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:
A constant is a number that stays the same. A variable is number that doesn't remain the same.
Answer: 7
Step-by-step explanation:
Step 1: Subtract 3 from both sides.
6a+3−3=45−3
6a=42
Step 2: Divide both sides by 6.
6a
/6
=
42
/6
Answer:
A
Step-by-step explanation:
1 over 10x10x10 is basically, 10 to the power of 3. 10x10 is 100, and 100x10 is 1000. An easy way to do this. Since we have 3 tens, we start with 10, then add a 0, then add another 0. Gives you 1000.
7. Answer is D! 1 to the 3rd power, 1^3, or 1 cubed as you'll hear it, is 1 because when something is cubed that means it's times itself 3 times. (EX: 4^3 = 4x4x4) 2 cubed is 8. 3 cubed is 27. 4 cubed is 64 and 5 cubed is 125!
8. Answer is C! A is gaining speed and B is the capped speed, meaning it can't get any higher, and C is the loss of speed.