Graham is folding a piece of paper to make an origami figure. each time he folds the paper, the thickness of the paper is doubled. the paper starts out flat, with a thickness of 3 millimeters. a. write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. explain how you came up with your ordered pairs. b. is this relation a function? explain why or why not using the ordered pairs you came up with in part a

A. Given,

The initial thickness of paper = 3 mm,

Also, the thickness of the paper is doubled in each fold,

In first fold,

The thickness of the paper = 2(3) mm

In second fold = mm

In third fold = mm

.......so on...

So, the thickness of the paper after x folds,

 (if y represents the thickness of paper ( in mm ) after x folds)

If x = 1, 2, 3, 4, 5, 6

y = 6, 12, 24, 48, 96, 192

Hence, the order pairs that shows the given situations are,

(1, 6), (2, 12), (3, 24), (4, 48), (5, 96), (6, 192)

B. A relation is called function if there is only one output for each input,

Here, for each values of x there is a different value of y,

Hence, the relation in numbers of fold and thickness of the paper is a function.

it would be:

c.parallelogram.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)