Answer:
No real solution
Step-by-step explanation:
First off I'm assuming that the 1 or -1 at the begging is just the problem number:
First you distribute on both sides
36 - 18x - 3 = 4 - 18x + 30
Then combine like terms
33 - 18x = 34 - 18x
Then rearrange the terms by adding 18x to both sides and subtracting both sides by 33. You should get:
0 = 1
When you add positive 18x it cancels the -18x out. And 34 - 33 is 1. Obviously, zero cannot equal 1 so there is no real solution
To compute how many groups of
elements we can extract out of a group of
elements, we can use the binomial coefficient:
![\binom{n}{k} = \dfrac{n!}{k!(n-k)!}](https://tex.z-dn.net/?f=%20%5Cbinom%7Bn%7D%7Bk%7D%20%3D%20%5Cdfrac%7Bn%21%7D%7Bk%21%28n-k%29%21%7D%20)
where the factorial is defined as
![n! = n(n-1)(n-2)(n-3)\ldots 3\cdot 2](https://tex.z-dn.net/?f=%20n%21%20%3D%20n%28n-1%29%28n-2%29%28n-3%29%5Cldots%203%5Ccdot%202%20)
So, this is the number of possible quintuplet out of 50 numbers:
![\binom{50}{5} = \dfrac{50!}{5!45!}= \dfrac{50\cdot 49\cdot 48 \cdot 47 \cdot 46}{5\cdot 4\cdot 3\cdot 2} = 2118760](https://tex.z-dn.net/?f=%20%5Cbinom%7B50%7D%7B5%7D%20%3D%20%5Cdfrac%7B50%21%7D%7B5%2145%21%7D%3D%20%5Cdfrac%7B50%5Ccdot%2049%5Ccdot%2048%20%5Ccdot%2047%20%5Ccdot%2046%7D%7B5%5Ccdot%204%5Ccdot%203%5Ccdot%202%7D%20%3D%202118760%20)
Similarly, this is the number of possible groups of six numbers out of 60:
![\binom{60}{6} = \dfrac{60!}{6!54!}= \dfrac{60\cdot 59\cdot 58 \cdot 57 \cdot 56 \cdot 55}{6\cdot 5\cdot 4\cdot 3\cdot 2} = 50063860](https://tex.z-dn.net/?f=%20%5Cbinom%7B60%7D%7B6%7D%20%3D%20%5Cdfrac%7B60%21%7D%7B6%2154%21%7D%3D%20%5Cdfrac%7B60%5Ccdot%2059%5Ccdot%2058%20%5Ccdot%2057%20%5Ccdot%2056%20%5Ccdot%2055%7D%7B6%5Ccdot%205%5Ccdot%204%5Ccdot%203%5Ccdot%202%7D%20%3D%2050063860%20)
So, you win with a combination out of 2118760 in state A, and with a combination every 50063860 in state B this means that winning in state A is easier with a ratio of
![\dfrac{50063860}{2118760} \approx 23](https://tex.z-dn.net/?f=%20%5Cdfrac%7B50063860%7D%7B2118760%7D%20%5Capprox%2023%20)
Whichi means that winning in state B is 23 times harder
-m = 20
m = -20
Answer m=-20
Answer:
v = -2
Step-by-step explanation:
-9v – 9 = -27
add 9 to each side
-9v – 9+9 = -27+9
-9v = -18
divide by -9
-9v/-9 = -18/-9
v = 2