Notes

coefficient short definition
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A coefficient is a numerical value or factor that quantifies the relationship or strength of association between variables in a mathematical or statistical equation, model, or formula. It represents the proportion or magnitude of the effect one variable has on another. Coefficients are commonly used in various fields, including mathematics, physics, economics, and statistics, to describe and analyze relationships between different quantities or variables.




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constant short definition
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A constant is a fixed and unchanging value or quantity in mathematics and science. Unlike variables, which can vary or change, constants remain the same throughout a particular equation, formula, or experiment. They are often used to represent fundamental physical quantities, such as the speed of light (c) in physics or mathematical constants like π (pi). Constants are typically represented by specific symbols or letters and play a crucial role in mathematical equations and scientific laws.




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difference short definition
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Difference refers to the result of subtracting one quantity or value from another. It represents the numerical distance or gap between two numbers, measurements, or quantities. In mathematics, the difference between two numbers (let's say a and b) is calculated as a - b. The term "difference" can also be used more broadly to describe distinctions or variations between two or more things in terms of characteristics, qualities, or attributes.




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product short definition
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A product is the result of multiplying two or more numbers or quantities together. In mathematics, the product of two numbers (e.g., a and b) is calculated as a multiplied by b, often represented as a × b or simply ab. The term "product" can also be used in a broader context to refer to the outcome of any operation or process that combines or interacts multiple elements or factors to produce a result.




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quotient short definition
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A quotient is the result of dividing one quantity by another. In mathematics, the quotient of two numbers (such as a and b) is obtained by dividing a by b, often represented as a ÷ b or a/b. It represents how many times one number is contained within another and is the outcome of a division operation. The term "quotient" can also be used more broadly to describe the result of dividing or separating something into parts or portions.




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sum short definition
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A sum is the result of adding two or more numbers or quantities together. In mathematics, the sum of two or more numbers (e.g., a and b) is calculated as a plus b, often represented as a + b. The term "sum" can also be used in a broader sense to describe the outcome of any operation or process that combines or accumulates multiple elements or quantities to produce a total or result.




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variable short definition
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A variable is a symbol or placeholder that represents a value that can vary or change in a mathematical equation, scientific experiment, or problem-solving context. Variables can take on different values, and their purpose is to allow for the generalization and analysis of relationships between quantities. In equations or formulas, variables are often denoted by letters such as x, y, or z, and their values can be manipulated or substituted to solve problems or explore mathematical relationships.




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distributive property short definition
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The distributive property is a fundamental concept in mathematics that describes how multiplication distributes over addition or subtraction. In a mathematical expression, it states that when you multiply a number by the sum (or difference) of two other numbers, you can distribute the multiplication to each term inside the parentheses. The distributive property can be succinctly summarized as follows:

a × (b + c) = a × b + a × c

This property is also applicable to subtraction:

a × (b - c) = a × b - a × c

The distributive property is an essential rule in algebra and is used to simplify expressions and perform calculations involving variables and constants.




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absolute value short definition
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Absolute value, often denoted by two vertical bars surrounding a number or expression (|x|), is a mathematical concept that represents the magnitude or distance of a number from zero on the number line, regardless of its sign. In other words, it gives the non-negative value of a quantity. The absolute value of a positive number is the number itself, and the absolute value of a negative number is its positive counterpart. For example:

The absolute value of |5| is 5.
The absolute value of |-5| is also 5.
In formal terms, the absolute value of a real number x is defined as:

| x | = x, if x is greater than or equal to 0
| x | = -x, if x is less than 0




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equation short definition
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An equation is a mathematical statement that asserts the equality of two expressions or values. It typically consists of an equal sign (=) between the left-hand side (LHS) and the right-hand side (RHS), where each side can contain numbers, variables, and mathematical operations. The fundamental purpose of an equation is to describe a relationship or condition in which both sides of the equal sign are equivalent. Solving an equation involves finding the values of the variables that make the equation true, which may involve various algebraic or mathematical techniques. Equations are widely used in mathematics, physics, engineering, and various other fields to model and solve real-world problems.




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expression short definition
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An expression is a mathematical statement or combination of numbers, variables, operations (such as addition, subtraction, multiplication, and division), and functions that can be evaluated to produce a single value or result. Expressions can be simple, like "2 + 3," or more complex, involving variables and mathematical operations, such as "3x - 2y" or "sin(x) + cos(x)." They are distinct from equations, which assert equality between two expressions, whereas expressions do not make such assertions and can represent values, formulas, or relationships. Expressions are used extensively in mathematics, computer programming, and various scientific and engineering disciplines for calculations and modeling.




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factoring short definition
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Factoring, in mathematics, refers to the process of breaking down a mathematical expression, usually a polynomial, into a product of simpler expressions or factors. This involves finding the numbers or algebraic expressions that, when multiplied together, produce the original expression. Factoring is a fundamental technique in algebra and is often used to simplify expressions, solve equations, and analyze mathematical relationships. It plays a crucial role in various mathematical and real-world applications, including finding roots, simplifying equations, and solving quadratic equations.




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reciprocal short definition
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The reciprocal of a number is a value that, when multiplied by the original number, equals 1. In other words, if you have a number x, its reciprocal is 1/x. For example:

The reciprocal of 2 is 1/2 because 2 * (1/2) = 1.
The reciprocal of 5 is 1/5 because 5 * (1/5) = 1.
The reciprocal is also referred to as the multiplicative inverse because it undoes the effect of multiplication by returning the product to the identity element, which is 1 in this case. Reciprocals are useful in various mathematical operations and applications, especially in division and solving equations involving fractions.




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equivalent short definition
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"Equivalent" means having the same value, meaning, or effect as something else, although it may be expressed differently or appear differently on the surface. In mathematics, two expressions or values are considered equivalent if they are equal or have the same mathematical significance. In a broader context, "equivalent" can also be used to describe items or situations that are essentially the same or interchangeable in terms of function, purpose, or outcome.




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horizontal short definition
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Horizontal refers to a direction or orientation that is parallel to the horizon or the Earth's surface. In a horizontal position, objects or lines extend from left to right when viewed from a typical upright position. It is the opposite of vertical, which extends from top to bottom. In various contexts, "horizontal" is used to describe things that are level, flat, or aligned along a horizontal plane.




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origin short definition
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The origin is a central point or starting point of reference in various contexts, often used in mathematics, physics, and geography. In mathematics, particularly in Cartesian coordinate systems, the origin is the point where the x-axis and y-axis intersect, typically designated as (0,0). It serves as the reference point for measuring coordinates of other points.

In other contexts, the term "origin" can refer to the starting point of something, such as the origin of a river (where it begins), the origin of a story (where it originates), or the origin of a product (where it was first created or produced). Essentially, it denotes the point or place from which something originates or originates.




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prime short definition
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"Prime" refers to a positive integer greater than 1 that has exactly two distinct positive divisors: 1 and itself. In other words, a prime number cannot be evenly divided by any other positive integer except for 1 and itself. Examples of prime numbers include 2, 3, 5, 7, 11, 13, and so on. Prime numbers play a fundamental role in number theory and have various applications in mathematics, computer science, and cryptography.




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vertical short definition
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Vertical refers to a direction or orientation that is perpendicular to the horizontal plane. In a vertical position, objects or lines extend from top to bottom when viewed from a typical upright position. It is the opposite of horizontal, which extends from left to right. "Vertical" is used to describe things that are upright or aligned along a vertical plane.






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