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Table:
Number of Pentagons n | Perimeter p |
---|---|
1 | 5 |
2 | 8 |
3 | 11 |
Words: See solution.
Equation: P=3n+2
Graph:
Let's take a look at the given figures.
Let's make a table that shows the perimeter of the figures p depending the number of pentagons n.
Number of Pentagons n | Perimeter p |
---|---|
1 | 5 |
2 | 8 |
3 | 11 |
Next, we will interpret this table.
The pattern we see is that the perimeter of the figures increases by 3 as the number of pentagons increases by 1. We can use this to write an equation that represents the perimeter of the figures.
Number of Pentagons n | P=3n | Perimeter Found by the Formula | Actual Perimeter |
---|---|---|---|
1 | P=3( 1) | 3 | 5 |
2 | P=3( 2) | 6 | 8 |
3 | P=3( 3) | 9 | 11 |
The perimeter found by the incomplete formula is always 2 less than the actual perimeter. Therefore, we can complete our formula by adding 2 to the formula. P= 3n+2 Next, we will make a graph that represents the perimeter of the given figures depending on the number of pentagons.
Using the table, we have three ordered pairs. (1,5) (2,8) (3,11) Plotting these points on the coordinate plane, we can have our graph. Let the x-axis represent the number of the pentagons that a figure has and let the y-axis represent the perimeter of the figure.