Question

In the diagram​ below, what is the relationship between the number of pentagons and the perimeter of the figure they​ form? Represent this relationship using a​ table, words, an​ equation, and a graph. Let xequalsthe number of pentagons. Let yequalsthe perimeter of the figure.
3
3
3
3
1 pentagon
2 pentagons
3 pentagons
3
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Part 1
Represent the relationship using a table. Complete the table below.
Number of Pentagons​, x
​Perimeter, y
Ordered Pair​ (x,y)
1
  
enter your response here
  
enter your response here
2
  
enter your response here
  
enter your response here
3
  
enter your response here
  
enter your response here

Answer 1

what are the order pair

Answer 2

To establish the relationship between the number of pentagons and the perimeter of the figure they form, we first need to determine how the perimeter changes as we increase the number of pentagons.

### Understanding the Configuration
- Each pentagon has 5 sides.
- When you connect pentagons together, some sides may overlap, affecting the total perimeter.

### Assuming a Specific Configuration:
Let's consider that when you add another pentagon, it shares one side with the previous pentagon. In this case:

- For **1 pentagon**, all 5 sides contribute to the perimeter, so:
- Perimeter = 5
- For **2 pentagons**, one side is shared, so:
- Perimeter = 5 + 4 = 9
- For **3 pentagons**, two sides are shared, so:
- Perimeter = 5 + 4 + 4 = 13

### Perimeter Calculations:
- 1 pentagon: \( y = 5 \)
- 2 pentagons: \( y = 9 \)
- 3 pentagons: \( y = 13 \)

### Completing the Table:
Using the information we computed, we can fill out the table as follows:

| Number of Pentagons, x | Perimeter, y | Ordered Pair (x,y) |
|-------------------------|---------------|---------------------|
| 1 | 5 | (1, 5) |
| 2 | 9 | (2, 9) |
| 3 | 13 | (3, 13) |

### Expressing the Relationship in Words:
The perimeter of the figure formed by the pentagons increases as the number of pentagons increases. Specifically, for each additional pentagon added, the perimeter increases by 4, accounting for the shared side.

### Equation Representing the Relationship:
From the values in the table, we can derive a linear equation:
\[ y = 4x + 1 \]
Where:
- \( y \) is the perimeter
- \( x \) is the number of pentagons

### Graphing the Relationship:
To create a graph:
- Plot the points (1, 5), (2, 9), and (3, 13) on a graph where the x-axis represents the number of pentagons and the y-axis represents the perimeter.
- You would see a straight line indicating a linear relationship between the number of pentagons and the perimeter.

This approach gives you a comprehensive view of how the perimeter of the figure changes with the number of pentagons.

Answer 3

The ordered pairs for the relationship between the number of pentagons \( x \) and the perimeter \( y \) are:

1. For 1 pentagon: \( (1, 5) \)
2. For 2 pentagons: \( (2, 9) \)
3. For 3 pentagons: \( (3, 13) \)

So the complete list of ordered pairs is:
- \( (1, 5) \)
- \( (2, 9) \)
- \( (3, 13) \)