 x 22 =  264 miles on a tankful of gas....so  you will have to stop and fill up

2100 / 264 =  7.954   times  =  8  times

98  =  14 x 7   =  2 x 7 x 7   =   2 x 7²

Consider two infinite geometric series. The first has leading term a, common ratio b, and sum S. The second has a leading term b, common ratio a, and sum S. Find the value of a+b. 

We have that

a / [ 1 - b]  = S       and b / [ 1 - a] =  S

Therefore

a / [ 1 - b ]  =  b / [ 1 - a]      cross-multiply

a [ 1 - a]    =   b [ 1 - b]    simplify

a - a^2   = b - b^2    rearrange

( a - b ) =   a^2 - b^2   factor the right side

(a - b) =  (a - b) ( a + b)         divide both sides by  (a - b)

1  =  a + b

21/35  = 3/5   =  .60