1. The coordinates of the vertices of parallelogram RMBS are R(-4 ,5), M(1, 4), B(2, -1), and S(-3, 0). using the diagonals, prove that RMBS is a rhombus. Show all your work and state appropriate formulas and theorems used.
2. Explain the purposes of inductive and deductive reasoning in mathematics. Be sure to define both inductive reasoning and deductive reasoning and describe how each can help you develop and prove theorems.
3. Write the expression in simplified radical form. Show your work.
3-2 sqrt of 11/ 2 + sqrt of 11
4. Solve the equation. Show your check and then write the solution set.
x-1 = sqrt of 6x + 10
5. Given the complex number, 5 - 3i:
(a): Graph the complex number in the complex plane
(b): Calculate the modulus. When necessary, round to the tenths place.