Solve the following algebraic problems: 1. Make h the subject of V = pi r2 h. 2. Expand (2x-3)(x-5). 3. Factor 9a - 27. 4. Solve 4/(x+10) = 3/(x+5).

29) Step 1: Start with the given formula. V = r^2 h Step 2: To make h the subject, divide both sides of the equation by r^2. (V)/( r^2) = ( r^2 h)/( r^2) Step 3: Simplify the equation. h = (V)/( r^2) The correct option is C. h = (V)/( r^2). 30) Step 1: Expand the expression (2x - 3)(x - 5) using the distributive property (FOIL method). (2x - 3)(x - 5) = 2x(x) + 2x(-5) - 3(x) - 3(-5) Step 2: Perform the multiplications. = 2x^2 - 10x - 3x + 15 Step 3: Combine the like terms (the x terms). = 2x^2 - (10x + 3x) + 15 = 2x^2 - 13x + 15 The correct option is D. 2x^2 - 13x + 15. 31) Step 1: Identify the common factor in the terms 9a and 27. The greatest common factor of 9 and 27 is 9. Step 2: Factor out the common factor. 9a - 27 = 9(a) - 9(3) = 9(a - 3) The correct option is A. 9(a - 3). Word Problem 1 (after 31) Step 1: Let the certain number be x. Translate the first part of the statement: "When 4 is divided by the sum of a certain number and 10" (4)/(x + 10) Translate the second part of the statement: "the result is the same as dividing 3 by the sum of that number and 5" (3)/(x + 5) Step 2: Set up the equation. (4)/(x + 10) = (3)/(x + 5) Step 3: Cross-multiply to solve for x. 4(x + 5) = 3(x + 10) Step 4: Distribute the numbers on both sides. 4x + 20 = 3x + 30 Step 5: Subtract 3x from both sides. 4x - 3x + 20 = 30 x + 20 = 30 Step 6: Subtract 20 from both sides. x = 30 - 20 x = 10 The number is E. 10 (assuming E is 10, as A, B, C, D are 5, 7, 9, 11). Word Problem 2 (after the previous word problem) Step 1: Let the father's age be F and the son's age be S. The difference between their ages is 28: F - S = 28 Step 2: Substitute the given father's age, F = 42. 42 - S = 28 Step 3: Solve for S. Subtract 42 from both sides: -S = 28 - 42 -S = -14 Multiply by -1: S = 14 The son's age is 14 years.