Complete the rule and calculate N. The rule for the table below is: Input: 1, Output: 3, Input: 2, Output: 5, Input: 3, Output: 7, Input: 4, Output: 9. Choose from the following options: a) Input numb

Let the input be $x$ and the output be $y$.
From the table:
For $(2, 3)$: $y = 3$ when $x = 2$.
For $(5, 18)$: $y = 18$ when $x = 5$.
For $(10, 43)$: $y = 43$ when $x = 10$.
For $(13, 58)$: $y = 58$ when $x = 13$.

Let's assume a linear rule of the form $y = ax + b$.
Using $(2, 3)$ and $(5, 18)$:
$3 = 2a + b$ (Equation 1)
$18 = 5a + b$ (Equation 2)

Subtract Equation 1 from Equation 2:
$18 - 3 = (5a + b) - (2a + b)$
$15 = 3a$
$a = \frac{15}{3}$
$a = 5$

Substitute $a = 5$ into Equation 1:
$3 = 2(5) + b$
$3 = 10 + b$
$b = 3 - 10$
$b = -7$

The rule is $y = 5x - 7$.
This means "Input number $\times 5 - 7$".
The missing operation in the flow diagram is $\times 5$.

For Input 9, the output is N.

The completed rule is: Input number $\times 5 - 7$.
The value of N is $\boxed{\text{38}}$.

2) The rule for the table below is:

Input: 1, Output: 3
Input: 2, Output: 5
Input: 3, Output: 7
Input: 4, Output: 9

• Option 1: Input number $\times 2 + 3$ For Input 1: $1 \times 2 + 3 = 5$ (Incorrect, should be 3)

• Option 2: Input number $\times 2 + 1$ For Input 1: $1 \times 2 + 1 = 3$ (Correct) For Input 2: $2 \times 2 + 1 = 5$ (Correct) For Input 3: $3 \times 2 + 1 = 7$ (Correct) For Input 4: $4 \times 2 + 1 = 9$ (Correct)

• Option 3: Input number $\times 3 + 2$ For Input 1: $1 \times 3 + 2 = 5$ (Incorrect, should be 3)

• Option 4: Input number $\times 2 - 1$ For Input 1: $1 \times 2 - 1 = 1$ (Incorrect, should be 3)

The correct rule is option 2.
The rule is $\boxed{\text{Input number} \times 2 + 1}$.

3) Use the rule below to determine the output value if the input value is 3.

Rule: "input value $\times 5 - 4$"
Input value = 3

Output value $= 3 \times 5 - 4$

Output value $= 15 - 4$
Output value $= 11$

Your answer of "output value = 14" is ❌ Incorrect.
The correct output value is $\boxed{\text{11}}$.