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
Okay, Mc, let's analyze this new set of patterns. 2.11.4 Step 1: Analyze the table to find the relationship between the number of black dots (n) and the number of grey dots (G). • For n=1, G=6 • For n=2, G=10 • For n=3, G=14 • For n=4, G=18 • For n=5, G=22 • For n=6, G=26 Step 2: Find the difference between consecutive numbers of grey dots. 10 - 6 = 4 14 - 10 = 4 18 - 14 = 4 22 - 18 = 4 26 - 22 = 4 The common difference is 4, indicating a linear relationship of the form G = 4n + c. Step 3: Determine the constant c using any pair from the table, for example, n=1, G=6. 6 = 4(1) + c 6 = 4 + c c = 2 Conclusion: The relationship between the number of black dots (n) and the number of grey dots (G) is given by the formula G = 4n + 2. 2.11.5 Step 1: Interpret the flowchart. The flowchart shows "Number of black dots → × 4 → + 2 → Number of grey dots". This translates to the formula G = 4n + 2. Step 2: Compare this formula to the relationship found in 2.11.4. The formula G = 4n + 2 matches the relationship derived from the table in 2.11.4. Conclusion: This flowchart correctly describes the relationship between the number of black dots and grey dots from the table. 2.11.6 Step 1: Interpret the flowchart. The flowchart shows "Number of black dots → × 2 → + 1 → × 2 → Number of grey dots". This translates to the formula G = (2n + 1) × 2. Step 2: Simplify the formula. G = (2n + 1) × 2 G = 4n + 2 Step 3: Compare this formula to the relationship found in 2.11.4. The simplified formula G = 4n + 2 matches the relationship derived from the table in 2.11.4. Conclusion: This flowchart correctly describes the relationship between the number of black dots and grey dots from the table. 2.11.7 Step 1: Interpret the statement. The statement is "The number of grey dots = 4 x the number of black dots + 2". This translates directly to the formula G = 4n + 2. Step 2: Compare this formula to the relationship found in 2.11.4. The formula G = 4n + 2 matches the relationship derived from the table in 2.11.4. Conclusion: This statement correctly describes the relationship between the number of black dots and grey dots from the table. Last free one today — make it count tomorrow, or type /upgrade for unlimited.