CPhill

"a"  would be the answer if we assumed that a ,b and c > 0

However......to cover all situations......assume that  a < 0    and bc < 0

Then the answer is   l a l

To see why :

√ [abc] * √ [ a / (bc) ]  =  √  [ (a^2 * bc ) / ( bc)]  =  √  a^2

If  "a"  <  0   and we wrote down  "a"  as a result......we would be obtaining a negative value from a positive root.......which isn't possible

√3/2tan30-√3sin60-√2cos45 =

[√3 / 2] [1  / √3] - √3] [√3 / 2 ] - √2 [ 1 / √2]  =

1/2  -  3/2  - 1  =

-1  - 1  =

-2

If the first farmer only sells his eggs....he makes $1.50   = .5 cent = 1/2  cent for each egg

If the second farmer sells only his eggs.....he makes $1.00 =  1/3 cent for each egg

So the total made is  300 * (1/2) cents + 300 * (1/3)cents  =  [150 + 100 ]  cents = 250 cents = $2.50

However....if they combine their products......they sell  600 eggs at  2/5 cents each  = 600 * (2/5) cents  = 240 cents = $2.40

To make the same profit by combining eggs........each egg should have been sold   at  [ 1/2 + 1/3 ] / 2  =  5/12 cents

Proof :   600 * 5/12 =  50 * 5   = 250 cents  = $2.50

3 / 4  = 0.75   ....so.....

0.75 * 37.5   = 

28.125

-3 / -4   =      [ -1 * 3 ] / [ -1 * 4 ]  =   3 / 4

PE + OP   =

EP + PO  =

EO

I agree with EP....however, let's suppose, just for the sake of argument, that 

f(x)  =  x^2 + 3x  - 2     and we want to find f ( x - 3)

So we have   (x - 3)^2 + 3(x - 3)  - 2     simplify

x^2 - 6x + 9  + 3x - 9  - 2

x^2 - 3x - 2  

Look at the graphs, here :   https://www.desmos.com/calculator/2fwmyzx9zo

Note that  f(x -3)  shifts f(x) to the right by 3 units  [which we should expect ]

a piece of paper is 0.0075 inch thick. How many sheets of paper will be in a that is 2.25 inches high. Both answers and explanation please. Thank you

Height of stack  / thicness of one sheet   = number of sheets    ......so.....

2.25 / 0.0075  = 300 sheets

Think of a hypothetical situation where the pile was one mile high - 5280 feet - and each sheet was 1 foot thick.....

Then....the number of sheets would be     5280 / 1    = 5280 sheets

Nice, HSC....!!!!

V _{of half sphere}  =   (2/3) * pi * ( 6/2)^3   ≈ 56.55 ft^3

V _{of silo}   =     pi  * ( 6/2)^2 * 35  ≈ 989.6 ft^3

So....the total volume  =   [56.55 + 989.6 ] ft^3   ≈ 1046.15 ft^3