Abstract Algebra Answers

What is the answer to y=2x+763-45y

Determine the number of solutions for the quadratic function f(x) = -x2 + 3x - 9

Task
1.) 32^ 2/5
2.)125 2/3
3)8 2/3
4.)16 2/3
5.)4 3/2
6.)32 2/5+64 2/3

Find the measure, in terms of x, of each side of a square if the Area = x^2– 16x +64.
Factor and solve.
x^2-x-72=0
2x^2+9x-5=0
x^2-64=0
4x^2-36x+72

A. A doctor writes a prescription for 20 mg of Tobramycin antibiotic saline solution. The solution is to be injected intravenously one time a day. On hand we have a 30 mg/ 2ml vial of Tobramycin, do the necessary calculations to give the patient the correct single dosage.

Prove that abelian group of order pq (p,q distinct prime) is cyclic.

Prove that if elements a,b of group G commutes, then LCM of their orders is multiply of order
of their product.

Prove that if all squares of all elements are equal identity of group, that it is abelian.

Suppose a nonhomogenous system of 9 linear equations and 10 variables has a solution for all possible values. Discuss whether it is possible for two nonzero solutions that are not multiples of each other to exist for the associated homogenous system.

Define transformation T: R^3 -> R^3 by T(x)=Ax where A (3x3) matrix and has eigenvalues 5 and -2. Is A similar to a diagonal matrix? explain