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
______
First we need to put it in slope intercept form (solve for y). Then we get tex]y= -\frac{2}{3} x+490[/tex]. So the slope is-2/3 and the y intercept is 490.
M5 is the same as m1 so it's 75°
The probability that it doesn't land on 4 would be 3/8. This is because theres a 5/8 chance it lands on 4 so just do the opposite which would be 3/8.
Given parameters:
Total length of curtains bought = 20m
She used 8m for the living room
She used 7m for the dining room
unknown:
Quantity used for the kitchen = ?
Solution:
Quantity used for the kitchen = Total length - (living room + dining room)
Input the parameters given solve;
Quantity used for the kitchen = 20 - (8 + 7) = 5m
The length of curtain used for the kitchen is 5m