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
Fresh day christina, let's solve. 1. Given y = 5x + 7. a) Step 1: Substitute x=5 into the equation. y = 5(5) + 7 Step 2: Perform the multiplication and addition. y = 25 + 7 y = 32 The value of y is 32. b) Step 1: Substitute x=20 into the equation. y = 5(20) + 7 Step 2: Perform the multiplication and addition. y = 100 + 7 y = 107 The value of y is 107. 2. Given y = 2x - 5. a) Step 1: Substitute y=11 into the equation. 11 = 2x - 5 Step 2: Add 5 to both sides of the equation. 11 + 5 = 2x 16 = 2x Step 3: Divide by 2 to solve for x. x = (16)/(2) x = 8 The value of x is 8. b) Step 1: Substitute y=37 into the equation. 37 = 2x - 5 Step 2: Add 5 to both sides of the equation. 37 + 5 = 2x 42 = 2x Step 3: Divide by 2 to solve for x. x = (42)/(2) x = 21 The value of x is 21. 3. Study the following table and determine the formula: Input (x) | 1 | 2 | 3 | 4 Output (y) | 5 | 9 | 13 | 17 Step 1: Find the common difference in the output (y) values. The difference between consecutive y values is 9-5=4, 13-9=4, 17-13=4. This indicates a linear relationship of the form y = mx + c, where m is the common difference. So, m = 4. The formula is y = 4x + c. Step 2: Use one of the (x, y) pairs to find the value of c. Let's use (x, y) = (1, 5). 5 = 4(1) + c 5 = 4 + c Step 3: Solve for c. c = 5 - 4 c = 1 Step 4: Write the complete formula. y = 4x + 1 The formula is y = 4x + 1. Send me the next one 📸