This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — Here are the solutions to the questions. Question 1: The construction below is required in constructing angle POQ. What is the size of angle POQ? Step 1: Observe the construction. The construction shows a method to bisect an angle. Step 2: The initial angle being bisected is a right angle (90^), indicated by the perpendicular construction marks. Step 3: Bisecting a 90^ angle means dividing it into two equal parts. (90^)/(2) = 45^ The final answer is A. 45^. Question 2: A car travels 160 miles on 4 gallons of diesel. Find the average mile per gallon. Step 1: Divide the total distance by the total fuel consumed. Average mile per gallon = Total milesTotal gallons Average mile per gallon = 160 miles4 gallons Step 2: Calculate the result. Average mile per gallon = 40 miles/gallon The final answer is A. 40 miles. Question 3: Find the gradient of the line in the equation 4y - 3x - 2 = 0. Step 1: Rearrange the equation into the slope-intercept form y = mx + c. 4y - 3x - 2 = 0 4y = 3x + 2 Step 2: Divide all terms by 4. y = (3)/(4)x + (2)/(4) y = (3)/(4)x + (1)/(2) Step 3: Identify the gradient (m), which is the coefficient of x. The gradient is m = (3)/(4). The final answer is C. (3)/(4). Question 4: Simplify (2a + 3)(b + 2). Step 1: Use the distributive property (FOIL method) to multiply the binomials. (2a + 3)(b + 2) = 2a(b) + 2a(2) + 3(b) + 3(2) Step 2: Perform the multiplications. = 2ab + 4a + 3b + 6 The final answer is C. 2ab + 4a + 3b + 6. Question 5: At what distance did the bus driver drove from Town A to Town B? Step 1: Locate Town A and Town B on the distance axis of the graph. Town A is at 0 km. Town B is at 4 km. Step 2: The distance driven from Town A to Town B is the difference between their distances from the origin. Distance = 4 km - 0 km = 4 km The final answer is A. 4 km. Question 6: The bus driver drove from Town A to Town B within how many hours? Step 1: Identify the time the bus left Town A and arrived at Town B from the graph. Left Town A (0 km) at 8:00 a.m. Arrived at Town B (4 km) at 9:00 a.m. Step 2: Calculate the duration of the journey. Duration = 9:00 a.m. - 8:00 a.m. = 1 hour The final answer is B. 1 hour. Question 7: The bus driver drove from Town C back to Town A in what time? Step 1: Identify the time the bus left Town C and arrived back at Town A from the graph. Left Town C (6 km) at 9:30 a.m. Arrived back at Town A (0 km) at 11:00 a.m. Step 2: Calculate the duration of the journey. Duration = 11:00 a.m. - 9:30 a.m. = 1 hour 30 minutes The final answer is A. 1 hour 30 minutes. Question 8: Find the value of (3e)/(5) + (e)/(2) when e = 10. Step 1: Substitute e = 10 into the expression. (3(10))/(5) + (10)/(2) Step 2: Simplify each term. (30)/(5) + 5 6 + 5 Step 3: Add the values. 11 The final answer is B. 11. Question 9: The equation of a straight line is y + 2x - 2 = 0. What is the gradient? Step 1: Rearrange the equation into the slope-intercept form y = mx + c. y + 2x - 2 = 0 y = -2x + 2 Step 2: Identify the gradient (m), which is the coefficient of x. The gradient is m = -2. The final answer is A. -2. Question 10: Factorize (1)/(2)ty^2 + (1)/(4)ty. Step 1: Identify the greatest common factor (GCF) of the terms. The numerical GCF of (1)/(2) and (1)/(4) is (1)/(4). The variable GCF of ty^2 and ty is ty. So, the GCF is (1)/(4)ty. Step 2: Factor out the GCF from each term. (1)/(2)ty^2 + (1)/(4)ty = \