proyaop

1(7.4) + 4(6.9) = 35$

Split up the 44 to + 9 and + 36 - 1

Factor out the 9:

9(x^2 - 2x + 1) + 9(y^2 + 4y + 4) - 1 = 0

(x-1)^2 + (y+2)^2 = 1/9 = r^2

r = 1/3

Hey weredumbmaster22: I found the original post to this question, here it is:

https://web2.0calc.com/questions/i-m-stuck-on-these

The function is in the image (the part w/o the shaded region)... So if you were to compress that that would be taking half the gray region right?

Thanks guest, you have a much smarter way of algebraically solving it --- I just plugged in random values of x and hoped for the best...

I got it! The answer is 9!

How I did it:

First I plugged in x as 0, f(0) = 0 / -1 = 0

(0p + q)/(0r + 1) = f(5 * 0) = 0 => q/1 = 0 => q = 0

Next I plugged in x as -1, f(-1) = 1/2

(p/2 + 0)/(r/2 + 1) = f(-5) = 5/6

p/(r + 2) = 5/6

6p = 5r + 10  (1)

Next I plugged in x as -2, f(-2) = 2/3

(2p/3)/(2r/3 + 1) = f(-10) = 10/11

2p/(2r + 3) = 10/11

22p = 20r + 30

11p = 10r + 15   (2)

Take equation (1) and multiply by 2 => 12p = 10r + 20 (1b)

Take equation 1b - equation 2 => p = 5

Plug it back into equation 1 => 30 = 5r + 10 => r = 4

p + q + r = 5 + 0 + 4 = 9

You can't have 0 reds.

You can have 1 red, and there are 2 scenarios for that.

You can have 2 reds, and there are 8 scenarios for that.

You can't have 3+ reds.

In total, there are 10 scenarios that work. There are 3^5 - 3 total cases, so the probability is 10 / 240 = 1/24

1) [already known number] = y

If GCD (y, x) = y, then x is divisible by y. 

2) 

If LCM (y, x) = y, then x is a factor of y.

If you are asking for an integer number --- no... Sextillion has 21 zeroes.

The square root of 9.5e+21 = 97467943448.1

This is relatively the same problem as posted above --- read the one above this to see how to graph:

Points: (5, 65) and (8, 99) --- also if you have a typo you can edit the problem (I know this is probably your typo-ed version)

Slope = (99-65)/(8-5) = 34/3 = 11.3 (infinite trailing 3s).