CPhill

Fredericton

7 consonants

4 vowels

So.....the ratio is :

7 / 4  

And that's in lowest terms

Just multiply 73 by  1.7699999999...........and that will be your answer

(2x + 7)^2  - 49   =  (2x + 7) (2x + 7 )   - 49   =  

           2x + 7 

           2x + 7

           --------

           14x  + 49

4x^2 + 14x

---------------------

4x^2 + 28x + 49

And subtracting 49 from this     gives us    4x^2 + 28x + 49 - 49

If it depreciates every month at 1.2%...then each successive month, it must be worth only   98.8%  = .988  of what it was the prior month......so we have

3000  =  12,500 (.988)^m        divide both sides by 12500

30/125  = (.988)^m     take the log of both sides

log (30/ 125)  = log .988 ^m      and we can write

log(30/ 125)   = m log .988      divide both sides by log.988

log(30 / 125)  / log(.988) = m  = about 118.2 months.....actually....  m > 118.2 months since,at any time after this, it will be worth less than $3000

Well.....I'm assuming a is a leg.... we have....with the Law of Sines

6/ sin 50   = b/ sin 40      [ note if B = 40, A must  = 50]

b =  6sin40 / sin50  = about 5.035

And the   hypotenuse  = c =   sqrt [6^2 + 5.035^2]  = about  7.833

Thanks, Guest.......here's a sightly easier appproach  using one variable

Call the number of 4 kilos he sold, x       and the number of 3 kilos,  30 - x     and we have

4x + 3(30 - x)  = 100   simplify

x + 90   = 100     subtract 90 from both sides

x = 10     = the number of 4 kilos sold          30 - x   = 30  - 10   = 20    =   the number of 3 kilos sold 

Drop back 10 yards and punt.........!!!!

OK, seriously  ......ask someone here.......

8)  This is like 7

.10 ( 16 - x)  + 1x  =  .35(16)   simplify

1.6 - .10x  + x  =  5.6      

1.6  + .90x   = 5.6      subtract 1,6 from both sides

.90x  = 4    divide both sides by .90

x = 4/.90   =  [40/9] quarts need to be drawn off   ≈  4.44 quarts

7)  80% cleansing powder = 20% water  = .20      60% cleansing powder = 40% water  = .40      pure water = 100%  = 1

This one is a little trickier......I hope I've done it correctly....!!!

Let's call the amount we draw off = x       And this is = to the amount of  pure water we replace it with....so we have....

.20water  * [ starting amount - amt drawn off]  plus   "x" amt of pure water =  40% water * 200L
 

.20(200-x) + 1x  =  .40 [ 200]    simplify

40 - .20x  + 1x   = 80   

40 + .80x  = 80       subtract 40 from each side

.80x  = 40            divide both sides by ..80

x = 40/.80   = 50 mL   = amt drawn off

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6)   I'm assuming that we want to end up with a solution that is 75% salt.....this is like 4.....and 75% salt = 25% water....so we have

50% solution of water* 4 L   -  100% water * unknown amt evaporated   =  25% water [ 4L  - unknown amt]

.50(4)   -  1x  = .25 [ 4 - x]     simplify

2 - 1x  = 1  - .25x       add 1x  to both sides,  subtract 1 from both sides

1  = ..75x   = (3/4)x       multiply both sides by  4/3

[4/3 ] L  = x      this is the amt to be evaporated

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