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
Okay, Chiomzy, let's continue with these problems. Problem 14b: Step 1: Expand the first term by distributing 3x: 3x(4a - 5b) = 12ax - 15bx Step 2: Expand the second term by distributing -5x: -5x(3a - 2b) = -15ax + 10bx Step 3: Combine the expanded terms: (12ax - 15bx) + (-15ax + 10bx) Step 4: Group like terms (ax terms and bx terms): (12ax - 15ax) + (-15bx + 10bx) Step 5: Perform the subtraction for each group: -3ax - 5bx The simplified expression is -3ax - 5bx. Problem 15a: Step 1: Since the denominators are the same, combine the numerators over the common denominator: (2x - 3)/(x - 1) Step 2: The expression cannot be simplified further. The expression as a single fraction is (2x - 3)/(x - 1). Problem 15b: Step 1: The equation is (2x)/(3) = 5 - 3x. Step 2: Multiply the entire equation by 3 to eliminate the denominator: 3 × ((2x)/(3)) = 3 × (5 - 3x) 2x = 15 - 9x Step 3: Add 9x to both sides to gather x terms: 2x + 9x = 15 11x = 15 Step 4: Divide by 11 to solve for x: x = (15)/(11) The value of x is (15)/(11). Problem 16a: Step 1: Let the certain number be y. Step 2: Translate the problem into an equation: "3 divided by the sum of a certain number and 8" is (3)/(y+8). "2 divided by the sum of that number and 3" is (2)/(y+3). (3)/(y+8) = (2)/(y+3) Step 3: Cross-multiply: 3(y+3) = 2(y+8) Step 4: Distribute on both sides: 3y + 9 = 2y + 16 Step 5: Subtract 2y from both sides: 3y - 2y + 9 = 16 y + 9 = 16 Step 6: Subtract 9 from both sides: y = 16 - 9 y = 7 The number is 7. Problem 16b: Step 1: The equation is (10)/(3x-5) = (2)/(1). Step 2: Cross-multiply: 10 × 1 = 2 × (3x - 5) 10 = 6x - 10 Step 3: Add 10 to both sides: 10 + 10 = 6x 20 = 6x Step 4: Divide by 6 to solve for x: x = (20)/(6) Step 5: Simplify the fraction: x = (10)/(3) The value of x is (10)/(3). Problem 17a: Step 1: Calculate the total length of the pitch. It is divided into 12 parts, each 25cm long. Total length = 12 × 25 cm = 300 cm Step 2: Find how many parts, each 20cm long, can be obtained from the total length. Number of parts = Total lengthLength of each new part = 300 cm20 cm Number of parts = 15 15 parts, each 20cm long, can be obtained from the pitch. 15 parts. Problem 17b: Step 1: Find the reciprocal of 0.65: Reciprocal = (1)/(0.65) Step 2: Calculate the value: (1)/(0.65) ≈ 1.53846... Step 3: Round to 3 significant figures. The first three significant figures are 1, 5, 3. The next digit is 8, which is 5, so round up the 3. 1.53846... ≈ 1.54 The reciprocal of 0.65 to 3 significant figures is 1.54. Problem 18a: Step 1: Calculate the fuel consumption rate (liters per km): Rate = 100 liters250 km = (10)/(25) liters/km = (2)/(5) liters/km = 0.4 liters/km Step 2: Calculate the fuel needed for 150 km: Fuel needed = Rate × Distance = 0.4 liters/km × 150 km Fuel needed = 60 liters It will use 60 liters of fuel. Problem 18b: Step 1: The equation is (P)/(15) = (5)/(3). Step 2: To solve for P, multiply both sides by 15: P = (5)/(3) × 15 Step 3: Perform the multiplication: P = 5 × (15)/(3) = 5 × 5 P = 25 The value of P is 25. Problem 19a: Step 1: Express ₦32.00 as a ratio of ₦72.00: (32)/(72) Step 2: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. Both are divisible by 8: (32 ÷ 8)/(72 ÷ 8) = (4)/(9) The ratio is 4:9. Problem 19b: Step 1: Calculate 15% of 4500kg: Increase amount = 15\% of 4500 kg = (15)/(100) × 4500 Increase amount = 15 × 45 = 675 kg Step 2: Add the increase amount to the original amount: New amount = 4500 kg + 675 kg = 5175 kg The increased amount is 5175 kg. Problem 20a: Step 1: Find the prime factorization of each number: 9 = 3^2 12 = 2^2 × 3 18 = 2 × 3^2 Step 2: Find the HCF (Highest Common Factor). This is the product of the lowest powers of common prime factors. The only common prime factor is 3, and its lowest power is 3^1. HCF(9, 12, 18) = 3 Step 3: Find the LCM (Least Common Multiple). This is the product of the highest powers of all prime factors present. Highest power of 2 is 2^2. Highest power of 3 is 3^2. LCM(9, 12, 18) = 2^2 × 3^2 = 4 × 9 = 36 Step 4: Find the product of the LCM and HCF: Product = LCM × HCF = 36 × 3 = 108 The product of the LCM and HCF is 108. Problem 20b: Step 1: Identify the given values for simple interest: Principal (P) = ₦30,000.00 Time (T) = 3(1)/(2) years = 3.5 years Rate (R) = 5% per annum = 0.05 Step 2: Use the formula for simple interest: Simple Interest (SI) = (P × R × T)/(100) Step 3: Substitute the values into the formula: SI = (30000 × 5 × 3.5)/(100) Step 4: Perform the multiplication in the numerator: SI = (30000 × 17.5)/(100) SI = (525000)/(100) Step 5: Perform the division: SI = ₦5250.00 The simple interest is ₦5250.00. Last free one today — make it count tomorrow, or type /upgrade for unlimited.