Page 2 of 9 VVS: 20-1 A4 Summer 23 C. -15x -10x 4y-2y2 15x2 d. 16y-32 k2 + k - 30 e. 2k2 - 50 f. 3x3 -13x -10 3x + 2 2. Simplify each rational expression. State the non-permissible values. a. 1 3 v 2 by 93 (2 marks) Page 3 of 9 VVS: 20-1 A4 Summer 23Page 3 of 9 VVS: 20-1 A4 Summer 23 4 2 x-3 b. (2 marks) x+1 x x+x C. a' -9 15a 3a+9 12a -36a (2 marks) d. 2x -x-6 2x+3 (2 marks) 3x+6 x +2 Page 4 of 9 VVS: 20-1 A4 Summer 23Page 4 of 9 VVS: 20-1 A4 Summer 23 e. x+1 x+4x-5 x-1 x-2 x+5x-14 x + 4x-21 (3 marks) 3. Solve the following rational equations algebraically. If a solution is not a whole number, leave as an exact value or round to the nearest hundredth. Verify all solutions. 5x +3 _ 6 a. 4-5x 4 (2 marks) Page 5 of 9 VVS: 20-1 A4 Summer 23Page 5 of 9 VVS: 20-1 A4 Summer 23 b. _x+2 x+5 x+3 (3 marks) C. 3 1 1 x+2 4 x-4 (3 marks) Page 6 of 9 VVS: 20-1 A4 Summer 23Page 7 of 9 VVS: 20-1 A4 Summer 23 5. Eva and Wilson are watching a Netflix movie at home. By himself, Wilson can eat a whole bag of popcorn in 20 minutes. Eva takes 30 minutes to eat a whole bag of popcorn. If they both eat popcorn at their usual rates, how long will it take Eva and Wilson to finish a single bag of popcorn if they share? (2 marks) 6. The quotient of 36 and a whole number increased by 3, is 20 less than four times the number. Determine the number(s). (2 marks)Page 8 of 9 VVS: 20-1 A4 Summer 23 7. In June 2020, Parks Canada closed the Bow Valley Parkway (Highway 1A) to vehicle traffic between Banff and Castle Junction near Johnston Canyon. This made for a bike ride that cut through a small piece of Canada's beautiful Rocky Mountains. A group of friends decide to cycle the trip, 25 km each way, from Banff to Johnston Canyon and back. They ride towards Johnston Canyon straight into the wind, and then have the wind at their backs on the return trip. The wind adds or subtracts 5 km/h from their speed. If the group of friends want to complete the round trip in 3 hours, algebraically find the average speed with no wind the group needs to cycle. Complete the distance speed time chart to help solve the question. Round your answer to the nearest hundredth of a km/h. (3 marks) Distance Speed Time Banff to Johnston Canyon Johnston Canyon to Banff Page 9 of 9 VVS: 20-1 A4 Summer 23 8. In Math 20-1 class, the teacher gives the class the following rational expressions.Page 9 of 9 VVS: 20-1 A4 Summer 23 8. In Math 20-1 class, the teacher gives the class the following rational expressions. 7x -42x x - 2x -35 x - x-30 x -49 a. State all non-permissible values of x in the expressions above. (1 mark) . Determine the simplified product of the two expressions above. (1 mark) c. The Math 20-1 teacher also gives the class a diagram of a rectangle with dimensions represented by rational expressions, where x > 2, as shown below. Explain why x > 2 for the rectangle. (1 mark) 35 5x - 10 - cm 6.x cm X - 2 d. The teacher reminds the class that the perimeter of a rectangle is the sum of the lengths of all the sides. Given that the perimeter of the given rectangle is 60 cm, write an equation that can be used to solve for x. Algebraically determine the value of x, to the nearest tenth, using this equation. (2 marks) End of Assignment