4. Determine whether the given value of is a root of this equation. Justify your answer. x ; 5. Consider the polynomial . Determine a value for so that is a factor of the polynomial. Explain your strategy. k The perimeter, of a rectangular concrete slab is 46 m and its area, is 90 m2. 6. P, A, Use the formula . Determine the dimensions of the slab. Show your work. 7. A ball is thrown in the air. The approximate height of the ball, metres, after seconds can be modelled by h t the equation . Will the ball ever reach a height of 15 m? Explain your answer. 8. a) Solve this quadratic equation by expanding, simplifying, then applying the quadratic formula: b) Solve the equation in part a using the quadratic formula without expanding. 9. Determine the values of for which the equation has no real roots, then write a possible equation. k 10. Use graphing technology to solve this equation: Explain your strategy. Determine the measures of and to the nearest tenth of a degree. Explain your strategy. 11. A B 12. A guy wire helps to support a tower as shown. Determine the height of the tower to the nearest tenth of a metre. What assumptions about the ground are you making? Explain your work. 13. Guy wires are attached to buildings as shown. A student says the angles of inclination of the wires are the same. Is the student correct? Justify your answer. 14. Point P(9, is a terminal point of an angle in standard position. Determine to the nearest degree, then   –4) sketch the angle. Show your work. In AB = 6 cm and . Complete the chart below for your own values of BC. 15. ABC, How does compare Description of possible Length of BC (cm) Value of with sin A? triangles No triangles are possible. 1 isosceles triangle 1 scalene triangle 2 scalene triangles 16. Two divers are 50 m apart. Each diver sees a treasure chest on the sea floor. The treasure chest is vertically below the line between the divers. From the divers, the angles of depression to the treasure chest are 35° and 51°. To the nearest metre, how far is the treasure chest from each diver? Consider possible cases and show your work.
4. Determine whether the given value of x is a root of this equation. Justify your answer. ; 5. Consider the polynomial . Determine a value for k so that is a factor of the polynomial. Explain your strategy. 6. The perimeter, P, of a rectangular concrete slab is 46 m and its area, A, is 90 m2. Use the formula . Determine the dimensions of the slab. Show your work. 7. A ball is thrown in the air. The approximate height of the ball, h metres, after t seconds can be modelled by the equation . Will the ball ever reach a height of 15 m? Explain your answer. 8. a) Solve this quadratic equation by expanding, simplifying, then applying the quadratic formula: b) Solve the equation in part a using the quadratic formula without expanding. 9. Determine the values of k for which the equation has no real roots, then write a possible equation. 10. Use graphing technology to solve this equation: Explain your strategy. 11. Determine the measures of A and B to the nearest tenth of a degree. Explain your strategy. 12. A guy wire helps to support a tower as shown. Determine the height of the tower to the nearest tenth of a metre. What assumptions about the ground are you making? Explain your work. 13. Guy wires are attached to buildings as shown. A student says the angles of inclination of the wires are the same. Is the student correct? Justify your answer. 14. Point P(9, –4) is a terminal point of an angle  in standard position. Determine  to the nearest degree, then sketch the angle. Show your work. 15. In ABC, AB = 6 cm and . Complete the chart below for your own values of BC. Length of BC (cm) Value of How does compare with sin A? Description of possible triangles No triangles are possible. 1 isosceles triangle 1 scalene triangle 2 scalene triangles 16. Two divers are 50 m apart. Each diver sees a treasure chest on the sea floor. The treasure chest is vertically below the line between the divers. From the divers, the angles of depression to the treasure chest are 35° and 51°. To the nearest metre, how far is the treasure chest from each diver? Consider possible cases and show your work.
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