Answer:
5 different numbers, 2 even
Step-by-step explanation:
Since we have 5 digits and they are non repeating we can use the permutation formula:
![P(n, k) = \frac{n!}{k!}, $where $ k \leq n ; k, n \in \mathbb{N}](https://tex.z-dn.net/?f=P%28n%2C%20k%29%20%3D%20%5Cfrac%7Bn%21%7D%7Bk%21%7D%2C%20%24where%20%24%20k%20%5Cleq%20n%20%3B%20k%2C%20n%20%5Cin%20%5Cmathbb%7BN%7D)
It gives us the amount of ways to arrange k objects out of n objects without repetition, but order does matter.
In our case the amount of 4 digit numbers that can be formed using the digits from 1 to 5 is: ![P(5, 4) = \frac{5!}{4!} = 5.](https://tex.z-dn.net/?f=P%285%2C%204%29%20%3D%20%5Cfrac%7B5%21%7D%7B4%21%7D%20%3D%205.)
And out of those 5, only 2 are even
![PQ^2 = PR \times PS](https://tex.z-dn.net/?f=%20PQ%5E2%20%3D%20PR%20%5Ctimes%20PS%20)
![(4x + 4)^2 = (3x + 3)(3x + 3 + 21)](https://tex.z-dn.net/?f=%20%284x%20%2B%204%29%5E2%20%3D%20%283x%20%2B%203%29%283x%20%2B%203%20%2B%2021%29%20)
![16x^2 + 32x + 16= (3x + 3)(3x + 24)](https://tex.z-dn.net/?f=%2016x%5E2%20%2B%2032x%20%2B%2016%3D%20%283x%20%2B%203%29%283x%20%2B%2024%29%20)
![16x^2 + 32x + 16= 9x^2 + 81x + 72](https://tex.z-dn.net/?f=%2016x%5E2%20%2B%2032x%20%2B%2016%3D%209x%5E2%20%2B%2081x%20%2B%2072)
![7x^2 - 49x- 56 = 0](https://tex.z-dn.net/?f=%207x%5E2%20-%2049x-%2056%20%3D%200%20)
![7(x^2 - 7x - 8)= 0](https://tex.z-dn.net/?f=%207%28x%5E2%20-%207x%20-%208%29%3D%200%20)
![(x - 8)(x + 1) = 0](https://tex.z-dn.net/?f=%20%28x%20-%208%29%28x%20%2B%201%29%20%3D%200%20)
![x - 8 = 0~~~or~~~x + 1 = 0](https://tex.z-dn.net/?f=%20x%20-%208%20%3D%200~~~or~~~x%20%2B%201%20%3D%200%20)
![x = 8~~~or~~~x = -1](https://tex.z-dn.net/?f=%20x%20%3D%208~~~or~~~x%20%3D%20-1%20)
x = -1 makes the lengths of segments PQ and PR equal zero.
That is not possible, so the solution x = -1 is discarded.
x = 8
PS = 3x + 3 + 21
PS = 3x + 24
PS = 3(8) + 24
PS = 24 + 24
PS = 48
The correct answer should be A because you have to have a common denominator in order to solve so you take 5/6x and 4/6x and solve.
Answer:
4/15 of an inch
Step-by-step explanation:
A worm wriggled forward 4/5 of an inch in 3 minutes.
=> At that rate, the distance the worm would go in 1 minute is:
D = (4/5)/3 = 4/(5x3) = 4/15 of an inch
Hope this helps!
Step-by-step explanation:
-9(-10-9)
90+81
171
hope it helps..