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
Item 1: Farmer's Maize Harvest a) Draw a table of values The relation is y = 3x + 9, where x is acres of land and y is bags of maize. The farmer cultivates between 1 and 9 acres. Step 1: Calculate y for each x value from 1 to 9. For x=1: y = 3(1) + 9 = 12 For x=2: y = 3(2) + 9 = 15 For x=3: y = 3(3) + 9 = 18 For x=4: y = 3(4) + 9 = 21 For x=5: y = 3(5) + 9 = 24 For x=6: y = 3(6) + 9 = 27 For x=7: y = 3(7) + 9 = 30 For x=8: y = 3(8) + 9 = 33 For x=9: y = 3(9) + 9 = 36 The table of values is: |c|c| x (acres) & y (bags) \\ 1 & 12 \\ 2 & 15 \\ 3 & 18 \\ 4 & 21 \\ 5 & 24 \\ 6 & 27 \\ 7 & 30 \\ 8 & 33 \\ 9 & 36 \\ b) Draw a graph that shows the relation between maize and land used To draw the graph, plot the points (x,y) from the table above. The recommended scale is 2cm to represent 1acre on the x-axis and 2cm to represent 5bags of maize on the y-axis. The points to plot are: (1, 12), (2, 15), (3, 18), (4, 21), (5, 24), (6, 27), (7, 30), (8, 33), (9, 36). Connect these points with a straight line. c) Determine how many: i) Bags of maize (y) can be harvested from 3.5 acres of land (x) Step 1: Substitute x = 3.5 into the equation y = 3x + 9. y = 3(3.5) + 9 Step 2: Calculate the value of y. y = 10.5 + 9 y = 19.5 The farmer can harvest 19.5 bags of maize. ii) Acres of land (x) are used to harvest 31 bags of maize (y) Step 1: Substitute y = 31 into the equation y = 3x + 9. 31 = 3x + 9 Step 2: Solve for x. 31 - 9 = 3x 22 = 3x x = (22)/(3) x ≈ 7.333 The farmer uses approximately 7.33 acres of land. Item 2: Mountain Climb Translations a) Help each group identify their new locations on the mountain. The initial position for all groups is (0,0). A translation (a,b) moves a point (x,y) to (x+a, y+b). • Group A: Initial position (0,0), translation T=(3,5). New location A' = (0+3, 0+5) = (3,5). • Group B: Initial position (0,0), translation M=(-2,7). New location B' = (0+(-2), 0+7) = (-2,7). • Group C: Initial position (0,0), translation N=(5,-8). New location C' = (0+5, 0+(-8)) = (5,-8). b) Illustrate on the same pair of axes the new locations of each group of learners To illustrate, plot the following points on a coordinate plane: • Group A: (3,5) • Group B: (-2,7) • Group C: (5,-8) Send me the next one 📸