26. Your boss asks you to package toy blocks into a box so he can
1 answer:
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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
8 units.
EXPLANATION
The first point, A is located at (-9,2) on the coordinate plane.
The second point, B is also located at (-9,10) on the coordinate plane.
You should be smart and observe that the x-coordinates of both points are the same. This means that, the two points lies on a vertical line.
Hence it will be faster to use the absolute value method rather than the distance formula.
According to this method, you only have to find the absolute value of the difference in the y-values.
8 units.
EXPLANATION
The first point, A is located at (-9,2) on the coordinate plane.
The second point, B is also located at (-9,10) on the coordinate plane.
You should be smart and observe that the x-coordinates of both points are the same. This means that, the two points lies on a vertical line.
Hence it will be faster to use the absolute value method rather than the distance formula.
According to this method, you only have to find the absolute value of the difference in the y-values.