IM 8.8.10 Practice: Applications of the Pythagorean Theorem

A man is trying to zombie-proof his house. He wants to cut a length of wood that will brace a door against a wall. The wall is 4 feet away from the door, and he wants the brace to rest 2 feet up the door.
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[/img][br][br]About how long should he cut the brace?[br]
[size=100][size=150]At a restaurant, a trash can’s opening is rectangular and measures 7 inches by 9 inches. The restaurant serves food on trays that measure 12 inches by 16 inches. Jada says it is impossible for the tray to accidentally fall through the trash can opening because the shortest side of the tray is longer than either edge of the opening. Do you agree or disagree with Jada’s explanation? Explain your reasoning.[/size][/size]
Select all the sets that are the three side lengths of right triangles.
Which of the two numbers is larger?
[math]12\cdot10^9[/math] and [math]4\cdot10^9[/math]
[size=100]How many times larger?[/size]
[math]1.5\cdot10^{12}[/math] and [math]3\cdot10^{12}[/math]
[size=100]How many times larger?[/size]
[math]20\cdot10^4[/math] and [math]6\cdot10^5[/math]
How many times larger?
[size=150]A line contains the point [math](3,5)[/math]. If the line has negative slope, which of these points could also be on the line?[/size]
[size=150]Noah and Han are preparing for a jump rope contest. Noah can jump 40 times in 0.5 minutes. Han can jump [math]y[/math] times in [math]x[/math] minutes, where [math]y=78x[/math]. [/size][br]If they both jump for 2 minutes, who jumps more times? 
How many more?
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Information: IM 8.8.10 Practice: Applications of the Pythagorean Theorem