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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Morning I — let's get this done. Here are the solutions to your math questions: 5. Without using mathematical tables or a calculator, evaluate leaving your answer as a simplified fraction: The expression to be evaluated for question 5 is missing from the image. Please provide the expression. 8. Simplify the expression: (9t^2 - 25a^2)/(6t^2 + 19at + 15a^2) Step 1: Factorize the numerator using the difference of two squares formula (A^2 - B^2 = (A-B)(A+B)). 9t^2 - 25a^2 = (3t)^2 - (5a)^2 = (3t - 5a)(3t + 5a) Step 2: Factorize the denominator by splitting the middle term. We need two numbers that multiply to 6 × 15 = 90 and add up to 19. These numbers are 9 and 10. 6t^2 + 19at + 15a^2 = 6t^2 + 9at + 10at + 15a^2 Factor by grouping: 3t(2t + 3a) + 5a(2t + 3a) (3t + 5a)(2t + 3a) Step 3: Substitute the factored forms back into the expression and simplify. ((3t - 5a)(3t + 5a))/((3t + 5a)(2t + 3a)) Cancel out the common factor (3t + 5a): (3t - 5a)/(2t + 3a) The simplified expression is (3t - 5a)/(2t + 3a). 9. Use reciprocals, square roots and cube root tables to evaluate: The expression to be evaluated for question 9 is missing from the image. Please provide the expression. 10. A Kenya company received US dollar M. The money was converted into Kenyan shillings in a bank which buys and sells foreign currencies: Currency | Buying in Ksh | Selling in Ksh ---|---|--- 1 Sterling Pound | 187.59 | 188.64 1 US Dollar | 128.00 | 131.00 a) If the company received Ksh 15,132,880,000, calculate M, the amount received in Dollars. Step 1: Identify the correct exchange rate. The company received US dollars and converted them into Kenyan Shillings. This means the bank bought US dollars from the company. Therefore, we use the "Buying in Ksh" rate for US Dollars. 1 US Dollar = Ksh 128.00. Step 2: Calculate the amount M in US Dollars. M = Total Kenyan Shillings receivedBuying rate per US Dollar M = Ksh 15,132,880,000Ksh 128.00/Dollar M = 118,225,625 US Dollars The amount M received in Dollars is 118,225,625 US Dollars. b) The company exchanged the above Kenyan Shillings into This part of the question is incomplete. Please provide the full question for part b. Send me the next one 📸