Lesson 1: growing and shrinking

han has a thin rectangular sheet of paper. its area is 450 square inches. he folds it into thirds, and then he folds the resulting rectangle into thirds again.

1.) han believes that after two rounds of folding, the visible area of the folded paper will be 150 square inches or one-third of the original area. do you agree? explain your reasoning.

2.) what is the visible area of the paper, in square inches, after 4 rounds of folding? explain or show your reasoning.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

Which zero pair could be added to the function f(x) = x2 + 12x + 6 so that the function can be written in vertex form? o 3, -3o 6,629,-936, 36

Due to bad planning, two of the local schools have their annual plays on the same weekend. while 457 people attend one, and 372 attend the other, only 104 people were able to attend both. how many people went to at least one play?