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9x-4y=30, 7x+y=11. 

We convert these to y-intercept form first.

9x-4y=30

4y=9x-30

y=9/4x-30/4

7x+y=11

y=-7x+11

Then set them equal to each other.

9/4x-30/4=-7x+11

37/4x=74/4

x=2

Then y=-3.

Therefore the point of intersection is (2, -3).

how do i find CY

1)  Use the Law of Cosines on triangle(ABC) to find the size of angle(A).

2)  Using this answer, find the size of angle(ABD).

3)  Now, use the Law of Cosines on triangle(ABD) to find the size of AD.

Since this is arithmetic, the middle term will be the average of the outside two:

       12  =  [ (y + 6) + (y) ] / 2

Solve ...

Let V be the midpoint of arc(AB) and Z the midpoint of arc(CD).

Draw VWXYZ, where W is the point of intersection with AB (W will be the midpoint of AB);

X is the point of intersection with AC;

Y is the point of intersection with CD (Y will be the midpoint of CD).

VWXYZ will be perpendicular to both AB and CD.

Since AB = 2, AW = 1 and WX = 1.

Since CD = 6, CY = 3 and XY = 3.

Call XW = a and call YZ = b.

Since WXYZ is a diameter and AB is a chord of the circle:  AW · WB  =  VW · WZ.

     --->     1 · 1  =  a · (1 + 3 + b)     --->     1  =  a · (4 + b)     --->     4a + ab  =  1     --->     ab  =  1 - 4a

Since WXYZ is a diameter and CD is a chord of the circle:  CY · YD  =  YZ · VY.

     --->     3 · 3  =  b · (1 + 3 + a)     --->     9  =  b · (4 + a)     --->     4b + ab  =  9     --->     ab  =  9 - 4b

Combining these two results:  1 - 4a  =  9 - 4b    --->     4b - 4a  =  8     --->     b - a  =  2

     --->     b  =  2 + a

Since     a · (4 + b)  =  1     --->     a · (4 + (2 + a) )  =  1     --->     a · (6 + a)   =  1 

                  --->     6a + a²  =  1     --->     a² + 6a - 1  =  0

                  --->     a  =  -3 + sqrt(10)      [quadratic formula]

Since      b · (4 + a)  =  9     --->     b · (4 + (b - 2) )  =  9     --->     b · (2 + b)   =  9

                 --->     2b + b²  =  9     --->     b² + 2b - 9  =  0

                 --->     b  =  -1 + sqrt(10)     [quadratic formula]

The diameter will be:     (a) + (1) + (3) + (b)  =  ( -3 + sqrt(10) ) + (1) + (3) + ( -1 + sqrt(10) )

                                                                      =  2sqrt(10)

So, the radius is:     sqrt(10)

jimkey17, you had the right idea, but you made a mistake in your work. It should be choose 5, not 4. The real answer is 11, as 11 choose 4 > 365, but 10 choose 4 isn't. (Note: I solved this problem on AoPS, and 11 is correct, so you need have no doubts in the solution)  

Since the medial triangle has half the area of the original triangle, AB^2 + AC^2 + BC^2 = 164.

A circle has diameter XY = 28.

Chord AB is perpendicular to XY, has length 12, and intersects XY at point P.

By theorem:  AP · PB  =  XP · PY

                           6 · 6  =  x · (28 - x)

                              36  =  28X - x²

             x² - 28x + 36  =  0

Now, use the quadratic formula:  x  =  [ - -28  +/-  sqrt( 28² - 4·1·36 ) ] / (2·1)

           x  =  ( 28 + sqrt(640) ) / 2     or     x  =  ( 28 - sqrt(640) ) / 2 

           x  =  14 + 4sqrt(10)                       x  =  14 - 4sqrt(10)

Distance between the chord and the center of the circle:  14 - ( 14 - 4sqrt(10) )  =  4sqrt(10)

Ok. Maybe I'm not an adult with some diploma in education.

Sure, maybe not all my answers, are ANSWERS.

But maybe, I've been answering lots of questions.

And maybe, those answers actually contain a correct answer.

Your failure to see beyond those limited hints, are making you feel that I do not want to help.

I do.

And also, the people who have replied to my, hints, and said that they actually helped get the right answer!

Yes, I'm no expert at education.

I don't look to be one either.

I will repeat, I do not inflate points.

Besides, you can't even add more than one.

So, of course, you know adding a point is called "inflation"

I don't give minus points to those who are incorrect or don't agree with me, and I add points to others' answers when I feel they are well written.

So yes, maybe they are useless. Maybe they are also the first 1 or 2 steps to solving.

Maybe, some people actually learned from them.

Stop focusing on my (and i admit), "rubbish answers," focus on the majority.

This is not a math question, or even STEM.

OH I’m glad you told us; some of us might be confused.

Hugo, what the fuck do you think the Off-Topic label is for? Decoration?

You need your own label: Obnoxious Ass-Hole

You should review the meaning of Liberal Arts. After you do, you will then know that Mathematics is one of the Liberal Arts. (See what I mean about arrogance?)

There are 90,000 integers between 10,000 and 99,999. Of those 90,000 exactly 909 are divisible by 99.

Therefore, the probability is: 909 / 90,000 =0.0101 = 1.01 %

I agree with tizzlybeth that it is t^3+3t^3+3t+1 

You can determine it for certain if you take its "continued fraction", which is as follows:

[0; 1, 2, 2, 1, 1, 1, 4, 8, 1, 2], which terminates in 2. Therefore, it tells you, with absolute certainty, that it is a rational number. If you work out the fractions backwards, starting with:2, 1, 8.......etc. you will actually get the original rational fraction. In fact, I worked it out and as it happens the fraction is: 2345 / 3331. However, the decimal expansion doesn't repeat for 3330 digits!! Finding the "continued fraction" will always tell you whether a decimal expansion is rational or irrational.

There are exactly 900 palindromes between 10,000  and  99,999 integers.

Of those 900 palindromes, only the following five are divisible by 135

(54945,   55755,   56565,   57375,   58185) >>Total = 5

*sighs*

It's the Art of Problem Solving...

also means

Artic offshore patrol boat

and

automated office protocol standard

These are the only combinations to give you the sum of 16:

466 , 556 , 565 , 646 , 655 , 664 , Total =  6

Therefore, the probability is: 6 / 6^3 =6 / 216 = 1 / 36

Ummm...

The ... means it goes on forever, but it doesn't have a pattern, and therefore cannot be written as a fraction. It is irrational

Yay!