A function machince accepts inputs as ordered pairs. The componeys of the ordered pairs are natural numbers and the first componet is the length of the rectangle and the second componet is the width. the given machince comptes the perimeter ( the distance around the rectangle) find the out put for(1,7) (7,6) (6,3) and (5,6)

FIND AN INPUT THAT GIVES AN OUTPUT OF 12
RECTANGLE 2L +2W

P = 2*L + 2*W

(1,7) --> 2*1 + 2*7 = 2+14 = 16
(7,6) --> 2*7 + 2*6 = 14 + 12 = 26
etc

if you want 12
pick an L, say 4

2*4 + 2*w = 12
4 + w = 6
w = 2
so (4,2)

To find the output of the function machine, we need to calculate the perimeter of each rectangle. The formula for the perimeter of a rectangle is 2L + 2W, where L is the length and W is the width.

Let's calculate the output for each of the given input ordered pairs:
1. For (1,7): Perimeter = 2(1) + 2(7) = 2 + 14 = 16
2. For (7,6): Perimeter = 2(7) + 2(6) = 14 + 12 = 26
3. For (6,3): Perimeter = 2(6) + 2(3) = 12 + 6 = 18
4. For (5,6): Perimeter = 2(5) + 2(6) = 10 + 12 = 22

Now, we need to find an input that gives an output of 12. We can solve this by substituting the perimeter formula and solving for one of the variables.

Let's assume L as the length and W as the width. We have the equation 2L + 2W = 12.

We can simplify this equation by dividing both sides by 2:
L + W = 6

To find an input that satisfies this equation, we need to find two natural numbers whose sum is 6. One such pair would be (2, 4).

So, for the input (2, 4), the output of the function machine would be:
Perimeter = 2(2) + 2(4) = 4 + 8 = 12

Therefore, an input that gives an output of 12 is (2, 4).