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:
±
2
√
2
+
2
Step-by-step explanation:
Answer:
guys just be like dat
Step-by-step explanation:
Answer:
The land which are used for exhibits are <u>89 acres</u> (approximately).
Step-by-step explanation:
Given:
Village is spread across 240 acres of land. 37% of land is used for the exhibits.
Now, we have to find acres of land which are used for exhibits.
So, here it is given that land used for exhibits is 37%, and we have to calculate the quantity from the percentage given:
According to question:
37% of 240 acres of land.
So, the land used for exhibits are 88.80 acres.
Therefore, the land which are used for exhibits are <u>89 acres </u>(approximately).
The whole number of minutes that Gianna complete each week as a function of x and y:
Since the above number is greater than 450 minutes, we get the inequality:
Also, "she can complete at most 10 workouts this week" so we deduce the inequality:
Therefore, the system of inequalities is the following:
The above system has many solutions, for example :
