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 Flora — missed you this week. Here are the solutions to your problems: Problem 2: Angles on a straight line sum up to 180^. Step 1: Set up the equation for the sum of angles on a straight line. P + 140^ = 180^ Step 2: Solve for P. P = 180^ - 140^ P = 40^ The size of angle P is 40^. Problem 3: The balloon rises at a steady rate. Step 1: Calculate the rate of ascent (height per minute). Rate = HeightTime Rate = 350 m7 minutes Rate = 50 m/minute Step 2: Calculate the height after 15 minutes using the rate. Height after 15 minutes = Rate × Time Height after 15 minutes = 50 m/minute × 15 minutes Height after 15 minutes = 750 m The balloon will be 750 m high after 15 minutes. Problem 4: The radius of the circular garden is 21 cm and the central angle of the sector is 120^. Step 1: Write the formula for the area of a sector. Area of Sector = ()/(360^) × r^2 where is the central angle and r is the radius. Step 2: Substitute the given values into the formula and calculate. Area of Sector = (120^)/(360^) × (21 cm)^2 Area of Sector = (1)/(3) × (441 cm^2) Area of Sector = 147 cm^2 Using ≈ 3.14159: Area of Sector ≈ 147 × 3.14159 cm^2 Area of Sector ≈ 461.81 cm^2 The area of the sector is approximately 461.81 cm^2. Problem 5: The equation of the straight line is y = 4x - 8. Step 1: To find where the line cuts the y-axis, set the x-coordinate to 0. x = 0 Step 2: Substitute x=0 into the equation and solve for y. y = 4(0) - 8 y = 0 - 8 y = -8 The coordinates of the point where the line cuts the y-axis are (0, -8). Send me the next one 📸