CH.4 Vocabulary

liketerms

"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.

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.

equation on 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 equation in one variable

A linear equation in one variable is an equation that can be written in the form ax+ b= c, where a, b, and c are real numbers and a=0 .Linear equations are also first-degree equations because the exponent on the variable is understood to be 1

mathematical modeling

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling.

variable

A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters $x$, $y$, and $z$ are common generic symbols used for variables.

The addition property of equality

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.

equation

An equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.

combined variation

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).

combine like terms

Combining like terms is a mathematical process used to simplify an expression or to add or subtract polynomials.

factors

Factors are numbers you can multiply together to get another number: Example: 2 and 3 are factors of 6, because 2 × 3 = 6. 3 and 4 are factors of 12, because 3 × 4 = 12. Also 2 × 6 = 12 so 2 and 6 are also factors of 12.

proportion

Proportion says that two ratios (or fractions) are equal.

root(s)

Square Root. more ... The square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4.

The multiplication property of equality

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal.

varies directly as x

To be more "mathematical" about it, if y varies directly as x, then the graph of ... The equation y/x = 6 states that y "varies directly as" x since the ratio of y to x (also written y:x) never changes. ... By definition, both ratios are equal: (24/16) = (y/12).

evaluating an algebraic expression

We have learned that, in in an algebraic expression, letters can stand for numbers. When we substitute a specific value for each variable, and then perform the operations, it's called evaluating the expression.

solution(s)

a means of solving a problem or dealing with a difficult situation.Result to problem

equivalent equation(s)

equations that have the same solution sets; in the case of multiple roots, the multiplicities of the respective roots must be equal.

varies inversely as x

if y varies inversely as x , and x = 5 when y = 2 , then the constant of variation is k = xy = 5(2) = 10 . Thus, the equation describing this inverse variation is xy = 10 or y = .

solution set

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

coefficient

A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. For example, 4 is the coefficient in the term 4x, and x is the coefficient in x(a + b). A numerical measure of a physical or chemical property that is constant for a system under specified conditions.

constant of variation

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.

solving an inequality

Graphing inequalities on either a number line or in the coordinate plane (with x and y axes) helps to visually represent several forms of inequalities: The graph of a linear inequality produces a region on the coordinate plane with a boundary line. Every point in that region is a solution of the inequality.

term(s)

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs.

constant

In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants. If it is not a constant it is called a variable.

ratio

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

algebraic expression

In mathematics, an algebraic expression is 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 equation

In mathematics, to solve 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).

satisfies the equation

We say that x=17 'satisfies' the equation. This process of finding the value of the unknowns is called "solving the equation". We often say that we "solve for x" ...

linear inequality in one variable

When you graph inequalities that have only one variable, we use a number line. We will use open and closed circles and arrows pointing to the left or right to graph our answers.

numerical term

When you look at a problem with numbers, you are most likely looking at a numerical expression. A numerical expression is a mathematical sentence involving only numbers and one or more operation symbols. Examples of operation symbols are the ones for addition (+), subtraction (-), multiplication (*) and division (/).

simplified

to make less complicated, clearer, or easier. to reduce (an equation, fraction, etc) to a simpler form by cancellation of common factors, regrouping of terms in the same variable, etc.