Find the common difference in the outputs to help find the missing outputs in the table. Be sure to show your work.
a
5
6
7
8
9
b
3.8
4.6
5.4
To find the common difference, we need to look at the difference between consecutive outputs in each column.
For column a, the difference between each consecutive output is 1.
For column b, the difference between each consecutive output is 0.8.
To find the missing outputs in column b, we can continue adding 0.8 to the previous output.
The missing output after 5.4 would be 6.2, and the next missing output would be 7.0.
Therefore, the completed table would be:
a | b
---|---
5 | 3.8
6 | 4.6
7 | 5.4
8 | 6.2
9 | 7.0
To find the common difference in the outputs in the table, we need to look at the differences between consecutive numbers.
Let's focus on the first set of outputs, labeled as "a". We start by subtracting each number in the set from its consecutive number:
6 - 5 = 1
7 - 6 = 1
8 - 7 = 1
9 - 8 = 1
Since the differences are all 1, we can conclude that the common difference in the outputs for set "a" is 1.
Now, let's move on to the second set of outputs, labeled as "b". We will repeat the process of finding the differences between consecutive numbers:
4.6 - 3.8 = 0.8
5.4 - 4.6 = 0.8
Since the differences are both 0.8, we can conclude that the common difference in the outputs for set "b" is 0.8.
Based on the common differences, we can find the missing outputs in the table.
To find the missing outputs for set "a", we start with the last known number (9) and add the common difference (1) four times:
9 + 1 = 10
10 + 1 = 11
11 + 1 = 12
12 + 1 = 13
So the missing outputs for set "a" are 10, 11, 12, 13.
To find the missing output for set "b", we start with the last known number (5.4) and add the common difference (0.8) twice:
5.4 + 0.8 = 6.2
6.2 + 0.8 = 7.0
So the missing outputs for set "b" are 6.2 and 7.0.
Therefore, the missing outputs in the table are:
a
5
6
7
8
9
10
11
12
13
b
3.8
4.6
5.4
6.2
7.0
To find the common difference in the outputs, we need to look for a pattern in the differences between consecutive outputs.
For the first set of outputs, the differences are:
6 - 5 = 1
7 - 6 = 1
8 - 7 = 1
9 - 8 = 1
So, the common difference in the first set is 1.
For the second set of outputs, the differences are:
4.6 - 3.8 = 0.8
5.4 - 4.6 = 0.8
So, the common difference in the second set is also 0.8.
Therefore, the missing outputs in the second set would be obtained by adding the common difference of 0.8 to the previous output. Since the previous output is 5.4, the missing outputs would be:
5.4 + 0.8 = 6.2
6.2 + 0.8 = 7.0
So, the missing outputs in the second set would be 6.2 and 7.0.