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.
ScanSolve AI Answer
Here are the solutions to the questions: 2.2.1 Represent the relationship shown in the diagram in words. The relationship shown in the diagram is that the input value is first multiplied by -1, and then that result is multiplied by 3 to get the output value. 2.2.2 Use the information provided in the flow diagram to complete the table below. Step 1: Determine the rule from the flow diagram. The flow diagram shows an input x is first multiplied by -1, then that result is multiplied by 3. So, the output y is given by the formula: y = (x × -1) × 3 y = -x × 3 y = -3x Step 2: Calculate the output values for each input using the rule y = -3x. • For Input x = 0: y = -3(0) = 0 • For Input x = 1: y = -3(1) = -3 • For Input x = 2: y = -3(2) = -6 (Note: The table in the question shows -5 for input 2, but based on the flow diagram's operations, the correct output is -6.) • For Input x = 4: y = -3(4) = -12 • For Input x = 8: y = -3(8) = -24 • For Input x = n: y = -3n Step 3: Complete the table. | Input | 0 | 1 | 2 | 4 | 8 | n | | :---- | :- | :- | :- | :- | :- | :- | | Output | 0 | -3 | -6 | -12 | -24 | -3n | 2.2.3 Describe, in words, the steps to follow to calculate the input value for the given output value of -21. Step 1: To reverse the operation of multiplying by 3, divide the output value by 3. Step 2: To reverse the operation of multiplying by -1, divide the result from Step 1 by -1. 3.1 The following shapes are made using squares. Step 1: Count the number of squares in each shape. • Shape 1 has 5 squares. • Shape 2 has 7 squares. • Shape 3 has 9 squares. 3 done, 2 left today. You're making progress.