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Questions and Answers
What is the definition of algebra?
What is the definition of algebra?
- The study of variables and their relationships (correct)
- The study of shapes and figures
- The study of measurements and conversions
- The study of numbers and their properties
What is the purpose of the distributive property in algebra?
What is the purpose of the distributive property in algebra?
- To combine like terms (correct)
- To apply the rules of exponents
- To solve linear equations
- To graph quadratic equations
What is the difference between an equation and an inequality?
What is the difference between an equation and an inequality?
- An equation expresses equality, while an inequality expresses a relationship (correct)
- An equation is linear, while an inequality is quadratic
- An equation has a variable, while an inequality does not
- An equation is used for graphing, while an inequality is used for solving systems
What is the highest power of the variable in a quadratic equation?
What is the highest power of the variable in a quadratic equation?
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What is the purpose of Cartesian coordinates in graphing?
What is the purpose of Cartesian coordinates in graphing?
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What is an example of a linear equation?
What is an example of a linear equation?
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Study Notes
Algebra
Definition
- Algebra is a branch of mathematics that deals with the study of variables and their relationships, often expressed through the use of symbols, equations, and functions.
Key Concepts
- Variables: Letters or symbols that represent unknown values or quantities.
- Constants: Numbers that do not change value.
- Algebraic Expressions: Combinations of variables, constants, and mathematical operations.
- Equations: Statements that express the equality of two algebraic expressions.
- Functions: Relations between variables, often represented as f(x) =...
Operations
- Addition and Subtraction: Combining like terms and applying the distributive property.
- Multiplication and Division: Applying the rules of exponents and the order of operations (PEMDAS).
- Exponents: Rules for multiplying and dividing expressions with exponents.
Equations and Inequalities
- Linear Equations: Equations in which the highest power of the variable(s) is 1.
- Example: 2x + 3 = 5
- Quadratic Equations: Equations in which the highest power of the variable(s) is 2.
- Example: x^2 + 4x + 4 = 0
- Systems of Equations: Sets of two or more equations with multiple variables.
- Inequalities: Statements that express a relationship between expressions using <, >, ≤, or ≥.
Graphing
- Cartesian Coordinates: A system of graphing points on a plane using x and y axes.
- Graphs of Functions: Visual representations of functions, including linear, quadratic, and polynomial functions.
Solving Equations and Inequalities
- Substitution Method: Replacing variables with values to solve for a specific variable.
- Elimination Method: Adding or subtracting equations to eliminate a variable.
- Graphing Method: Using the intersection of graphs to solve systems of equations.
- Quadratic Formula: A formula for solving quadratic equations: x = (-b ± √(b^2 - 4ac)) / 2a.
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