12:11 PM'@ {9 M ..ul ..ul '49 6 Untitled document / Z l. (5 marks ) Solve the given system of equations by using an appropriate algebraic method. 90.x - 1101' = 40 303' - l5y : 25 2/4 2. l 5 marks) Factor the given expressions completely, a) b) 21-3 + 13.1 + ll 0) 27x3 7 8a\" Factor the given expression completely. It is from the technical area indicated. d) l)4 7 (I'D (machine design) 3. l 5 marks) Solve the given equations. 21' 3 l 211 7 5.- .x' = 4x 10 -- 12:11 PMCOM .Ill R .ill 44 F Untitled document . . . 4. ( 5 marks ) A train leaves Toronto for Montreal at the same time as another train leaves Montreal for Toronto. The cities are 500 km apart. The trains pass each other 2 h later. The train from Montreal is traveling 50 km/h faster than the one from Toronto. At what distance away from Toronto do the trains pass each other ? 5. (5 marks ) Determine the values of b so that each trinomial is a perfect square. a) 16x2 - 88xy + by2 b ) 3k2 + 12km - 36m2 Determine all values of k so that each trinomial is a perfect square. c) 25x2 - 60xy + ky2 Factor the given expressions completely. d) 8x2 - 8x - 70 e ) 4x2 - 64y2 6. ( 5 marks ) Express each of the given expressions in simplest form with only positive exponents. a) b) ( RT ' + R2 ' ) -1 3/4 . . C) ( 1 2 - 20-1) 2 d) 6 -1 O12:11 PMCOM F Untitled document . . . b ) 3k2 + 12km - 36m2 Determine all values of k so that each trinomial is a perfect square. c) 25x2 - 60xy + ky2 Factor the given expressions completely. d 8x2 - 8x - 70 e) 4x2 - 64y2 6. ( 5 marks ) Express each of the given expressions in simplest form with only positive exponents. a) b) ( RT' + R2' ) -1 c) (1 2 - 20-1)2 d) 6-1 - 2 e ) 7. ( 5 marks ) Solve the given equations for x: a) 2 Z-5 10 - 2Z b ) Alex runs a snowboard rental business that charges $12 per snowboard and averages 36 rentals per day. She discovers that for each $0.50 decrease in price, her business rents out two additional snowboards per day. At what price can Alex maximize her revenue? 4/4 O