VOCAB

Equation of variation

: mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. : an equation or function expressing direct variation — compare inverse variation.

Linear inequality in one varaiable

A linear inequality is a mathematical statement that relates a linear expression as either less than or greater than another.

Combining like terms

A mathematical process used to simplify an expression or to add or subtract polynomials.

Formula

A mathematical relationship or rule expressed in symbols.

Root(s)

A number is a number which multiplied by itself, gives you the original number.

Factors

A number or quantity that when multiplied with another produces a given number or expression.

Coefficient

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Proportion

A part, share, or number considered in comparative relation to a whole.

Equation

A statement that the values of two mathematical expressions are equal (indicated by the sign =)

Solving a formula for a variable

A variable in mathematics is a symbol that is used in place of a value. The value of a variable depends on the other values in the expression or equation. As a result, the variable can at times change accordingly.

Term(s)

A word or phrase used to describe a thing or to express a concept, especially in a particular kind of language or branch of study.

Linear equation in one variable

An algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables.

Satisfies the equation

An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign. For example: This equation states that 12 is equal to the sum of 7 and 5, which is obviously true. In an equation, the left side is always equal to the right side.

Algebraic expression

An expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Solving an inequality

An inequality says that two values are not equal. a ≠ b says that a is not equal to b There are other special symbols that show in what way things are not equal.

Solution(s)

Any means of solving a problem.

Like terms

Are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.

Combined variation

Describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others (when the rest of the variables are held constant).

Mathematical modeling

Description of a system using mathematical concepts and language.

Equivalent equations

Equations with the same solution.

Varies inversely as x

In an inverse variation, the values of the two variables change in an opposite manner - as one value increases, the other decreases.

Solving an equation

Is to find what values (numbers, functions, sets, etc.) fulfill a condition stated in the form of an equation (two expressions related by equality).

Evaluating an algebraic expression

Letters can stand for numbers. When we substitute a specific value for each variable, and then perform the operations.

Simplified

Make (something) simpler or easier to do or understand.

Inverse variation

Mathematical relationship between two variables which can be expressed by an equation in which the product of two variables is equal to a constant.

Variable

Not consistent or having a fixed pattern; liable to change.

Constant

Occurring continuously over a period of time.

Numerical term

Of, relating to, or denoting a number or numbers. measured or expressed in numbers: numerical value. (maths) containing or using constants, coefficients, terms, or elements represented by numbers: 3x² + 4y = 2 is a numerical equation Compare literal (sense 6)

The multiplication property of equality

States that if you multiply both sides of an equation by the same number, the sides remain equal (i.e. equality is preserved).

The addition property of equality

The property that states that if you add the same number to both sides of an equation, the sides remain equal.

Ratio

The quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Constant of variation

The ratio between two variables in a direct variation or the product of two variables in an inverse variation. In the direct variation equations = k and y = kx , and the inverse variation equations xy = k and y = , k is the constant of variation.

Solution set

The set of all the solutions of an equation or condition.

Varies directly as x

When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.

Capture - recapture method

a method commonly used in ecology to estimate size

Mathematical model

same as Mathematical modeling.