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: 39. Step 1: Substitute the given values of x=7 and y=-2 into the expression P = 9x - 5y. P = 9(7) - 5(-2) Step 2: Perform the multiplications. P = 63 - (-10) Step 3: Simplify the expression. P = 63 + 10 P = 73 40. Each face of a cube is in the shape of a Square. The correct option is c) Square. 2. (a) Step 1: Define variables for their present ages. Let the son's present age be S years. Let the mother's present age be M years. Step 2: Formulate equations based on the given information. "A mother is 10 times as old as her son": M = 10S (1) "In 6 years' time, she will be four times as old as her son": M+6 = 4(S+6) (2) Step 3: Substitute equation (1) into equation (2). 10S + 6 = 4(S+6) 10S + 6 = 4S + 24 Step 4: Solve for S. 10S - 4S = 24 - 6 6S = 18 S = (18)/(6) S = 3 Step 5: Substitute S=3 back into equation (1) to find M. M = 10(3) M = 30 The son's present age is 3 years and the mother's present age is 30 years. 2. (b) Step 1: Rewrite the equation. (x+2)/(3) + 2x = 10 Step 2: Find a common denominator for the terms on the left side. (x+2)/(3) + (2x · 3)/(3) = 10 (x+2+6x)/(3) = 10 Step 3: Combine like terms in the numerator. (7x+2)/(3) = 10 Step 4: Multiply both sides by 3. 7x+2 = 10 × 3 7x+2 = 30 Step 5: Subtract 2 from both sides. 7x = 30 - 2 7x = 28 Step 6: Divide by 7 to solve for x. x = (28)/(7) x = 4 3. (a) Step 1: Calculate the total value of each type of item sold. Value of 2 guitars: 2 × N35,400 = N70,800 Value of 5 tennis rackets: 5 × N9,900 = N49,500 Value of 14 electric kettles: 14 × N2,550 = N35,700 Step 2: Calculate the total value of all sales. Total sales = N70,800 + N49,500 + N35,700 Total sales = N156,000 Step 3: Convert the commission percentage to a decimal. 8(1)/(2)\% = 8.5\% = (8.5)/(100) Step 4: Calculate the commission. Commission = (8.5)/(100) × N156,000 Commission = 8.5 × 1,560 Commission = N13,260 3. (b) Step 1: Find a common denominator for the two fractions. The least common multiple of 2 and 3 is 6. (5a+2)/(2) - (2(3a+1))/(3) Step 2: Rewrite each fraction with the common denominator. (3(5a+2))/(6) - (2 · 2(3a+1))/(6) (3(5a+2))/(6) - (4(3a+1))/(6) Step 3: Combine the fractions. (3(5a+2) - 4(3a+1))/(6) Step 4: Expand the terms in the numerator. (15a + 6 - (12a + 4))/(6) (15a + 6 - 12a - 4)/(6) Step 5: Combine like terms in the numerator. ((15a - 12a) + (6 - 4))/(6) (3a + 2)/(6)