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:
34) A
35) C
36) D
Step-by-step explanation:
34) The perimeter of a triangle is equal to the sum of the lengths of its sides
Sides: (6.2p + 4.5q) + (3.4p - 0.7r) + (2.9r - 4.1q)
Combine like terms (same variables)
(6.2p + 3.4p) + (4.5q - 4.1q) + (2.9r - 0.7r)
9.6p + 0.4q + 2.2r
A
35)
Time possibilities
1 hour - $3 - $5 = $-2 No
2 hours - $6 - $5 = $1 Yes
3 hours - $9 - $5 = $4 Yes
4 hours - $12 - $5 = $7 Yes
5 hours - $15 - $5 = $10 Yes
6 hours - $18 - $5 = $13 Yes
7 hours - $21 - $5 = $16 Yes
8 hours - $24 - $5 = $19 No
9 hours - $27 - $5 = $22 No
The possible hours that Ms. Barnes can park are 2 - 7 hours
The only inequality graph that represents all of these values is C
36)
<h3>Convert to improper fractions
<h3>Divide by finding the reciprocal
<h3>Convert back to a mixed number
D
Hope this helps :)