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:
44 square feet were used to build the aquarium
Step-by-step explanation:
∵ The area of the rectangular prism = Lateral area + 2 Base area
∵ The top of the aquarium is open
∴ The area of the aquarium = Lateral area + Base area
∵ Lateral area = perimeter of base × height
∵ Its base is a rectangle
∵ The dimensions of the base are 4 feet and 2 feet
∵ Its height = 3 feet
∴ Perimeter of the base = 2(4 + 2) = 12 feet
∴ Area of the base = 4 × 2 = 8 feet²
∴ Area of aquarium = 12 × 3 + 8 = 36 + 8 = 44 feet²
Answer:
(4, -2)
Step-by-step explanation:
if you do process of elimination you find that 'a' doesn't work out but 'b' will . . . substitute -2 for 'y' and 4 for 'x' and see if the equation is true
-2 = -3/4(4) + 1
-2 = -3 + 1
-2 = -2
Answer:
AC = 13.3
Step-by-step explanation:
6+4 = AB
10 / 6 = AC / 8
AC = 13.3
