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:
(s-6)/r
option D
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.
Compare y=mx+b and y=cx+6, we see that m=c and c is the slope.
Now we are also given that (r,s) is on our line which means s=c(r)+6.
We need to solve this for c to put c in terms of r and s as desired.
s=cr+6
Subtract 6 on both sides:
s-6=cr
Divide both sides by r:
(s-6)/r=c
The slope in terms of r and s is:
(s-6)/r.
Step-by-step explanation:
total working duration = 2 weeks
Working duration in hours = 38× 2= 76 hours
a) per year
24*3115.35 = $74768
b) 3115.35/2
$1557.675
c)
3115.35/76
$40.99
Answer:
y = -3x + 4
Step-by-step explanation:
y = 4, this is where your line intersects with the y axis.
x = 1 is where your line is on the x axis (you want to include the part of the line that hits a point straight on, not one that goes past it.) So when it lands on the corner of the grids like the 4 for the y axis does, that is the point you are going to use.
Rise/Run is then your equation, so since you go down 3 and over 1 (counting from your y axis point), your slope is -3/1 or -3.
Then goes your y axis, so the final equation is
y= -3x + 4
I hope this helped!
Step-by-step explanation:
Parallel lines have the same slope, so we know that our line will have a slope of 3 because y = 3x + 9 has a slope of 3. Now, we can use the point-slope formula of the line to find the equation.
We have y - y₁ = m (x - x₁) (m = 3, x₁ = 2, y₁ = -2)
y- (-2) = 3 (x - 2)
y + 2 = 3x - 6
y = 3x - 8
Hope this helps!
