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The solution to a division problem, as long
as the denominator is non-zero. For example:
21 divided by 2 gives a quotient of 10½;
and 2xy divided by y
gives a quotient of 2x
quadratic function
A function in which the greatest power is 2. For example: f(x) = 3x2 + x 3 is a function in which the greatest power of any one term is 2.
A number that can be written as a fraction of two integers. For example: ½ or -½ Symbolically, a/b where b is not equal to zero..
rational numbers
The set of numbers that can be written as a ratio of two integers in the form a/b where b is not equal to zero. Symbolically For example: the numbers ½, 2/2 and -Ύ are rational numbers.
real numbers
Rational numbers together with the non-rational numbers form the set of real numbers. Symbolically, IR
reciprocal
Another name for a multiplicative inverse
replacement set
A specific set of numbers from which to choose values, one-at-a-time, to substitute for a variable in order to evaluate an expression, equation, or function. For example: When x = {-1, 0, 2} is used as a replacement set in the expression 2x + 1, after substituting each value, one-at-a-time, from the replacement set, the solution set would be {-1, 1, 5}.
root
One of none, one, or many possible solutions to an equation having a power greater than 1. For example, x22x + 1 is an equation of power 2 that factors to (x 1)(x 1) and has one real root, namely x = 1
Numbers expressed as the product of a number that is at least 1 but not greater than 10, and a power of 10. For example: 2,002,400 would be written 2.0024 x 106 ,and 0 .0524 would be written 5.24 x 10-4 in scientific notation. The exponent indicates the number of decimal places the decimal point was moved when converting the original number. If the exponent is negative, the decimal places were moved to the left during conversion. If the exponent is positive, the decimal places were moved to the right during conversion.
simplify
To rewrite an expression or equation so that all common or like terms are combined by addition or so that all common factors are cancelled by division. For example: the expression 2x 3x + 10 18 simplifies to x 8 , 14x/2 simplifies to 7x, and (x 1)/(x 1) simplifies to 1
solution(s)
All values for a variable that makes an equation true. For example: When substituting x = 3 in the equation 3x 4 = 5, the equation is true, so x = 3 is a solution to the equation. Likewise, when substituting x = 8 or x = -8 in the equation x2 = 64, the equation is true, so x = 8 and x = -8 are both solutions to the equation.
solve
Given an equation, find a solution or set of solutions for its variable. Or, given a formula, find a solution for one of its variables. (See solution(s) for examples.)
substitution
To substitute or replace one or more variables in an equation or formula, creating a numerical expression that can be evaluated.
sum
The solution to the addition of two or more numbers or terms. For example: 1 + 2 has the solution 3, and 24 16 + 8 has the solution 16
symbol
A special character used to replace an English word or words. For example: "is less than" can be abbreviated by replacing the words with the symbol <
system of equations
A common solution for two or more equations.
A number, a variable, or the product of numbers and variables.
A letter or symbol used as a placeholder to represent a number in expressions and equations. For example: x, y, z, P, b, and others can all be used as a variable.
variable term
A term in an expression or equation that contains a variable. For example: In the expression 3x + 10, the term 3x is a variable term.
The set of positive integers and zero. Written {0, 1, 2, 3, . . .}
The identity element for additive inverses. When added together additive
inverses equal zero. For example: 3 and 3
are additive inverses and their sum is 0
, and x and x are
additive inverses and their sum is 0
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