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:
c=1/3F
Step-by-step explanation:
Answer:
3x + y = -5
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Distributive Property
- Equality Properties
<u>Algebra I</u>
Standard Form: Ax + By = C
Point-Slope Form: y - y₁ = m(x - x₁)
- x₁ - x coordinate
- y₁ - y coordinate
- m - slope
Step-by-step explanation:
<u>Step 1: Define</u>
[PS] y - 11 = 3(x - 2)
<u>Step 2: Rewrite</u>
<em>Find Standard Form</em>
- Distribute 3: y - 11 = 3x - 6
- Subtract 3x on both sides: -3x - y - 11 = -6
- Add 11 to both sides: -3x - y = 5
- Factor -1: -1(3x + y) = 5
- Divide -1 on both sides: 3x + y = -5
The dimensions would be 40 m by 40 m.
To maximize area and minimize perimeter we make the dimensions as close to equal as possible. Since we only need fencing on 3 sides, 120/3 = 40; we can use 40 for each side.
Answer: 42
Step-by-step explanation:
if the bookstore has 64 copies,
yesterday it was sold 1/4 , so it was sold 64/4=16
today it was sold 1/8 from what remained, which is 6(see below)
64-16=48
48/8=6
the store has left 48-6=42
