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
Welcome back L.A.D.Y. — missed you this week. 1.1 Step 1: Evaluate each term in the expression. sqrt(144) - 2^2 + sqrt(8) sqrt(144) = 12 2^2 = 4 sqrt(8) = sqrt(4 × 2) = 2sqrt(2) Step 2: Substitute the evaluated terms back into the expression. 12 - 4 + 2sqrt(2) Step 3: Perform the subtraction. 8 + 2sqrt(2) Since 2sqrt(2) ≈ 2 × 1.414 = 2.828, the expression is approximately 8 + 2.828 = 10.828. Comparing this to the given options: A. 11 B. 14 C. 12 D. 10 The closest option is 11. However, the question implies an exact answer from the options. Let's re-check the question. It's possible there's a typo in the question or options, as 8 + 2sqrt(2) is not an integer. Assuming the question intended a simpler form or that sqrt(8) was meant to be something else, but based on the exact expression, none of the integer options are precisely correct. If we are forced to choose the closest integer, it would be 11. Let's assume the question might have intended sqrt(144) - 2^2 + sqrt(4) or similar for an integer answer. But strictly following the given expression: sqrt(144) - 2^2 + sqrt(8) = 12 - 4 + 2sqrt(2) = 8 + 2sqrt(2) None of the options A, B, C, D are exactly 8 + 2sqrt(2). If we consider the possibility of a typo and that sqrt(8) was intended to be sqrt(0) or sqrt(16) or similar to yield an integer, it's not explicitly stated. Given the options are integers, it's highly probable that sqrt(8) was not intended to be part of the final integer calculation, or there's a misunderstanding of the question. However, if we must choose the closest integer, 8 + 2sqrt(2) ≈ 10.828, which is closest to 11. Let's re-evaluate if there's any other interpretation. No, it's a direct calculation. If the question was sqrt(144) - 2^2 + sqrt(9), then 12 - 4 + 3 = 11. This would make option A correct. Given it's a multiple choice question with integer answers, it's very likely that sqrt(8) was a typo for sqrt(9). I will proceed with the assumption that it was meant to be sqrt(9) to match one of the options. Step 1: Evaluate each term in the expression, assuming sqrt(8) was a typo for sqrt(9). sqrt(144) - 2^2 + sqrt(9) sqrt(144) = 12 2^2 = 4 sqrt(9) = 3 Step 2: Substitute the evaluated terms back into the expression. 12 - 4 + 3 Step 3: Perform the operations from left to right. 8 + 3 = 11 The correct option is A. The final answer is A. 11 1.2 Step 1: Identify the terms in the expression. Terms are parts of an expression separated by addition or subtraction. The given expression is (2x + 8x^3 + (2)/(4x^2)). The terms are: • 2x • 8x^3 • (2)/(4x^2) Step 2: Count the distinct terms. There are 3 distinct terms. The correct option is B. The final answer is B. 3 terms 1.3 Step 1: Substitute the given values of x=2 and y=-5 into the expression 4x^2 + y^2. 4(2)^2 + (-5)^2 Step 2: Calculate the squares. 4(4) + (25) Step 3: Perform the multiplication and addition. 16 + 25 = 41 The correct option is D. The final answer is D. 41 1.4 Step 1: Calculate the product of -6 and 8. -6 × 8 Step 2: Perform the multiplication. -6 × 8 = -48 The correct option is B. The final answer is B. -48 Drop the next question 📸