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
Hey wanguisherlyn45, good to see you again. Here are the solutions to your questions: 1. Cost of rice Step 1: Find the cost per kilogram of rice. Cost per kg = Total costTotal kilograms = sh 500025 kg = sh 200/kg Step 2: Calculate the cost for 10 kg of rice. Cost for 10 kg = 10 kg × sh 200/kg = sh 2000 The cost to buy 10 kg of rice is sh 2000. 2. Cultivating land Step 1: Determine the rate of cultivation in acres per day. Rate = 12 acres2 days = 6 acres/day Step 2: Calculate the number of days needed to cultivate 36 acres. Days = Total acresRate = 36 acres6 acres/day = 6 days It will take 6 days to cultivate 36 acres. 3. Complete the following expressions a) Factor out the common term from 4x+12. 4x+12 = 4(x+3) The missing term is 4. b) Factor out 2x from 4x-14xy. 4x-14xy = 2x(2 - 7y) The missing terms are 2 - 7y. 4. Simplify into a single fraction Step 1: Find a common denominator for D and 4, which is 4D. (y)/(D) + 5 + (y-1)/(4) = (y · 4)/(D · 4) + (5 · 4D)/(1 · 4D) + ((y-1) · D)/(4 · D) Step 2: Combine the fractions with the common denominator. = (4y)/(4D) + (20D)/(4D) + (D(y-1))/(4D) = (4y + 20D + Dy - D)/(4D) The simplified single fraction is (4y + 20D + Dy - D)/(4D). 5. Solve by substitution Given equations: 1) 2p+4q=44 2) 5p+3q=68 Step 1: Solve equation (1) for p. 2p = 44 - 4q p = 22 - 2q Step 2: Substitute this expression for p into equation (2). 5(22 - 2q) + 3q = 68 110 - 10q + 3q = 68 110 - 7q = 68 Step 3: Solve for q. -7q = 68 - 110 -7q = -42 q = (-42)/(-7) q = 6 Step 4: Substitute the value of q back into the expression for p. p = 22 - 2(6) p = 22 - 12 p = 10 The solution is p=10, q=6. 6. Distance covered by minute hand Step 1: Identify the given values. The length of the minute hand is the radius, r = 7 cm. The angle moved is = 45^. Step 2: Use the formula for arc length. The distance the tip covers is the arc length L. L = ()/(360^) × 2 r L = (45^)/(360^) × 2 × × 7 cm Step 3: Calculate the arc length. L = (1)/(8) × 14 cm L = (14)/(8) cm L = (7)/(4) cm Using ≈ 3.14159: L ≈ (7 × 3.14159)/(4) cm L ≈ (21.99113)/(4) cm L ≈ 5.49778 cm The distance the tip covers is approximately 5.50 cm. 7. Find the area of the sector below Step 1: Identify the given values from the image and formula. Angle = 135^. Radius r = 14.7 cm. Formula: Area of a sector = ()/(360) × r^2. Step 2: Substitute the values into the formula. Area = (135^)/(360^) × × (14.7 cm)^2 Step 3: Calculate the area. Area = (3)/(8) × × 216.09 cm^2 Area = (648.27)/(8) cm^2 Area ≈ 81.03375 × cm^2 Using ≈ 3.14159: Area ≈ 81.03375 × 3.14159 cm^2 Area ≈ 254.59 cm^2 The area of the sector is approximately 254.59 cm^2. Drop the next question! 📸