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
Here's how to solve the pattern problems: First, let's identify the pattern from the given examples. The pattern relates the numbers in the circle (Top, Left, Right) to the number in the square. Let L be the Left number, T_p be the Top number, and R be the Right number in the circle. Let S_q be the number in the square. From the first example: Circle: T_p = 8, L = 20, R = 5 Square: S_q = 49 The formula given is: [20 - (8 + 5)]^2 = 49. This simplifies to [20 - 13]^2 = 7^2 = 49. This matches. From the second example: Circle: T_p = 3(1)/(2), L = 14(1)/(2), R = 5 Square: S_q = 36 The formula given is: [14 - (3 + 5)]^2 = 36. This simplifies to [14 - 8]^2 = 6^2 = 36. This matches. Note: The formula uses the integer parts of the mixed numbers from the circle. For problems 3 and 4, all numbers are integers. The general pattern is: (L - (T_p + R))^2 = S_q Problem 3: T_p = 9 R = 3 S_q = 64 L = ? Step 1: Apply the pattern formula. (L - (9 + 3))^2 = 64 Step 2: Simplify the sum inside the parenthesis. (L - 12)^2 = 64 Step 3: Take the square root of both sides. sqrt((L - 12)^2) = sqrt(64) L - 12 = ± 8 Step 4: Solve for L for both positive and negative roots. Case 1: L - 12 = 8 L = 8 + 12 L = 20 Case 2: L - 12 = -8 L = -8 + 12 L = 4 Step 5: Choose the correct option. The options are A. 6, B. 12, C. 20, D. 14, E. 17. Since 20 is an option, and the numbers in the examples are positive, we select L=20. The answer for Problem 3 is C. 20. Problem 4: L = 11 R = 3 S_q = 1 T_p = ? Step 1: Apply the pattern formula. (11 - (T_p + 3))^2 = 1 Step 2: Take the square root of both sides. sqrt((11 - (T_p + 3))^2) = sqrt(1) 11 - (T_p + 3) = ± 1 Step 3: Solve for T_p for both positive and negative roots. Case 1: 11 - (T_p + 3) = 1 11 - T_p - 3 = 1 8 - T_p = 1 T_p = 8 - 1 T_p = 7 Case 2: 11 - (T_p + 3) = -1 11 - T_p - 3 = -1 8 - T_p = -1 T_p = 8 - (-1) T_p = 9 Step 4: Choose the correct option. The options are A. 7, B. 11, C. 14, D. 15, E. 20. Since 7 is an option, we select T_p=7. The answer for Problem 4 is A. 7. 3 done, 2 left today. You're making progress.