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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Step 1: Answer Question 4.1. A graph showing the relationship between minutes and total cost would have the following characteristics: • Title: Relationship between Minutes and Total Cost • X-axis label: Minutes (m) • Y-axis label: Total Cost (R) • Scale: A suitable scale would be 5 units per major grid line on the x-axis (for minutes) and 10 or 20 units per major grid line on the y-axis (for cost). • Plotted points: At least five points from the table (0,0), (5, 12.50), (10, 25.00), (15, 37.50), (20, 50.00), (30, 75.00) would be plotted. • Line: A straight line would be drawn connecting these points, starting from the origin (0,0). Step 2: Answer Question 5.1. The type of relationship shown is a linear relationship or direct proportion. Step 3: Answer Question 5.2. The value at m=0 represents the initial cost or the cost when no minutes are used, which is R0. Step 4: Answer Question 5.3. The gradient represents the cost per minute. In this case, it is R2.50 per minute. Step 5: Answer Question 5.4. Yes, the graph passes through the origin. This is because when m=0 minutes are used, the total cost C = 2.50 × 0 = 0. So, the point (0,0) is on the graph. Step 6: Answer Question 5.5. Yes, this relation is a function. For every input value of minutes (m), there is exactly one output value for the total cost (C). It satisfies the vertical line test. Step 7: Answer Question 6.1. The formula for the total cost is C = 2.50m. • For 25 minutes: C = 2.50 × 25 C = 62.50 The cost for 25 minutes is R62.50. • For 60 minutes: C = 2.50 × 60 C = 150.00 The cost for 60 minutes is R150.00. Step 8: Answer Question 6.2. If a person spends R100, we need to find the number of minutes (m). C = 2.50m 100 = 2.50m m = (100)/(2.50) m = 40 If a person spends R100, they use 40 minutes. Step 9: Answer Question 6.3. For another company, the charges are R10 fixed fee and R3 per minute. Let C' be the total cost for this company and m be the number of minutes. The formula for the total cost is: C' = 10 + 3m That's 2 down. 3 left today — send the next one.