A man is five times as old as his son. If the son's age is y, set up the quadratic equation that represents the product of their ages in four years being 340.

Here are the solutions to the questions. Question 22: A man is five times as old as his son. If the son's age is y, then the man's current age is 5y. In four years' time: Son's age will be y+4. Man's age will be 5y+4. The product of their ages in four years will be 340. Step 1: Set up the equation for the product of their ages in four years. (y+4)(5y+4) = 340 Step 2: Expand the left side of the equation. 5y^2 + 4y + 20y + 16 = 340 5y^2 + 24y + 16 = 340 Step 3: Rearrange the equation to the standard quadratic form Ay^2 + By + C = 0. 5y^2 + 24y + 16 - 340 = 0 5y^2 + 24y - 324 = 0 The final answer is D. 5y^2 + 24y - 324 = 0. Question 23: Simplify: (a)/(b) - (b)/(a)(b)/(a) - (c)/(b) Step 1: Simplify the numerator (a)/(b) - (b)/(a). Find a common denominator, which is ab. (a)/(b) - (b)/(a) = (a · a)/(b · a) - (b · b)/(a · b) = (a^2)/(ab) - (b^2)/(ab) = (a^2 - b^2)/(ab) Step 2: Simplify the denominator (b)/(a) - (c)/(b). Find a common denominator, which is ab. (b)/(a) - (c)/(b) = (b · b)/(a · b) - (c · a)/(b · a) = (b^2)/(ab) - (ac)/(ab) = (b^2 - ac)/(ab) Step 3: Divide the simplified numerator by the simplified denominator. (a^2 - b^2)/(ab)(b^2 - ac)/(ab) To divide by a fraction, multiply by its reciprocal. (a^2 - b^2)/(ab) × (ab)/(b^2 - ac) Step 4: Cancel out the common term ab. (a^2 - b^2)/(b^2 - ac) The final answer is D. (a^2 - b^2)/(b^2 - ac). Question 24: In the diagram, XYZ is an equilateral triangle of side 6 cm. T is the midpoint of XY. Find ( XZT). Step 1: Identify properties of an equilateral triangle. Since XYZ is equilateral, all sides are equal (XY = YZ = ZX = 6 cm) and all interior angles are 60^ ( X = Y = Z = 60^). Step 2: Determine the length of XT. T is the midpoint of XY, so XT = (1)/(2) XY = (1)/(2)(6 cm) = 3 cm. Step 3: Identify properties of the line segment ZT. In an equilateral triangle, the line segment from a vertex to the midpoint of the opposite side (a median) is also an altitude and an angle bisector. Therefore, ZT XY, which means XZT is a right-angled triangle with the right angle at T. Also, ZT bisects XZY, so XZT = (1)/(2) XZY = (1)/(2)(60^) = 30^. Step 4: Calculate ( XZT). We need to find (30^). (30^) = (1)/(sqrt(3)) The final answer is A. (1)/(sqrt(3)). Question 25: A fence 2.4 m tall is 10 m away from a tree of height 16 m. Calculate the angle of elevation of the top of the tree from the top of the fence. Step 1: Identify the relevant lengths for the right-angled triangle formed by the observer's eye (top of the fence), the top of the tree, and the horizontal line from the top of the fence to the tree. The horizontal distance (adjacent side) is 10 m. The vertical height difference (opposite side) is the height of the tree minus the height of the fence. Opposite side = 16 m - 2.4 m = 13.6 m Step 2: Use the tangent function to find the angle of elevation (). () = OppositeAdjacent () = 13.6 m10 m () = 1.36 Step 3: Calculate the angle . = (1.36) Using a calculator: ≈ 53.679^ Rounding to two decimal places, ≈ 53.68^. Comparing with the options, 53.67^ is the closest. The final answer is B. 53.67^.