Math Mania 2001

  1. In the diagram shown, all angle measures are in degrees. Given that y = 80 degrees and z = 120 degrees , find x.
    triangle with three labeled points x, y and z
  2. Find the next term in the sequence: 4, 5, 8, 17, 44, 125, ...
  3. If 2x3 - 9x2 + 15x + k is evenly divisible by x - 2, what is the value of k?
  4. Find the equation of the circle passing through the points (0,0), (1,7), and (2,4).
  5. Solve the equation |x + 2| = 2|x - 3|.
  6. How many six-digit numbers contain at least one 7 in their decimal expansion?

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