Solve the following algebraic problems: 1. Make h the subject of V = pi r2 h. 2. Expand (2x−3)(x−5). 3…

Question

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).

ScanSolve AI Tutor · Accepted Answer

29) Step 1: Start with the given formula. V = π r² h Step 2: To make h the subject, divide both sides of the equation by π r². (V)/(π r²) = (π r² h)/(π r²) Step 3: Simplify the equation. h = (V)/(π r²); The correct option is C. h = (V)/(π r²). 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. = 2x² − 10x − 3x + 15 Step 3: Combine the like terms (the x terms). = 2x² − (10x + 3x) + 15; = 2x² − 13x + 15 The correct option is D. 2x² − 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.

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).

Step-by-step solution

Start with the given formula.

To make $h$ the subject, divide both sides of the equation by $\pi r^2$ .

Simplify the equation.

Expand the expression $(2x - 3)(x - 5)$ using the distributive property (FOIL method).

Perform the multiplications.

Combine the like terms (the $x$ terms).

Identify the common factor in the terms $9a$ and 27.

Factor out the common factor.

Let the certain number be $x$ .

Set up the equation.

Cross-multiply to solve for $x$ .

Distribute the numbers on both sides.

Subtract $3x$ from both sides.

Subtract 20 from both sides.

Let the father's age be $F$ and the son's age be $S$ .

Substitute the given father's age, $F = 42$ .

Solve for $S$ .

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