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:
Les trois nombres sont 5, 6 et 7.
Step-by-step explanation:
Soit x le premier nombre.
x + 1 sera le second et x + 2 sera le troisième.
On pose l'équation :
2x + 3(x + 1) = 4(x + 2)
2x + 3x + 3 = 4x + 8
5x - 4x = 8 - 3
x = 5
Answer:
by 3/4ftmrs torrer is shorter than her husband
6 1/4-5 1/2=25/4-11/2=3/4ft
<h3><em>
Hey! </em></h3>
<u>let the numbers be n and m</u>
<u>n+m=65</u>
<u>n=4m</u>
<em>So when we put our work in:</em>
<u>4m+m=65</u>
<u>5m=65</u>
<u>m=13</u>
<u>n=52</u>
So therefore your two numbers are 52 and 13!
<em>Hope this helped! °ω°</em>
Answer:
x = 3
Hope this helps!
Step-by-step explanation:
ΔABC is a 45°, 45°, 90° triangle. The longest side ( 6
) can be
while AB and CB are x. Because 6
is equal to
, you can see that x is equal to 6. Both AB and CB are equal to 6. ΔBDC ( CDB ) is a right triangle ( 30°, 60°, 90° ) so, BD = x, CB = 2x, and CD =
. CB is equal to 6 so 2x = 6, x = 3.