The perimeter of a triangle is 54 in. The shortest side is 11 in. less than the longest side. The middle side is 20 in. less than the combined lengths of the shortest and longest sides. Find the lengths of the three sides.

Jeffery conducted a survey in his school and found that 30 of the 50 eighth grade students' favorite subject is mathematics. based on the results, jeffery concluded that out of the 200 students in his school, 120 students' favorite subject is mathematics. select the statement that is true about jeffery's conclusion. a. jeffery's conclusion is not valid because the sample was biased since only 200 students were surveyed. b. jeffery's conclusion is valid because the sample was random since all of the students were eighth grade students. c. jeffery's conclusion is valid because the sample was random. d. jeffery's conclusion is not valid because the sample was biased since all of the students were eighth grade students.

If 2(a^2+b^2)=(a+b)^2 then, > a+b=0, > ab=0, > a=b, > 2a=b

Evaluate the expression for the given value of the variable. | ? 4 b ? 8 | + ? ? ? 1 ? b 2 ? ? + 2 b 3 -4b-8+-1-b2+2b3 ; b = ? 2 b=-2