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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Here are the solutions to the questions: Question 1: If 3n + 2 = 8, find the value of n. Step 1: Subtract 2 from both sides of the equation. 3n + 2 - 2 = 8 - 2 3n = 6 Step 2: Divide both sides by 3. (3n)/(3) = (6)/(3) n = 2 The correct option is D. D. 2 Question 2: Arrange the following: (3)/(4), 0.8, (5)/(8), 0.65 in descending order. Step 1: Convert all numbers to decimal form for easy comparison. (3)/(4) = 0.75 0.8 = 0.80 (5)/(8) = 0.625 0.65 = 0.650 Step 2: Arrange the decimal values in descending order (from largest to smallest). 0.80, 0.75, 0.650, 0.625 Step 3: Write the numbers back in their original form. 0.8, (3)/(4), 0.65, (5)/(8) The correct option is A. A. 0.8, (3)/(4), 0.65, (5)/(8) Question 3: Mr Mensah left his house at 9:45 am and reached his village at 4:15 pm. Find the time spent. Step 1: Calculate the time from 9:45 am to 12:00 pm. From 9:45 am to 10:00 am = 15 minutes. From 10:00 am to 12:00 pm = 2 hours. Total time from 9:45 am to 12:00 pm = 2 hours 15 minutes. Step 2: Calculate the time from 12:00 pm to 4:15 pm. This is 4 hours 15 minutes. Step 3: Add the two time durations. Total time spent = (2 hours 15 minutes) + (4 hours 15 minutes) Total time spent = 6 hours 30 minutes. The correct option is C. C. 6 hours 30 minutes Question 4: In a test, (2)/(3) of the learners passed. If the number of learners who failed was 69, how many passed? Step 1: Determine the fraction of learners who failed. If (2)/(3) of the learners passed, then the fraction who failed is 1 - (2)/(3). 1 - (2)/(3) = (3)/(3) - (2)/(3) = (1)/(3) So, (1)/(3) of the learners failed. Step 2: Use the number of failed learners to find the total number of learners. If (1)/(3) of the total learners is 69, then the total number of learners is 3 × 69. Total learners = 3 × 69 = 207 Step 3: Calculate the number of learners who passed. The number of learners who passed is (2)/(3) of the total learners. Number passed = (2)/(3) × 207 Number passed = 2 × (207)/(3) Number passed = 2 × 69 = 138 The correct option is B. B. 138 Question 5: Factorize: 3a^2b - 9ab^2. Step 1: Identify the greatest common factor (GCF) for the terms 3a^2b and 9ab^2. The GCF of the numerical coefficients (3 and 9) is 3. The GCF of the variable a^2 and a is a. The GCF of the variable b and b^2 is b. So, the overall GCF is 3ab. Step 2: Factor out the GCF from each term. 3a^2b - 9ab^2 = 3ab(a) - 3ab(3b) 3a^2b - 9ab^2 = 3ab(a - 3b) The correct option is A. A. 3ab(a - 3b) That's 2 down. 3 left today — send the next one.