A two-digit number is such that the product of its digits is 20. When the digits are reversed, the number formed is greater than the original number by 9. Find the two-digit number.

Morning Karanjamugo😎 — let's get this done. Here are the answers to your questions: 6. To find the two-digit number: Step 1: Define the number using variables. Let the two-digit number be 10t + u, where t is the tens digit and u is the units digit. Step 2: Formulate equations based on the given conditions. Condition 1: The product of its digits is 20. t × u = 20 (1) Condition 2: When the digits are reversed, the number formed is greater than the original number by 9. The reversed number is 10u + t. 10u + t = (10t + u) + 9 10u + t = 10t + u + 9 9u - 9t = 9 Divide by 9: u - t = 1 (2) Step 3: Solve the system of equations. From equation (2), express u in terms of t: u = t + 1 Substitute this into equation (1): t(t + 1) = 20 t^2 + t = 20 t^2 + t - 20 = 0 Step 4: Solve the quadratic equation for t. Factor the quadratic equation: (t + 5)(t - 4) = 0 This gives two possible values for t: t = -5 or t = 4. Since t must be a positive digit, we take t = 4. Step 5: Find the value of u. Using u = t + 1: u = 4 + 1 = 5 Step 6: Form the original number. The number is 10t + u = 10(4) + 5 = 45. The two-digit number is 45. 9. To calculate the total cost for hiring the car: Step 1: Calculate the cost for the days of hire. Daily rate = Sh 2500 Number of days = 5 Cost for days = 2500 Sh/day × 5 days = 12500 Sh Step 2: Calculate the cost for kilometers covered. Total kilometers driven = 40 km Free kilometers per day = 30 km Total free kilometers for 5 days = 30 km/day × 5 days = 150 km Since the total kilometers driven (40 km) is less than the total free kilometers (150 km), there is no charge for the kilometers. Cost for kilometers = 0 Sh Step 3: Calculate the total cost. Total Cost = Cost for days + Cost for kilometers Total Cost = 12500 Sh + 0 Sh = 12500 Sh The total cost is Sh 12500. 7. a) To write the equation of the circle: Step 1: Write the standard equation of a circle. The standard equation of a circle with center (h, k) and radius r is (x - h)^2 + (y - k)^2 = r^2. Given center P(5, 5), so h=5, k=5. Given radius r=5. Step 2: Substitute the values into the standard equation. (x - 5)^2 + (y - 5)^2 = 5^2 Step 3: Expand the equation. (x^2 - 10x + 25) + (y^2 - 10y + 25) = 25 Step 4: Rearrange into the general form ax^2 + by^2 + cx + dy + e = 0. x^2 + y^2 - 10x - 10y + 25 + 25 - 25 = 0 x^2 + y^2 - 10x - 10y + 25 = 0 The equation of the circle is x^2 + y^2 - 10x - 10y + 25 = 0. b) The point A is not provided in the question or any accompanying diagram. Therefore, the gradient of PA cannot be determined. c) The point Q is not provided in the question or any accompanying diagram. Therefore, the equation of the tangent at Q cannot be determined. 10. To calculate the amount Amwaindo has to pay: Step 1: Identify the principal, rate, and time.