a) Calculate the total water used in 3 days if Day 1 used sqrt(5)L, Day 2 used 2sqrt(5)L, and Day 3 used 3sqrt(5)L. b) Calculate the total cost if water costs Ksh 15 per litre.

Here are the solutions to the questions: 16. a) Step 1: Identify the water used each day. Day 1: sqrt(5) litres Day 2: 2sqrt(5) litres Day 3: 3sqrt(5) litres Step 2: Add the amounts to find the total water used. Total water = sqrt(5) + 2sqrt(5) + 3sqrt(5) Total water = (1 + 2 + 3)sqrt(5) Total water = 6sqrt(5) litres The total water used is 6sqrt(5) litres. b) Step 1: Identify the cost per litre and the total water used. Cost per litre = Ksh 15 Total water used = 6sqrt(5) litres Step 2: Calculate the total cost. Total cost = Total water used × Cost per litre Total cost = 6sqrt(5) × 15 Total cost = 90sqrt(5) Ksh The total cost is 90sqrt(5) Ksh. 17. a) Step 1: Identify the battery life of one device. Battery life of one device = sqrt(11) hours Step 2: Calculate the total time for 8 phones. Total time for 8 phones = 8 × sqrt(11) Total time for 8 phones = 8sqrt(11) hours The total time for 8 phones is 8sqrt(11) hours. b) Step 1: Write the expression to be rationalized. Expression = (4)/(sqrt(11)) Step 2: Multiply the numerator and denominator by sqrt(11) to rationalize. (4)/(sqrt(11)) = (4)/(sqrt(11)) × sqrt(11)sqrt(11) = 4sqrt(11)11 The rationalized expression is 4sqrt(11)11. 18. a) Step 1: Write the expression. Expression = 2x^2 - 13x + 20 Step 2: Find two numbers that multiply to (2 × 20 = 40) and add to -13. The numbers are -5 and -8. Step 3: Rewrite the middle term using these numbers. 2x^2 - 5x - 8x + 20 Step 4: Group terms and factor out common factors. (2x^2 - 5x) - (8x - 20) x(2x - 5) - 4(2x - 5) Step 5: Factor out the common binomial. (2x - 5)(x - 4) The factorized expression is (2x - 5)(x - 4) . b) Step 1: Write the equation. 2x^2 - 13x + 20 = 0 Step 2: Use the factorized form from part (a). (2x - 5)(x - 4) = 0 Step 3: Set each factor equal to zero and solve for x. 2x - 5 = 0 or x - 4 = 0 2x = 5 or x = 4 x = (5)/(2) or x = 4 The solutions are x = (5)/(2) and x = 4. 19. a) Step 1: Write the expression. F = (a^3b^5)/(a^2b^3) Step 2: Apply the index law (x^m)/(x^n) = x^m-n. F = a^3-2b^5-3 F = a^1b^2 F = ab^2 The simplified expression is ab^2. b) Step 1: Substitute the given values a = 2 and b = 3 into the simplified expression. F = ab^2 F = (2)(3^2) Step 2: Calculate the numerical value. F = 2 × 9 F = 18 The numerical value is 18. 20. a) Step 1: Write the expression for the area. A = x^2 - 4x - 21 Step 2: Factorize the quadratic expression. Find two numbers that multiply to -21 and add to -4. The numbers are -7 and 3. Step 3: Rewrite the expression in factored form. A = (x - 7)(x + 3) The dimensions of the garden are (x - 7) and (x + 3) units. (Assuming units are in metres, for example). b) Step 1: Determine the perimeter of the garden. The dimensions are (x - 7) and (x + 3). Perimeter P = 2(length + width) P = 2((x + 3) + (x - 7)) P = 2(x + 3 + x - 7) P = 2(2x - 4) P = 4x - 8 metres Step 2: Calculate the total cost of fencing. Cost per metre = KSh 150 Total cost = Perimeter × Cost per metre Total cost = (4x - 8) × 150 Total cost = 150(4x - 8) Total cost = 600x - 1200 Ksh The cost of fencing the garden is (600x - 1200) Ksh. Send me the next one 📸