CPhill

( [2x] / 5  - 9 )   + 9       note that we could write 

[ 2x ]/ 5  +   ( -9  + 9)  =

[2x ] / 5   +  0  =

[2x] / 5

Perimeter  =  2  [  Width + Height  ]  = 

2 [ (3y - 5)  + ( 2y) ]  =

2  [  3y + 2y  - 5 ] =

2 [ 5y  - 5 ]  =

10y  - 10

(2.9*10^6) + (2.07*10^7)

Note that we can write this as :

(2.9 *  2.07)  * (10^6 * 10^7)  =

 6.003   x  10^13 

See if this helps  :

http://www.purplemath.com/modules/exponent3.htm

Thanks...I have made the correction!!!!!

Thanks, knownhappyman   !!!!!

Number of zeroes from 100 to 200 [inclusive] =

Each multiple of "5"  from 100 to 200 adds an additional  "0"  =    20

Each multiple of 25 from 100 to 200  adds another "0"  =   4

Each multiple of 125 adds another  "0"  = 1

So.....  we have 2 "0s"  in 100  +  20  + 4 + 1   = 2 + 20 + 4 + 1  =   27

We  can confirm this by evaluating    200!  / 99!   here : https://www.wolframalpha.com/input/?i=200!+%2F99!

9 l 9 - 8x l  = 2x + 3

We have two equations here

9 (9- 8x)   =   2x + 3                 and              9 (9 - 8x)  = -[ 2x + 3]

                    simplify

81  - 72x   = 2x + 3                                  and                                                      81 - 72x  =  -2x  - 3

add 72 x  to both sides, subtract 3 from both sides                      add 72 x  to both sides, add 3 to both sides

78   =  74x                            and                  84  = 70x

divide both sides by 74                                divide both sides by 70

78/ 74 = x                                                       84 / 70  = x

                                    reduce

39 / 37  = x                                                   6 / 5    = x

Real world situation...let's suppose that a bus will hold 50 people and the number of people on it = 35

So......the number of additional people, x, that the bus will hold can be modeled by

35  + x  ≤  50

3.14 x 10^-3 

  [ write two "0s" in front  and move the decimal point 3 places to the left ]

.00314

l  -4b  - 8 l  +   l  -1  - b² l + 2b³, b  = -2

So we have

l  -4 (-2) - 8 l   +  [  -1 - (-2)² l  + 2 (-2)³   =

l  8 - 8  l   +  l  -1 - 4 l  + 2 (-8)  =

l 0 l   +  l  -5 l   -  16  =

0  +  5   - 16  =

5 - 16

-11

 CORRECTED ANSWER  !!!!!

Let the number of pounds of copper to be added  =  C

Note.....that  if the final mixture is 10% zinc.....then  the final mixture must contain 90% copper

So

[amt of copper present + amt of copper added]  / [ whole mixture ]    =  90% copper

Note that the whole mixture amt  =  150 + amt of copper to be added

So

[ 100 + C ]  / [ 150 + C]   = .90    multiply both sides by   150 + C

100 + C  = .90 [ 150 + C]  simplify

100 + C  = 135 + .90C        subtract  100, .90C from both sides

.1C  =  35                      divide both sides by .1

C  = 350 lbs of copper are  to be added

Proof

[350 + 100] / [ 150 + 350 ]  =  .90  = 90%