Hello :
all n in N ; n(n+1)(n+2) = 3a a in N or : <span>≡ 0 (mod 3)
1 ) n </span><span>≡ 0 ( mod 3)...(1)
n+1 </span>≡ 1 ( mod 3)...(2)
n+2 ≡ 2 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 0×1×2 ( mod 3) : ≡ 0 (mod 3)
2) n ≡ 1 ( mod 3)...(1)
n+1 ≡ 2 ( mod 3)...(2)
n+2 ≡ 3 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 1×2 × 3 ( mod 3) : ≡ 0 (mod 3) , 6≡ 0 (mod)
3) n ≡ 2 ( mod 3)...(1)
n+1 ≡ 3 ( mod 3)...(2)
n+2 ≡ 4 ( mod 3)...(3)
by (1), (2), (3) : n(n+1)(n+2) ≡ 2×3 × 4 ( mod 3) : ≡ 0 (mod 3) , 24≡ 0 (mod3)
Answer:
x = 10.5
Step-by-step explanation:
we know that ZP = PX (its the midpoint of the rectangle)
11 = PX
ZP + PX = ZX
11+11 = ZX
22 = ZK
2x + 1 = 22
2x = 22 -1
2x = 21
x = 21/2
x = 10.5
Answer:
8x less than or equal to $50
Step-by-step explanation:
bc the x represents the amount of books you can get for 8 dollars per book and can be less than or equal to, but not greater than 50, the max amount you may spend
hope this helped :)
Rearrange slightly...
12xy-8y-9x+6 now factor 1st and 2nd pair of terms
4y(3x-2)-3(3x-2)
(4y-3)(3x-2)
Answer:
It's a true solution.
Step-by-step explanation:
![3(5) + 4 - 5 = 4(5) - 6](https://tex.z-dn.net/?f=3%285%29%20%2B%204%20-%205%20%3D%204%285%29%20-%206)
![15 + 4 - 5 = 20 - 6](https://tex.z-dn.net/?f=15%20%2B%204%20-%205%20%3D%2020%20-%206)
![19 - 5 = 14](https://tex.z-dn.net/?f=19%20-%205%20%3D%2014)
![14 = 14](https://tex.z-dn.net/?f=14%20%3D%2014)