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.
130 degrees is the answer
Answer:
12.4 feet
Step-by-step explanation:
A ladder placed against the wall forms a right angle triangle
Hypotenuse ² = opposite ² + adjacent ²
Hypotenuse = 13 feet
Opposite = 4 feet
Adjacent = x
Hypotenuse ² = opposite ² + adjacent ²
13² = 4² + x²
169 = 16 + x²
169 - 16 = x²
153 = x²
Find the square root of both sides
√153 = √x²
12.369316876852 = x
x = 12.4 feet
Adjacent = x = 12.4 feet
Answer:
y = 700 +22x
Step-by-step explanation:
The CD account balance is 722 after the first year and increases by $22 each year. The function rule is a linear function with a y-intercept of 700 and a slope of $22 per year.
y = 700 +22x . . . . . . ending balance after x years
