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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14. To show that ADF and ABE are similar: Step 1: Identify properties of the square ABCD. Since ABCD is a square, all its angles are 90^. Therefore, ADF = 90^ and ABE = 90^. So, ADF = ABE. Step 2: Use the given condition. It is given that AEB = AFD. Step 3: Apply the Angle-Angle (AA) similarity criterion. In ADF and ABE: • ADF = ABE (Both are 90^ angles of the square). • AFD = AEB (Given). Since two pairs of corresponding angles are equal, the third pair of angles must also be equal ( DAF = BAE). Therefore, by the AA similarity criterion, ADF is similar to ABE. 15. The table below shows the values of x and y for the equation y = 2x - 3. a) Complete the table. To complete the table, substitute the given x values into the equation y = 2x - 3. When x = 0: y = 2(0) - 3 = 0 - 3 = -3 When x = 1: y = 2(1) - 3 = 2 - 3 = -1 When x = 2: y = 2(2) - 3 = 4 - 3 = 1 The completed table is: | x | 0 | 1 | 2 | |-----|-----|------|-----| | y | -3 | -1 | 1 | b) Using a scale of 2 cm to represent 1 unit on both axes, draw the graph of y = 2x - 3 on page 7. To draw the graph: Step 1: Draw a horizontal x-axis and a vertical y-axis on your graph paper. Step 2: Label the x-axis and y-axis. Step 3: Apply the given scale: For every 2 cm along an axis, mark 1 unit. For example, mark 0, 1, 2, 3... on the positive x-axis and -1, -2, -3... on the negative x-axis, with 2 cm spacing between each integer. Do the same for the y-axis. Step 4: Plot the points from the completed table: (0, -3), (1, -1), and (2, 1). Step 5: Draw a straight line that passes through all three plotted points. This line represents the graph of y = 2x - 3. That's 2 down. 3 left today — send the next one.