7/3 3 I think that is the answer good luck
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:

Step-by-step explanation:

<u>Multiply both sides of the equation by 6:</u>

<u>Subtract 12 from both sides:</u>

<u>Subtract 12 from 96:</u>

<u>_________________________________</u>
Answer:
2x - y = 6
Step-by-step explanation:
The equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
Given
y = 2x - 6 ( add 6 to both sides )
y + 6 = 2x ( subtract y from both sides )
6 = 2x - y, that is
2x - y = 6 ← in standard form