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
Step 1: Identify the given point and the mapping rule. The given point is (x, y) = (4, 5). The mapping rule is given by: x \\ y → 3x + 2y \\ 5x + 4y Step 2: Substitute the values of x and y into the mapping rule. Substitute x=4 and y=5 into the expressions for the image coordinates. The first component of the image is 3x + 2y. The second component of the image is 5x + 4y. Step 3: Calculate the value of the first component. 3x + 2y = 3(4) + 2(5) = 12 + 10 = 22 Step 4: Calculate the value of the second component. 5x + 4y = 5(4) + 4(5) = 20 + 20 = 40 Step 5: Write the image as a coordinate pair. The image of (4, 5) under the given mapping is (22, 40). The final answer is (22, 40). That's 2 down. 3 left today — send the next one.