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
To solve this problem, we first need to identify the pattern relating the number of black dots to the number of grey dots. Step 1: Analyze the given patterns to find the number of grey dots for each number of black dots. • For 1 black dot (first pattern), there are 8 grey dots. • For 2 black dots (second pattern), there are 12 grey dots. • For 3 black dots (third pattern), there are 16 grey dots. • For 4 black dots (fourth pattern), there are 20 grey dots. Step 2: Determine the relationship. Let n be the number of black dots and G be the number of grey dots. We observe that as n increases by 1, G increases by 4 (12-8=4, 16-12=4, 20-16=4). This indicates a linear relationship of the form G = mn + c, where m=4. Using the first data point (n=1, G=8): 8 = 4(1) + c 8 = 4 + c c = 4 So, the formula describing the relationship is G = 4n + 4. Now, we use this formula to answer each question. 2.1 Step 1: Use the formula G = 4n + 4 with n=1. G = 4(1) + 4 Step 2: Calculate the number of grey dots. G = 4 + 4 = 8 2.2 Step 1: Use the formula G = 4n + 4 with n=2. G = 4(2) + 4 Step 2: Calculate the number of grey dots. G = 8 + 4 = 12 2.3 Step 1: Use the formula G = 4n + 4 with n=3. G = 4(3) + 4 Step 2: Calculate the number of grey dots. G = 12 + 4 = 16 2.4 Step 1: Use the formula G = 4n + 4 with n=4. G = 4(4) + 4 Step 2: Calculate the number of grey dots. G = 16 + 4 = 20 2.5 Step 1: Use the formula G = 4n + 4 with n=5. G = 4(5) + 4 Step 2: Calculate the number of grey dots. G = 20 + 4 = 24 2.6 Step 1: Use the formula G = 4n + 4 with n=6. G = 4(6) + 4 Step 2: Calculate the number of grey dots. G = 24 + 4 = 28 2.7 Step 1: Use the formula G = 4n + 4 with n=7. G = 4(7) + 4 Step 2: Calculate the number of grey dots. G = 28 + 4 = 32 2.8 Step 1: Use the formula G = 4n + 4 with n=10. G = 4(10) + 4 Step 2: Calculate the number of grey dots. G = 40 + 4 = 44 2.9 Step 1: Use the formula G = 4n + 4 with n=20. G = 4(20) + 4 Step 2: Calculate the number of grey dots. G = 80 + 4 = 84 2.10 Step 1: Use the formula G = 4n + 4 with n=100. G = 4(100) + 4 Step 2: Calculate the number of grey dots. G = 400 + 4 = 404 That's 2 down. 3 left today — send the next one.