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Here is where

I believe the x lie in between c and d

Mathcourts24, 

How about saying thankyou to heueka for all his time consuming effort which he afforded you!

Don'r just grumble about getting it wrong!

You tried to vote your question up about 10 times but you have not even attempted to give Heureka a point.

That is incredibly rude of you!  Do you think that will encourage anyone to help you next time?

Coolstuff, could you put only one of these questions per post.

It makes it more confusing to hve 2 or more  plus there should only be one question per post anyway. :)

ok so you use    \cap = intersection    only for sets

           and      \wedge  for the same thing when it is not written in set notation.

But 

you use  \cup = union    for sets and non-sets notation...

Thanks  Rom.

Well youv'e been worrking up since the late 2013's right XD

LOL!!!

Man You sure are an active user no wonder you maintain such a prestine score XD

AB =  BC = CD = DA                                                 given

BD = BD                                                                    reflexive property

Triangle ADB congruent to Triangle CDB                 SSS congruency

Is there another way to do it without trig? Either way, thanks :D

The dfenition of congruent is this Having the same size and shape; expressed with the symbol ≅. these triangles are congruent the only diffrenece is only A B D has been flipped or in a more math liked term its been reflected.

Assuming that some boxes could remain empty.....

For the first one....let the number of balls = k   and the number of boxes = n

So...we have

C( k + n - 1 , n - 1)   = C( 6 + 3 - 1 , 3 - 1)  = C (8, 2)  = 28 ways

For the second one.....we have the following partitions of 5 indistinguishable balls in 3 indistinguishable  boxes

5, 0, 0

4, 1, 0

3, 2, 0

3, 1, 1

2, 2, 1   =  5 ways

If you have a score above 120, then you might have a chance

K. Cannot be determined

We need at least 3 pieces of info to solve a triangle

Only knowing two side lengths isn't enough

C. gross income - (required deductions + optional deductions)

We have the form

y = Asin (Bx)  + D

A = the amplitude =  6

B =  2pi / period

The period = 4

So

B =  2pi / 4  =    pi/2

D = the shift up/down.....since the resting position is y = 0....we have no shift

The equation for the displacement from the resting position is

y =    6 sin [  (pi/2) t  ]

Here is the graph :  https://www.desmos.com/calculator/jn8ipp0b2g

x = y^4      (1)      and     x + y^2 = 1      (2)

Sub   (1)  into (2)   and we have that

y^4 + y^2 = 1         

Let  y^2  =  a      and we have

a^2 + a   =   1        complete the square on a

a^2 + a + 1/4   =  1 + 1/4       factor the left....simplify the right

(a + 1/2)^2  =  5/4           take both roots

a + 1/2   =   ±√5  /  2       subtract   1/2 from both sides

a =   ( - 1 ±√5 ) / 2

Since  y^2  must be positive, then  a  must be   ( √ 5 - 1 ) / 2    =  y^2      (3)

Using   x + y^2 = 1

x =  1 - y^2

x = 1 -  [  ( √ 5 - 1 ) / 2   ]  =    ( 3 - √ 5 ) / 2

These curves intersect at the same x values

So...the distance between the y values is the distance between the intersection points 

So.....using (3)

y =  √  [ ( √ 5 - 1 ) / 2 ]       or y =  - √ [ ( √ 5 - 1 ) / 2 ] 

So... the distance between these points is just

√  [ ( √ 5 - 1 ) / 2 ]   -  [  - √ [ ( √ 5 - 1 ) / 2 ]  ]  =

2 √  [ ( √ 5 - 1 ) / 2 ]   =

√ [ 4 ( √5 - 1 ) / 2 ]  =

√ [ 2√ 5 - 2 ]  =

√ [ - 2 + 2√ 5 ]   ⇒  (u, v)   =  (-2, 2)

The answer is 26 sq units  

you can calaculate the area by spiliting this shape into sperate rectangles then calaculate the area of the individuals then add the numbers.