The third term of (2x-1)^6 is... something so long it puts thomas the tank engine to the size of a quark.
I'm not adding that. I just won't. It is not something I will do.
That's the most I can do. I needed to eat 3 advils. I had a witch doctor see into my brain and she had a stroke and died. The 3 gummy vitamins in my system are not enough. You should pay for my psychiatric bills. You caused it. You're the root of all evil.
ok maybe im just annoyed.
Let's put it into this way.
If a player wins game 1: (1/3)*(1/2)=1/6
If the player wins before the 4th turn: P(wins game 1)+P(lose game 1, wins game 2)+P(loses game 1 and 2, but wins game 3)
Player loses game 1 but wins game 2: (5/6)*(1/6)=5/36
Player loses game 1 and 2, but wins game 3: [(5/6)^2](1/6)=25/216 (very confusing, I'm sorry)
Player wins before 4th turn: 1/5+5/36+25/216=91/216
Let a, b, and c be length of the three sides of the brick.
From the ratios given, we can write these equations.
(I put too much effort into this... why didn't I just use sqrt(#) whatever)
The longest and shortest are c, b.
The equation isn't prime...
It's in the form of a^2-b^2
IT CANNOT BE PRIME!
It is the factors of (a-b) x (a+b).
Factoring the equation, we get the following factors:
(2 ^ 1024) - 1=(2^512 - 1) x (2^512 + 1)
Now you may see something that you can do.
We can factor this equation for a long time until you get:
(2 - 1) x (2 + 1) .
Do you really need help with this?
We can draw a square around the triangle, then take out parts of it to make the shaded triangle.
The square around it has an area of 16. (4x4=16)
The three triangles we take out of the square to get the shaded triangle have an area of:
2, 4.5, and 2
Add them up to find 8.5
16-8.5 is 7.5
I think it's relatively simple...
You can use this fancy website called desmos to graph things.
If it is parallel to x+3y=-5 then it should have the same slope: x+3y, just change the x intercept.
x+3y is equivalent to y=-1/3x
So we graph -7, 2 then we move down using y=-1/3x.
If you do that you'll see that the equation you get is x+3y=-1
Hey I'm back yippee
The number of ways to get 3 integers is 6c3=20
A triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers... but only when the sum of any 2 selected numbers is greater than the third number.
Cases possible when the longest side of the triangle is 6:
(6, 5, 4), (6, 5, 3), (6, 5, 2), (6, 4, 3)
Cases possible when the longest side of the triangle is 5:
(5, 4, 3), (5, 4, 2)
Cases possible when the longest side of the triangle is 4:
(4, 3, 2)
So we get 7/20 as our answer.