In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect BA−→ and BC−→
. Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs. Based on this construction, what is the measure of ∠ABC ?.
2 answers:
Answer:
Step-by-step explanation:
Alright , lets get started.
From point B, two arcs are formed, BE and BD.
From the point, E and D, two again arcs are made which are intersecting each other at point P.
It means, line BP is bisector of angle ABC.
Hence the angle ABC is 64 degrees. : Answer
Hope it will help :)
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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
______
