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
______
58.51%
however, it is estimating so depending on the answer choices it would be around 55-60% or so
LETS prove the 2nd part of the Question
Here concept of right angles is used
We can see BA is perp to BD
and BC is perp to BE
We have to prove angle 1 = angle 3
i will denote angle by a
therefore we need to prove a1 = a3
as BA is perp to BD hence angle between them will be 90 degree
a1 + a2 = 90 degree
Similarly BC is perp to BE
a2 + a3 = 90 degree
as both equations add up gives 90 degree so will equate them
a1 + a2 = a2 + a3
which means a1 = a3
Hence Proved
To learn more about Right Angles:
brainly.com/question/7116550
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Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Terms/Coefficients
- Factoring
Step-by-step explanation:
<u>Step 1: Define</u>
<u />
<u />
<u />
<u>Step 2: Simplify</u>
- [Fraction] Factor numerator:
- [Fraction] Factor denominator:
- [Fraction] Divide:
Answer:
6:9 ÷3
2:3
Step-by-step explanation:
1st write the ratio then simplify it with dividing with the Highest common factor on both sides
