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.
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Step 1: Solve the linear equation for h. 2h - 7 = 1 Add 7 to both sides: 2h = 1 + 7 2h = 8 Divide by 2: h = (8)/(2) h = 4 The value of h is 4. Step 2: Convert ₦45.62 to kobo. Assuming ₦1 = 100 kobo. 45.62 Naira × 100 koboNaira = 4562 kobo ₦45.62 is equal to 4562 kobo. Step 3: Calculate the amount paid after a discount. Original cost = ₦200 Discount = 30% Discount amount = 30\% of ₦200 0.30 × 200 = 60 Discount amount = ₦60 Amount paid = Original cost - Discount amount 200 - 60 = 140 The buyer will pay ₦140. Step 4: Solve for X. X × 9 = 648 Divide by 9: X = (648)/(9) X = 72 The value of X is 72. Step 5: Calculate the perimeter of the rectangular field. Length (L) = 10 cm Breadth (W) = 5 cm Perimeter (P) = 2(L + W) P = 2(10 cm + 5 cm) P = 2(15 cm) P = 30 cm The perimeter of the rectangular field is 30 cm. Step 6: Calculate the perimeter of the rhombus. A rhombus has four equal sides. Assuming the side length is 8 cm. Side length (s) = 8 cm Perimeter (P) = 4s P = 4 × 8 cm P = 32 cm The perimeter of the rhombus is 32 cm. Step 7: Find the cost price. Selling Price (SP) = ₦14 Profit = 40% Let Cost Price (CP) be x. SP = CP + Profit SP = CP + (Profit % of CP) 14 = x + 0.40x 14 = 1.40x Divide by 1.40: x = (14)/(1.40) x = 10 The cost price is ₦10. Step 8: Simplify the ratio. Ratio = 18:45 Find the greatest common divisor (GCD) of 18 and 45. The GCD of 18 and 45 is 9. Divide both parts of the ratio by 9: (18)/(9) : (45)/(9) 2 : 5 The ratio in its lowest term is 2:5. Step 9: Calculate C's share. Total amount = ₦48 Ratio A:B:C = 2:3:5 Total ratio parts = 2 + 3 + 5 = 10 C's share = C's ratio partTotal ratio parts × Total amount C's share = (5)/(10) × 48 C's share = (1)/(2) × 48 C's share = 24 C's share is ₦24. Step 10: Calculate the number of years. Principal (P) = ₦800 Amount (A) = ₦960 Interest (I) = A - P = ₦960 - ₦800 = ₦160 Interest Rate (R) = 5% per annum = 0.05 Simple Interest formula: I = P × R × T 160 = 800 × 0.05 × T 160 = 40 × T Divide by 40: T = (160)/(40) T = 4 The money was in the bank for 4 years. Step 11: Convert Naira to Pounds. Assuming the conversion rate is £1 = ₦300. Amount in Naira = ₦27,000 Amount in Pounds = Amount in NairaNaira per Pound Amount in Pounds = (27000)/(300) Amount in Pounds = 90 You could get £90. Step 12: Find the profit or loss. Cost Price (CP) = ₦75 Selling Price (SP) = ₦63 Since SP < CP, there is a loss. Loss = CP - SP 75 - 63 = 12 The loss is ₦12. Step 13: Find the value of sqrt(1(1)/(16)). Convert the mixed number to an improper fraction: 1(1)/(16) = (1 × 16 + 1)/(16) = (17)/(16) Find the square root: sqrt((17)/(16)) = sqrt(17)sqrt(16) = sqrt(17)4 The value is sqrt(17)4. Step 14: Simplify (3)/(729) ÷ (3)/(729). When a non-zero number is divided by itself, the result is 1. (3)/(729) ÷ (3)/(729) = 1 The simplified expression is 1.