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:
-67
Step-by-step explanation:
2^3-(3*5^2)
simplify exponents
8-3*25
8-75
=-67
Answer:
-40
Step-by-step explanation:
f(a) = a³ - a² + a - 1
f(-3) = (-3)³ - (-3)² + (-3) - 1
f(-3) = (-27) - (9) + (-3) -1
f(-3) = -27 - 9 -3 - 1
f(-3) = -40
Well, 10x4=40 because 10+10+10+10=40 and that means your answer must be 40 ones or you asked something else.
Answer:the answer should be c
Step-by-step explanation:So, the 11 is an exponent. That means that the problem can be written as 11 x 7/4 so it should be c.