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
Here are the solutions to the questions. QUESTION 1 a) Step 1: Calculate the number of seniors. Number of seniors = (1)/(8) × 720 = 90 Step 2: Calculate the number of juniors. Number of juniors = (1)/(3) × 720 = 240 i) Step 3: Calculate the number of young learners. Number of young learners = Total students - Seniors - Juniors Number of young learners = 720 - 90 - 240 = 390 The number of young learners in the school is 390. ii) Step 4: Calculate the fraction of young learners. Fraction of young learners = Number of young learnersTotal students = (390)/(720) Step 5: Simplify the fraction. (390)/(720) = (39)/(72) = (13)/(24) The fraction of young learners in the school is (13)/(24). b) i) Step 1: Use the distance formula for points A(1,1) and B(4,5). The distance formula is d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). d = sqrt((4 - 1)^2 + (5 - 1)^2) d = sqrt((3)^2 + (4)^2) d = sqrt(9 + 16) d = sqrt(25) d = 5 The length of AB is 5 units. ii) Step 1: Rearrange the formula w + 2r = 2f - r to make r the subject. w + 2r = 2f - r Step 2: Add r to both sides. w + 2r + r = 2f w + 3r = 2f Step 3: Subtract w from both sides. 3r = 2f - w Step 4: Divide by 3. r = (2f - w)/(3) The formula with r as the subject is r = (2f - w)/(3). c) Step 1: Determine the sum of interior angles of a pentagon. The sum of interior angles for an n-sided polygon is (n-2) × 180^. For a pentagon, n=5. Sum of angles = (5-2) × 180^