Triangular sequence = n(n + 1)/2
If 630 is a triangular number, then:
n(n + 1)/2 = 630
Then n should be a positive whole number if 630 is a triangular number.
n(n + 1)/2 = 630
n(n + 1) = 2*630
n(n + 1) = 1260
n² + n = 1260
n² + n - 1260 = 0
By trial an error note that 1260 = 35 * 36
n² + n - 1260 = 0
Replace n with 36n - 35n
n² + 36n - 35n - 1260 = 0
n(n + 36) - 35(n + 36) = 0
(n + 36)(n - 35) = 0
n + 36 = 0 or n - 35 = 0
n = 0 - 36, or n = 0 + 35
n = -36, or 35
n can not be negative.
n = 35 is valid.
Since n is a positive whole number, that means 630 is a triangular number.
So the answer is True.
Answer:
( 1/3, 5 2/3) Or (0.33, 5.66)
Step-by-step explanation:
If you graph the 2 equations and see where they intersect, they will land on the answer.
Find AC using Pythagorean theorem
6^2 + 8^2 = AC^2
36 + 64 = AC^2
100 = AC^2
10 = AC
6+8+10 = 24
24/60 = 2/5
10/x = 2/5
50 = 2x
25 = x
I can help! With the Greatest Common Factor you figure out the greatest number that can go into all numbers. The number here would be the 2. You then divide 2 by all the numbers in the problem.
You would end up getting x^2 + 6x + 9
I use to struggle with this too. Hope this helps! Have a great day!!