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The answer to page 13.10 in the Punchline Algebra book is typically a math problem or exercise that requires solving equations or manipulating algebraic expressions. As for where the tree invited all its friends on Friday night, this is likely a joke or riddle included in the book to add humor and engage students in the learning process. The answer to the joke would be a playful or imaginative location, not a literal event.
the redwood tree
Your best bet here would be to use trigonometry. One stand a given distance away from the tree and sight the top of the tree, say with a clinometer, to measure the angle of elevation. Then knowing the angle and the distance you are from the tree, the height of the tree can be calculated with a tangent function.
No, it is not an adverb. The word tree is a noun, or verb (to chase up a tree). The adjective is "treed" (active or passive) but there is no adverb form.
When there's a tree that has iron and usually uses analogy to be happy.