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Ede4ka [16]
2 years ago
13

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

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

Answer:

C on edg

Step-by-step explanation:

Ahat [919]2 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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hodyreva [135]

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Step-by-step explanation:

7 0
2 years ago
a cleaning service charges an hourly rate plus a flat fee of $15 for supplies. philip uses the service for 3.5 hours for his spr
Sergeu [11.5K]

Using linear function concepts, it is found that he can correctly determine the hourly rate as follows:

subtract the supply fee, 15 dollars from the total cost, then, divide the difference by the number of hours.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, which can also be interpreted as the initial value of a function that is valid only for x \geq 0, such as is the case in this problem.

The flat fee is of $15, hence b = 15, then:

y = mx + 15

Philip uses the service for 3.5 hours for his spring cleaning, and his total is $232, hence when x = 3.5, y = 232, so we use it to find the hourly rate m.

y = mx + 15

232 = 3.5m + 15

m = \frac{232 - 15}{3.5}

Hence, the correct option is:

subtract the supply fee, 15 dollars from the total cost, then, divide the difference by the number of hours.

You can learn more about linear function concepts at brainly.com/question/24808124

7 0
2 years ago
Part A: Write the measure of each exterior angle directly on the diagram.
ololo11 [35]

Answer:

360°

Step-by-step explanation:

Sum of exterior angle of any polygon = 360

Sum of exterior angle of pentagon = 360

3 0
1 year ago
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y^2 (y + 2) + 16(y + 2)

(y+2) (y^2+16)

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