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)
|a| = b gives
a =b or a = -b
so,
|-x| = -10
gives
-x = -10 or -x = 10
x = 10, -10
now let us verify,
when x = 10, |-10| = +10 and it is not = -10
so, x= 10 is NOT a solution.
when x = -10, |-(-10)| = |10| = 10 and it is not = -10
so, x= -10 is NOT a solution.
hence, this equation does not have a solution.
If we know that |...| can never be negative, we can directly deduce that this equation does not have any solution.
Answer:
Step-by-step explanation:
so let’s say x is the length. Then the width will be 3x-4. You add them together and multiply by two. The perimeter is 72 so the equation equala 72.
Equation:
(x+3x-4)*2=72
(4x-4)*2=72
8x-8=72
8x=80
x=10
length:10
width:26
Answer: 
Step-by-step explanation:
Given : The total number of cards in a deck = 52
Number of red cards = 26
There are two types of red cards : diamond and heart.
Number of diamond cards = 13
The probability that the first card is a diamond :-
Since diamond is also a red card.
Now, the total cards left = 51
The number of red cards left = 12
The probability that the second card is a red card (without repetition) is given by :-
Now, the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a diamond :-
the answer is 5. hope this helps
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