Questions and Answers
What is the result of adding (3x^2 + 4x - 1) + (-2x^2 - x + 3)?
x^2 + 3x + 2
How many cubic feet are in 18 cubic yards?
486
What is the factored form of 4x^2 - 4x - 3?
(2x - 3)(2x + 1)
What property justifies that (70 + 20) + 5 is equivalent to 70 + (20 + 5)?
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If Linda buys a package of 12 cartons of tomato soup for $30 and each carton holds 16 ounces, what is the cost per quart?
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Which ordered pair (x, y) represents the solution for the system of equations 3.5x + 0.5y = 7 and x - y = 10?
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Simplify the expression 6x(x + 3y) + 7y^2 - 2y(3x + y).
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What are the coordinates of the midpoint of a line segment with endpoints (10, -5) and (-6, -3)?
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What is the result of simplifying (a^3 b)^2?
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What are the domains of the following set {(5, 70), (7, 10), (2, 1), (6, 5)}?
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Study Notes
Algebraic Expressions and Operations
- Adding polynomials: (3x² + 4x - 1) + (-2x² - x + 3) simplifies to x² + 3x + 2.
Volume Conversion
- 18 cubic yards is equivalent to 486 cubic feet.
Factoring Quadratics
- Factor the expression 4x² - 4x - 3 to get (2x - 3)(2x + 1).
Associative Property
- The total cost calculation by Kris and Sam illustrates the associative property: ($70 + $20) + $5 = $70 + ($20 + $5).
Cost per Quart Calculation
- Linda's purchase of 12 cartons of tomato soup for $30 results in a cost of $5.00 per quart, with each carton holding 16 ounces.
System of Equations
- The ordered pair (x, y) that represents the solution to the system 3.5x + 0.5y = 7 and x - y = 10 is (3, -7).
Simplifying Expressions
- Simplification of 6x(x + 3y) + 7y² - 2y(3x + y) results in 6x² + 12xy + 5y².
Midpoint of a Line Segment
- The midpoint of the segment with endpoints (10, -5) and (-6, -3) is calculated as (2, -4).
Power of a Product
- Simplifying the expression (a³b)² gives a⁶b².
Domain of a Set of Points
- The domain of the set {(5, 70), (7, 10), (2, 1), (6, 5)} includes the unique x-values: D = {5, 7, 2, 6}.
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