Let alpha and beta be conjugate complex numbers such that frac{\alpha}{\beta^2} is a real number and alpha - \beta| = 2 \sqrt{3}. find alpha.

Two language majors, anna and megan, took exams in two languages. anna scored 85 on both exams. megan scored 74 on the first exam and 85 on the second exam. overall, student scores on the first exam had a mean of 82 and a standard deviation of 4, and the second exam scores had a mean of 71 and a standard deviation of 13. a) to qualify for language honors, a major must maintain at least an 85 average across all language courses taken. so far, which of anna and megan qualify? b) which student's overall performance was better?

The room above is shaped like a rectangle anthe room above is shaped like a rectangle and has a perimeter of 34 feet. if the room is 11 feet long, how wide is it?

Find the simplified product: 2sqrt 5x^3(-3sqrt10x^2) a: -30sqrt2x^5 b: -30x^2sqrt2x c: -12x^2sqrt5x d: -6sqrt50x^5