find a rule for the output values. write the rule as an eqution that includes the variable A and B.

1. output B: 5,7,9,11
2. output B: 10,7,4,1
3. output B: 6,12,24,48

To find the rule for the output values, we need to observe the pattern in each sequence. Let's examine each sequence step-by-step.

1. In sequence 1, the output values for B increase by 2 each time. Therefore, we can write a rule as follows: B = 2A + 3.

2. In sequence 2, the output values for B decrease by 3 each time. Therefore, we can write a rule as follows: B = -3A + 13.

3. In sequence 3, the output values for B double each time. Therefore, we can write a rule as follows: B = 6 x 2^(A-1).

So, the rule for the output values, written as an equation that includes the variables A and B, are as follows:

1. B = 2A + 3
2. B = -3A + 13
3. B = 6 x 2^(A-1)

To find the rule for the output values, we need to look for a pattern or a relationship between the input variables (A) and the output variables (B) in each set of data.

Let's analyze each set of output values:

1. When A increases by 1, B increases by 2. So, we can define the rule as B = 2A + 3.

2. When A decreases by 1, B decreases by 3. So, we can define the rule as B = -3A + 13.

3. When A increases by 1, B doubles. So, we can define the rule as B = 6 * 2^(A-1).

Therefore, the equations that include the variables A and B for each set of data are as follows:

1. B = 2A + 3
2. B = -3A + 13
3. B = 6 * 2^(A-1)