Let <em>S</em> denote the sum
![1\cdot3+2\cdot4+3\cdot5+\cdots+n\cdot(n+2)](https://tex.z-dn.net/?f=1%5Ccdot3%2B2%5Ccdot4%2B3%5Ccdot5%2B%5Ccdots%2Bn%5Ccdot%28n%2B2%29)
We can condense this to sigma notation:
![S=\displaystyle\sum_{k=1}^nk(k+2)](https://tex.z-dn.net/?f=S%3D%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5Enk%28k%2B2%29)
Expand the summand:
![S=\displaystyle\sum_{k=1}^nk^2+2\sum_{k=1}^nk](https://tex.z-dn.net/?f=S%3D%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5Enk%5E2%2B2%5Csum_%7Bk%3D1%7D%5Enk)
Recall the Faulhaber formulas,
![\displaystyle\sum_{k=1}^nk=\frac{n(n+1)}2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5Enk%3D%5Cfrac%7Bn%28n%2B1%29%7D2)
![\displaystyle\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}6](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bk%3D1%7D%5Enk%5E2%3D%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D6)
So we have
![S=\dfrac{n(n+1)(2n+1)}6+n(n+1)=\boxed{\dfrac{n(n+1)(2n+7)}6}](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7Bn%28n%2B1%29%282n%2B1%29%7D6%2Bn%28n%2B1%29%3D%5Cboxed%7B%5Cdfrac%7Bn%28n%2B1%29%282n%2B7%29%7D6%7D)
We need to find the scale factor, which is given as
![\text{factor}=\frac{115\text{ meters}}{\text{23 millimeters}}=5](https://tex.z-dn.net/?f=%5Ctext%7Bfactor%7D%3D%5Cfrac%7B115%5Ctext%7B%20meters%7D%7D%7B%5Ctext%7B23%20millimeters%7D%7D%3D5)
then, this means that 1 millimeter : 5 meters
Answer:
the answer is true
Step-by-step explanation:
the x values don't repeat themselves so therefore it is a function
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
The given equation is
12x + 2y = 6
we would make this equation to look like the slope intercept equation.
12x + 2y = 6
If we subtract 12x from both sides of the equation, it becomes
12x - 12x + 2y = 6 - 12x
2y = 6 - 12x
2y = - 12x + 6
Dividing both sides of the equation by 2, it becomes
y = - 6x + 3
Thus, by comparing with the slope intercept equation,
slope = - 6
y intercept = 3
Step-by-step explanation:
9% tax means 9% increase
multiplier ×1.09
149.33×1.09=162.7967
plss mark brainliest