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
Kimberly, let's knock this out. Here are the rules for each of the number mappings: Mapping 1: Step 1: Identify the input (x) and output (y) values. The inputs are -3, -2, -1, 0, 1. The corresponding outputs are 14, 9, 4, -1, -6. Step 2: Determine the pattern. Observe the change in y for each unit increase in x: 9 - 14 = -5 4 - 9 = -5 -1 - 4 = -5 -6 - (-1) = -5 The output decreases by 5 for every 1 unit increase in the input. This means the slope m = -5. Step 3: Find the equation. Using the linear equation y = mx + c and a point, for example (0, -1): -1 = -5(0) + c -1 = 0 + c c = -1 The rule for this mapping is y = -5x - 1. Mapping 2: Step 1: Identify the input (x) and output (y) values. The inputs are -10, -9, -8, -7, -6. The corresponding outputs are 16, 14, 12, 10, 8. Step 2: Determine the pattern. Observe the change in y for each unit increase in x: 14 - 16 = -2 12 - 14 = -2 10 - 12 = -2 8 - 10 = -2 The output decreases by 2 for every 1 unit increase in the input. This means the slope m = -2. Step 3: Find the equation. Using the linear equation y = mx + c and a point, for example (-6, 8): 8 = -2(-6) + c 8 = 12 + c c = 8 - 12 c = -4 The rule for this mapping is y = -2x - 4. Mapping 3: Step 1: Identify the input (x) and output (y) values. The inputs are 1, 2, 3, 4, 5. The corresponding outputs are -6, -8, -10, -12, -14. Step 2: Determine the pattern. Observe the change in y for each unit increase in x: -8 - (-6) = -2 -10 - (-8) = -2 -12 - (-10) = -2 -14 - (-12) = -2 The output decreases by 2 for every 1 unit increase in the input. This means the slope m = -2. Step 3: Find the equation. Using the linear equation y = mx + c and a point, for example (1, -6): -6 = -2(1) + c -6 = -2 + c c = -6 + 2 c = -4 The rule for this mapping is y = -2x - 4. Mapping 4: Step 1: Identify the input (x) and output (y) values. The inputs are 1, 2, 3, 4, 5. The corresponding outputs are 8, 15, 22, 29, 30. Step 2: Determine the pattern. Observe the change in y for each unit increase in x: 15 - 8 = 7 22 - 15 = 7 29 - 22 = 7 The output increases by 7 for every 1 unit increase in the input. This means the slope m = 7. Step 3: Find the equation. Using the linear equation y = mx + c and a point, for example (1, 8): 8 = 7(1) + c 8 = 7 + c c = 8 - 7 c = 1 The rule for this mapping is y = 7x + 1. Step 4: Check the last value. Using the rule y = 7x + 1 for x=5: y = 7(5) + 1 y = 35 + 1 y = 36 The value written in the image for x=5 is 30. Based on the established pattern, the value should be 36. The rules for the mappings are: Mapping 1: y = -5x - 1 Mapping 2: y = -2x - 4 Mapping 3: y = -2x - 4 Mapping 4: y = 7x + 1 (with the last value 30 likely being a mistake, it should be 36) Send me the next one 📸