Make a table with a process column to represent each pattern. Write an expression for the number of tiles in the nth figure.
The picture is a column of squares that is 6x4, and each figure its subtracting a square.
Description of picture is inadequate to understand.
Sure! Here is a table with a process column representing the pattern of square figures, and an expression for the number of tiles in the nth figure:
| Figure (n) | Process | Number of Tiles |
|------------|---------|-----------------|
| 1 | 6x4 | 24 |
| 2 | 5x3 | 15 |
| 3 | 4x2 | 8 |
| 4 | 3x1 | 3 |
The expression for the number of tiles in the nth figure can be represented as:
Number of Tiles = (7 - n) x (5 - n)
Where n is the figure number.
To create a table with a process column that represents each pattern, we need to analyze the given information and find a general expression for the number of tiles in the nth figure. Let's break down the problem step by step.
The initial figure has dimensions 6x4, which means it consists of 6 rows and 4 columns of squares. Let's label this figure as Figure 1.
To calculate the number of tiles in each subsequent figure, we observe that each figure subtracts a square from the previous one. This deduction indicates that the number of tiles in each figure follows a decreasing pattern.
Now, let's create a table to represent the process column and find a general expression for the number of tiles in the nth figure:
| Figure (n) | Process (Subtracting a square) | Number of Tiles |
|------------|-------------------------------|-----------------|
| 1 | - | 6x4 |
| 2 | - 1 square | 5x3 |
| 3 | - 1 square | 4x2 |
| 4 | - 1 square | 3x1 |
| 5 | - 1 square | 2x0 |
From the table, we notice that the length and width of each figure decrease by 1 unit compared to the previous figure. Using this information, we can create an expression for the number of tiles in the nth figure.
The general expression for the number of tiles in the nth figure can be calculated using the formula:
Number of Tiles = (6 - (n - 1)) × (4 - (n - 1))
This expression incorporates the concept of decrementing the length and width by 1 unit for each subsequent figure.
For example, when n = 3, the expression becomes:
Number of Tiles = (6 - (3 - 1)) × (4 - (3 - 1))
= (6 - 2) × (4 - 2)
= 4 × 2
= 8
Therefore, the number of tiles in the 3rd figure is 8.
Using the general expression, you can substitute different values of n to find the number of tiles in any given figure.