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Advanced Algebra with Trigonometry Unit 1 Take-Home Test Name Directions: Show all work and reasoning to receive full credit. 1) Write each expression in the standard form a bi if z 4 3i and w 2 8i . a) z w c) z w b) z w 2) Solve the following equations in the complex number system. a) x3 729 0 b) 5 x6 30 x 4 35x 2 0 c) 2x 2 3x 5 0 d) x(3x 2 5x 27) 45 3) Solve the inequality. Express your answer using interval notation. Graph the solution set. 4 x 3 1 3 a) 9 b) x 3 5 2 3 2 4) Simplify each expression. 3 a) 15x 53 4 7 9x y xy10 xy b) 32 x8 y 4 c) 6 x2 (4 x 3)5 3 9 x(4 x 3)2 3 5) Using the Pythagorean Theorem, determine whether or not the points are the vertices of a right triangle: (-9, 7), (-3, 7), (-3, 15). 6) Determine the center (h, k) and radius r of the circle 4 x2 4 y 2 12 x 16 y 5 0 . Graph the circle. 1 1 7) Determine the general form of the equation of the circle with endpoints of a diameter at (6, -2) and (-4, 4). For Questions 8 & 9, determine an equation, in slope-intercept form, for the line with the given properties. 8) Parallel to the line 4 x 3 y 3 ; 9) Perpendicular to the line 2 x 9 y 66 ; containing the point (6, 0). containing the point (6, -13). 10) Determine the equation, in general form, of the line in the graph illustrated below. 10 8 6 (5,5) 4 (5,1) 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6 -8 -10 11) At 2:00 p.m. there was 9 feet 8 inches of snow at Breckenridge Ski Resort. By 10:00 p.m. the same night there was 10 feet 3 inches of snow. What is the average rate of change (in inches) for the snow level?