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9)

If the little red arrows in the triangles mean "parallel," then the first two triangles are similar by AA congruency

So   Δ FGH  is simillar ΔFBC

10)  Not similar....we can see this by taking ratios of the two shortest sides....that is....

44/66   =  11/18 ???

4/6  =  11/18  ???   cross-multiply..

18 * 4  =  11 * 6   ???

72  =  66     not equal....so ....not simillar

I just posted the picture again...I don't know why it isn't showing.

Yes, but I can't see the picture... ... 

It should be there....Can you see this? 

I don't see the picture....

I think I'm slowly getting it.....  you are choosing a PAIR at a time (Which I think, is actually what the question is asking)..I am selecting one sock at a time in my answer....

The socks must be either both white, both brown, or both blue. If the socks are white, there are \(\binom{4}{2} = 6\) choices. If the socks are brown, there are \(\binom{4}{2} = 6\) choices. If the socks are blue, there is \(\binom{2}{2} = 1\) choice. So the total number of choices for socks is \(6+6+1=\boxed{13}\).         6 away, EP!

Haha!   HOW close???     I told Ant offline I was not very good at these type Q's, but I would try!

You're close, EP! 

I'll try , Ant!

Say your fist pick is

white       then there are 3 choices w    4 choices br     2 choices bl

First pick is

brown    then there are 4 choices w    3 choices br    2 choices bl

First pick is

blue      then there are  4 choices w   4 choices br     1 choice bl

Add the red choices up....looks like 7 ways to get a pair of mathcing socks !

(I do not promise this is correct , Ant.....just my best try)

Thank you!

Yes,  'A'

Nope, thank you for all the help :) 

...and you got the correct answer!   Good job, Julius.  Thanx for finding my error...I corrected it anyway.

Yep! No need to re-do it, I copied your steps with the correct derivative. Thanks :)

You are correct Julius   ...I got the derivative of  5x^2 + 3x.....

    sorry the solution methodology is the same though ...I will correct it.

I totally messed up what I was trying to say lol, but oh well. Am I right though? Is it A)

IF the little red arrows mean the lines are 'slanted' the same, then you would have similar triangles because all three angles in each are the same

I'm not sure what the red arrows mean...>.< Sorry 

For 8) I think it's and they are similar but I don't know how to explain it. Triangle ALM

First one

take the ratio of the long sides of each triangle   66/55  = 1.2

   take the ratio of the NEXT longest legs             60/50 = 1.2     Good so far

IF the ratio of the third legs is the same (1.2), the triangles are similar

   55/45 = 1.2222    Uh-Oh......    the triangle are NOT similar (Close though)

Second one

    can you tell me for what the little red arrows stand ?

Good job, EP! 

sqrt 1/4   /   (1/8)^1/4

= 1/2   /   (1/2^3)^1/4

= 1/2   /  1/2^3/4

=2^-1  * 2^3/4

= 2^-(1/4)

1/2^(1/4)

=.841

finding the circumference: 2pir or pi d, so pi d=100, d= 100/3.14=31.83 in

So the Point of Intersection would be: (-17/21,-17/21) 

Since the actual slope is -20 

23=-20(-2)+b 

b=-17 

y=-20x-17 

Setting them equal to one another 

x=-17/21 -- Plugging in to find y

POI = (-17/21,-17/21)Is that correct?

√(1/4) = 1/2 (or 0.5) If you think about it square root of 1 is 1 and the square root of 4 is 2. 

0.5/4√1/8 = √2/4