Answer:
f(x) = 1.5x - 0.5x
Step-by-step explanation:
The function of the pattern represented by the pentagonal numbers is the sum of three triangular numbers.
The triangular number general formula
x (x + 1) / 2
For example,
The sequence
1, 3, 6, 10
*
* * *
* * * * * *
* , * *, * * *, * * * *
_____________________________
The pentagonal numbers
The sequence:
1, 5, 12, 22, 35
As shown in the picture can be divided into three triangles
Triangle 2
x (x + 1) / 2
Triangle 1 and 3 (they are triangles one unit smaller than 2)
n (n + 1) / 2
n= x-1
Replacing n
(x-1) ((x-1) + 1) / 2
(x-1) (x) / 2
(x-1) x / 2
______________
Function represents the pattern
Triangle 2 + (Triangle 1 + Triangle 3)
Triangle 1 = Triangle 3
So then,
Triangle 2 + 2* Triangle 1
x (x +1) /2 + 2* (x -1) x/2
Rearranging
0.5 x (x +1) + x(x -1)
0.5x^2 + 0.5x + x^2 -x
(0.5 x^2 + x^2) + (0.5x -x )
1.5 x^2 - 0.5 x
______
Answer:
40, 48, 56
Step-by-step explanation:
8x5 is 40
8x6 is 48
8x7 is 56
I hope this helps have a good day
It would be 57 suvs and 38 sedans sold to be a rational of 3:2
Answer:
copied from InesWalston expert
Money in the bank account after 3 years will be $329.18
Step-by-step explanation:
Jackie deposited $315 into a bank account that earned 1.5% simple interest each year for 3 year, while no money was deposited into or withdrawn from the account.
We know that,
i = p.r.t / 100
Where,
i = interest
P = Principal = $315
r = Rate of interest = 1.5% annual
t = time period = 3 years
Putting the values,
i = 315 × 1.5 × 3 / 100 = $14.18
Total money in bank account = Principal + interest = 315 + 14.18 = $329.18