Given the relation f: x (2x-1)/(x2+3x+2).

You're on a roll — Here are the solutions to the questions. Question 1: Given the relation f: x (2x-1)/(x^2+3x+2). i) Find the zero of the relation. Step 1: The relation is zero when the numerator is equal to zero. 2x - 1 = 0 Step 2: Solve for x. 2x = 1 x = (1)/(2) The zero of the relation is (1)/(2). ii) Find the value of x which makes the relation undefined. Step 1: The relation is undefined when the denominator is equal to zero. x^2 + 3x + 2 = 0 Step 2: Factor the quadratic equation. (x+1)(x+2) = 0 Step 3: Solve for x. x+1 = 0 or x+2 = 0 x = -1 or x = -2 The values of x which make the relation undefined are -1, -2. Question 2: Calculate the (i) Area (ii) Perimeter of the given foundation drawing. i) Area Step 1: Divide the L-shaped figure into two rectangles. We can split it into a large bottom rectangle and a smaller top-left rectangle. The bottom rectangle has dimensions 22 cm × 8 cm. The top-left rectangle has a width of 22 cm - 14 cm = 8 cm and a height of 19 cm - 8 cm = 11 cm. Step 2: Calculate the area of each rectangle. Area of bottom rectangle = 22 cm × 8 cm = 176 cm^2. Area of top-left rectangle = 8 cm × 11 cm = 88 cm^2. Step 3: Add the areas to find the total area. Total Area = 176 cm^2 + 88 cm^2 = 264 cm^2. The area is 264 cm^2. ii) Perimeter Step 1: Identify all the outer side lengths of the figure. The given lengths are 19 cm, 8 cm, 11 cm, 14 cm, 8 cm, and 22 cm. Step 2: Sum all the outer side lengths. Perimeter = 19 cm + 8 cm + 11 cm + 14 cm + 8 cm + 22 cm Perimeter = 82 cm. The perimeter is 82 cm. Question 3: Find the value of x and y in the diagram below if O is the centre of the circle. Step 1: Use the property of angles in a cyclic quadrilateral. The sum of opposite angles in a cyclic quadrilateral is 180^. The angles x and 3x are opposite angles in the cyclic quadrilateral. x + 3x = 180^ 4x = 180^ Step 2: Solve for x. x = (180^)/(4) x = 45^ Step 3: Use the property that the angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the remaining part of the circle. The angle at the center is y, and the angle at the circumference subtended by the same arc is x. y = 2x Step 4: Substitute the value of x to find y. y = 2(45^) y = 90^ The value of x is 45^ and the value of y is 90^. Question 4: a) y varies directly as x. If y = 18 when x = 6, find: i) the equation connecting y and x ii) the value of y when x = 15 i) The equation connecting y and x Step 1: For direct variation, the relationship is y = kx, where k is the constant of proportionality. Step 2: Use the given values y=18 and x=6 to find k. 18 = k(6) k = (18)/(6) k = 3 The equation connecting y and x is y = 3x. ii) The value of y when x = 15 Step 1: Use the equation y = 3x found in part (i). Step 2: Substitute x=15 into the equation. y = 3(15) y = 45 The value of y when x=15 is 45. b) y varies inversely as x. If y = 4 when x = 3, find y when x = 12. Step 1: For inverse variation, the relationship is y = (k)/(x), where k is the constant of proportionality. Step 2: Use the given values y=4 and x=3 to find k. 4 = (k)/(3) k = 4 × 3 k = 12 The equation connecting y and x is y = (12)/(x). Step 3: Find y when x=12. y = (12)/(12) y = 1 The value of y when x=12 is 1. Drop the next question!