A student is given a flow diagram with inputs and outputs. The rule is to multiply the input by 9 and add 8. Fill in the missing values, identify the input and output values, state the rule, write num

Here are the solutions based on the provided flow diagram and questions:

a.i. Complete the flow diagram:

The rule is "$\times 9 + 8$".

• For input 3: $3 \times 9 + 8 = 27 + 8 = 35$
• For output 89: Let input be $x$. $x \times 9 + 8 = 89 \implies 9x = 81 \implies x = 9$
• For input 4: $4 \times 9 + 8 = 36 + 8 = 44$
• For input 6: $6 \times 9 + 8 = 54 + 8 = 62$
• For input 7: $7 \times 9 + 8 = 63 + 8 = 71$
• For output 17: Let input be $y$. $y \times 9 + 8 = 17 \implies 9y = 9 \implies y = 1$

The completed flow diagram values are:

• Inputs: $3, 9, 4, 6, 7, 1$
• Outputs: $35, 89, 44, 62, 71, 17$

a.ii. What are the input values?
The input values are $\boxed{\text{3, 9, 4, 6, 7, 1}}$.

a.iii. What are the output values?
The output values are $\boxed{\text{35, 89, 44, 62, 71, 17}}$.

a.iv. What is the rule?
The rule is $\boxed{\text{multiply by 9 and add 8 (or } \times 9 + 8)}$.

a.v. Number sentences:

• $3 \times 9 + 8 = 35$
• $9 \times 9 + 8 = 89$
• $4 \times 9 + 8 = 44$
• $6 \times 9 + 8 = 62$
• $7 \times 9 + 8 = 71$
• $1 \times 9 + 8 = 17$

a.vi. What will the output values be if the rule is + 2 x 7?
Assuming the rule means (input + 2) $\times$ 7, and using the input values from the flow diagram (3, 9, 4, 6, 7, 1):

• For input 3: $(3 + 2) \times 7 = 5 \times 7 = 35$
• For input 9: $(9 + 2) \times 7 = 11 \times 7 = 77$
• For input 4: $(4 + 2) \times 7 = 6 \times 7 = 42$
• For input 6: $(6 + 2) \times 7 = 8 \times 7 = 56$
• For input 7: $(7 + 2) \times 7 = 9 \times 7 = 63$
• For input 1: $(1 + 2) \times 7 = 3 \times 7 = 21$

The output values would be $\boxed{\text{35, 77, 42, 56, 63, 21}}$.