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two vertices of a triangle are (0,0) and (8,0). the x-coordinate on the third vertex is 4. imagine that you draw, on a coordinate plane, several triangles that meet all these conditions. what would be the same about all the triangles you drew? what would be different?

What basic trigonometric identity would you use to verify that csc x sec x cot x = csc^(2)x

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

41/17 as a decimal rounded to the nearest hundredth