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Ede4ka [16]
3 years ago
13

Look at the pentagonal numbers. Use finite differences to determine which function represents the pattern.

Mathematics
2 answers:
Alecsey [184]3 years ago
5 0

Answer:

C on edg

Step-by-step explanation:

Ahat [919]3 years ago
3 0

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  

______

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Step-by-step explanation:

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2) ∛24x³y^8=

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7 0
3 years ago
Simplify the expression.<br> -5+i/2i
Lostsunrise [7]

Answer:

\rm - \dfrac{11}{2}

Step-by-step explanation:

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7 0
3 years ago
The average reading score on certain tests is given by y = 0.153x + 255.4, where x is the number of years past 1970. In what yea
nirvana33 [79]

Average reading score is given by the expression,

        y = 0.153x + 255.4

Here, x in the number of years past 1970.

To find the year in which the average reading score is 259.378, substitute the value of 'y' in the given expression.

y = 0.153x + 255.4

259.378 = 0.153(x) + 255.4

0.153x = 259.378 - 255.4

0.153x = 3.978

x = \frac{3.978}{0.153}

x = 26

That means given average reading score 259.378 will be 26 years after 1970.

       Therefore, 1996 is the year in which the average reading score will be 259.378.

Learn more,

brainly.com/question/2883790

3 0
2 years ago
Which equation is written in slope-intercept form?
dlinn [17]

Answer:

y=3x+2

Step-by-step explanation:

slope intercept form

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b= y-intercept

5 0
3 years ago
The two triangles below are similar. What is the similarity ratio of ΔABC to ΔDEF?
Evgesh-ka [11]
It would be a 2:1 ratio because sides AC and DF are 8:4 which simplifies to 2:1

Hope this helps!
5 0
3 years ago
Read 2 more answers
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