In the diagram​ below, what is the relationship between the number of rectangles and the perimeter of the figure they​ form? Represent this relationship using a​ table, words, an​ equation, and a graph. Let xequalsthe number of rectangles. Let yequalsthe perimeter of the figure.

Question

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3
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1 rectangle
3 rectangles
2 rectangles
Question content area bottom
Part 1
Represent the relationship using a table. Complete the table below.
Number of Rectangles​, 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
​(Simplify your​ answers.)

Answer 1

To represent the relationship between the number of rectangles and the perimeter of the figure they form, we begin by filling out the required table.

We can assume a common scenario with rectangles of uniform size stacked together, such that each addition of a rectangle increases the perimeter by a certain amount. However, without specific dimensions or a diagram to reference, I'll provide a hypothetical example illustrating a linear relationship.

Let's assume the following:

• For 1 rectangle, the perimeter is 4 units.
• For 2 rectangles, the perimeter is 8 units (if they're aligned side by side).
• For 3 rectangles, the perimeter is 12 units (again, if they're aligned side by side).

Here’s how you can represent the relationship:

Part 1: Represent the relationship using a table.

| Number of Rectangles, x | Perimeter, y | Ordered Pair (x,y) | |-------------------------|---------------|---------------------| | 1 | 4 | (1, 4) | | 2 | 8 | (2, 8) | | 3 | 12 | (3, 12) |

Part 2: Represent the relationship in words.

As the number of rectangles increases, the perimeter of the figure they form also increases. This shows a linear relationship where each rectangle contributes a consistent amount to the overall perimeter.

Part 3: Represent the relationship as an equation.

We can express the relationship with the equation: \[ y = 4x \] Where \( y \) is the perimeter and \( x \) is the number of rectangles.

Part 4: Represent the relationship graphically.

To create a graph, plot the ordered pairs from the table:

• Point (1, 4)
• Point (2, 8)
• Point (3, 12)

You would see a straight line starting at the origin (0, 0) and passing through the points listed, showcasing a linear relationship. The slope of the line would be 4, indicating that for each additional rectangle, the perimeter increases by 4 units.

Graph

The graph will look like a straight line increasing from the origin with a slope of 4.

• The x-axis will represent the number of rectangles (x).
• The y-axis will represent the perimeter (y).

This is how you can represent the relationship between the number of rectangles and the perimeter both tabularly and graphically!

Answer 2

simplify the answer

Answer 3

Certainly! Let's clarify and simplify the answer step by step.

Part 1: Table of Values

| Number of Rectangles (x) | Perimeter (y) | Ordered Pair (x,y) | |--------------------------|----------------|---------------------| | 1 | 4 | (1, 4) | | 2 | 8 | (2, 8) | | 3 | 12 | (3, 12) |

Part 2: Description in Words

As the number of rectangles increases, the perimeter also increases in a linear fashion.

Part 3: Equation

The relationship can be represented by the equation: \[ y = 4x \] where \( y \) is the perimeter and \( x \) is the number of rectangles.

Part 4: Graph Representation

• X-axis: Number of Rectangles (x)
• Y-axis: Perimeter (y)

Points to Plot:

• (1, 4)
• (2, 8)
• (3, 12)

Summary

Table:

| x | y | (x,y) | |---|---|-------| | 1 | 4 | (1,4) | | 2 | 8 | (2,8) | | 3 | 12| (3,12)|

Equation: \( y = 4x \)

This representation provides a clear and simplified summary of the relationship between the number of rectangles and the perimeter.