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
You're on a roll — To complete the table for the relation y = 3 x + 2 x, we will substitute each value of x into the equation and calculate the corresponding y value, rounding to 1 decimal place. Step 1: Calculate y for x = 30^. y = 3(30^) + 2(30^) = 3(0.5) + 2(sqrt(3)2) = 1.5 + sqrt(3) ≈ 1.5 + 1.732 = 3.232 Rounded to 1 d.p., y = 3.2. Step 2: Calculate y for x = 60^. y = 3(60^) + 2(60^) = 3(sqrt(3)2) + 2(0.5) = 3sqrt(3)2 + 1 ≈ 2.598 + 1 = 3.598 Rounded to 1 d.p., y = 3.6. Step 3: Calculate y for x = 90^. y = 3(90^) + 2(90^) = 3(1) + 2(0) = 3 + 0 = 3 Rounded to 1 d.p., y = 3.0. Step 4: Calculate y for x = 120^. y = 3(120^) + 2(120^) = 3(sqrt(3)2) + 2(-(1)/(2)) = 3sqrt(3)2 - 1 ≈ 2.598 - 1 = 1.598 Rounded to 1 d.p., y = 1.6. Step 5: Calculate y for x = 150^. y = 3(150^) + 2(150^) = 3(0.5) + 2(-sqrt(3)2) = 1.5 - sqrt(3) ≈ 1.5 - 1.732 = -0.232 Rounded to 1 d.p., y = -0.2. Step 6: Calculate y for x = 210^. y = 3(210^) + 2(210^) = 3(-0.5) + 2(-sqrt(3)2) = -1.5 - sqrt(3) ≈ -1.5 - 1.732 = -3.232 Rounded to 1 d.p., y = -3.2. Step 7: Calculate y for x = 300^. y = 3(300^) + 2(300^) = 3(-sqrt(3)2) + 2(0.5) = -3sqrt(3)2 + 1 ≈ -2.598 + 1 = -1.598 Rounded to 1 d.p., y = -1.6. Step 8: Calculate y for x = 330^. y = 3(330^) + 2(330^) = 3(-0.5) + 2(sqrt(3)2) = -1.5 + sqrt(3) ≈ -1.5 + 1.732 = 0.232 Rounded to 1 d.p., y = 0.2. The completed table is: |c|c|c|c|c|c|c|c|c|c|c|c|c|c| x & 0 & 30 & 60 & 90 & 120 & 150 & 180 & 210 & 240 & 270 & 300 & 330 & 360 \\ y & 2.0 & 3.2 & 3.6 & 3.0 & 1.6 & -0.2 & -2.0 & -3.2 & -3.6 & -3.0 & -1.6 & 0.2 & 2.0 \\ What's next? 📸