#### Study sets matching "algebra chapter 8 rational"

#### Study sets matching "algebra chapter 8 rational"

inverse variation

Combined Variation

Joint Variation

Reciprocal Function

Has the form xy=k, y+K/x, where k is not equal to 0.

When one quantity varies with respect to two or more quantiti…

When one quantitiy varies directy with two or more quantities.

Functions that model inverse variation have the form f(x)+ a/…

inverse variation

Has the form xy=k, y+K/x, where k is not equal to 0.

Combined Variation

When one quantity varies with respect to two or more quantiti…

Inverse Variation

Constant of Variation

Rational Function

Simplified Form of a Rational Expression

In an inverse variation, k is the constant of variation.

a rational expression in which the numerator and denominator…

Inverse Variation

Constant of Variation

In an inverse variation, k is the constant of variation.

Rational expression

Excluded value

Complex fraction

Rational equation

A ratio of two polynomials. The value of the variable cannot…

A value of x for which a rational expression f(x) is undefined.

A fraction that has a fraction in its numerator or denominato…

An equation containing rational expressions.

Rational expression

A ratio of two polynomials. The value of the variable cannot…

Excluded value

A value of x for which a rational expression f(x) is undefined.

factoring

term

quadratic

binomial

the process of changing a sum to a product

numbers, letters, or combinations of letters and numbers that…

an expression that can be written in the form ax(x) + bx + c,…

an expression with 2 terms

factoring

the process of changing a sum to a product

term

numbers, letters, or combinations of letters and numbers that…

asymptote

Distance Formula

major axis

ellipse

a line that a graph approaches but never crosses

the square root of the sum of the squares of the differences…

the longer of the two line segments that form the axes of sym…

the set of all points in a plane such that the sum of the dis…

asymptote

a line that a graph approaches but never crosses

Distance Formula

the square root of the sum of the squares of the differences…

inverse variation

constant of variation

joint variation

rational function

two variables x and y show this relationship when y=a/x, a do…

the nonzero constant a in a variation equation.the constant a…

variation that occurs when a quantity varies directly with th…

a rational function is a function of the form f(x)=p(x)/q(x).…

inverse variation

two variables x and y show this relationship when y=a/x, a do…

constant of variation

the nonzero constant a in a variation equation.the constant a…

inverse variation

constant of variation

joint variation

rational function

two variables x and y show this relationship when y=a/x, a do…

the nonzero constant a in a variation equation.the constant a…

variation that occurs when a quantity varies directly with th…

a rational function is a function of the form f(x)=p(x)/q(x).…

inverse variation

two variables x and y show this relationship when y=a/x, a do…

constant of variation

the nonzero constant a in a variation equation.the constant a…

difference of two squares

factoring by grouping

perfect square trinomial

prime polynomial

x² - 121

factoring technique often used if a polynomial... has 4 or more…

x² + 12x + 36

x² + 64

difference of two squares

x² - 121

factoring by grouping

factoring technique often used if a polynomial... has 4 or more…

Difference of two squares

Factoring

Factoring by grouping

FOIL method

two perfect squares separated by a subtraction sign. a² - b²…

to express a polynomial as the product of monomials and polyn…

the use of the Distributive Property to factor some polynomia…

to multiply two polynomials find the sum of the products of t…

Difference of two squares

two perfect squares separated by a subtraction sign. a² - b²…

Factoring

to express a polynomial as the product of monomials and polyn…

combined variation

complex fraction

constant of variation

direct variation

when one quantity varies with respect to two or more quantiti…

a rational expression whose numerator and/or denominator cont…

K= constant of variation. The rate.

a relationship in which one variable quantity increases as an…

combined variation

when one quantity varies with respect to two or more quantiti…

complex fraction

a rational expression whose numerator and/or denominator cont…

combined variation

complex fraction

continuous graph

discontinuous graph

a relation in which one variable varies with respect to each…

a rational expression that has a fraction in its numerator or…

a graph is continuous if it has no jumps, breaks, or holes

a graph is discontinuous if it has a jump, break, or hole

combined variation

a relation in which one variable varies with respect to each…

complex fraction

a rational expression that has a fraction in its numerator or…

Coefficient

Complex numbers

Conjugate

discriminate

variable(s) are multiplied by a number

Numbers written in the form a + bi where a and b are real num…

Every complex number a + bi has a conjugate, a − bi , and bot…

identifies the number of solutions to a quadratic equation

Coefficient

variable(s) are multiplied by a number

Complex numbers

Numbers written in the form a + bi where a and b are real num…

Additive inverses

Cube root

Integers

Irrational number

Two numbers whose sum is 0 are additive inverses.

A cube root of a number is a number that, when used as a fact…

Integers are the set of positive whole numbers, their opposit…

An irrational number is a number the cannot be written in the…

Additive inverses

Two numbers whose sum is 0 are additive inverses.

Cube root

A cube root of a number is a number that, when used as a fact…

binomial

degree of a monomial

degree of a polynomial

difference of two squares

a polynomial made of two monomials. [p. 487]

the sum of the exponents of its variables. [p. 486]

one variable is the same as the degree of the monomial with t…

a binomial that is created by multiplying two different binom…

binomial

a polynomial made of two monomials. [p. 487]

degree of a monomial

the sum of the exponents of its variables. [p. 486]

Inverse Variation

Constant of variation

Joint variation

Rational function

two variables related as follows, y = a/x

value that stays same in variation problems

variation occurs when a quantity varies directly with the pro…

form of f(x) = p(x)/q(x) where p and q are polynomials

Inverse Variation

two variables related as follows, y = a/x

Constant of variation

value that stays same in variation problems

System of linear equations

Eliminating a variable

System of linear inequalities

Maximum

Two or more linear equations with the same variables

Removing one variable in a system of equations

Tow or more linear inequalities with the same variables

Largest number in a group

System of linear equations

Two or more linear equations with the same variables

Eliminating a variable

Removing one variable in a system of equations

binomial

degree of a monomial

degree of a polynomial

difference of two squares

the sum of 2 monomials. [p. 503]

the sum of the exponents of the variables of a monomial. [p.…

the greatest degree of any term in the polynomial. [p. 503]

the difference of two perfect square monomials. [p. 547]

binomial

the sum of 2 monomials. [p. 503]

degree of a monomial

the sum of the exponents of the variables of a monomial. [p.…

combined variation

complex fraction

continuous graph

discontinuous graph

when one quantity varies with respect to two or more quantiti…

a rational expression whose numerator and/or denominator cont…

an unbroken graph made up of connected lines or curves. [p. 5…

a graph which has one or more jumps, gaps, or holes. [p. 516]

combined variation

when one quantity varies with respect to two or more quantiti…

complex fraction

a rational expression whose numerator and/or denominator cont…

Order of magnitude

Scientific Notation

Exponential function

Exponential growth

the power of 10 nearest the quantity

number written of the form c x 10n where 1 < c < 10

function of the form y = ab^x

function y = ab^x where a > 0 and b > 1

Order of magnitude

the power of 10 nearest the quantity

Scientific Notation

number written of the form c x 10n where 1 < c < 10

exponential function

exponential growth

exponential decay

growth factor

a function that can be described by an equation of the form y…

A quantity that is increasing by the same percent in each uni…

A quantity that is decreasing by the same percent in each uni…

the expression (1 + r) in the model y = C(1 + r)t

exponential function

a function that can be described by an equation of the form y…

exponential growth

A quantity that is increasing by the same percent in each uni…

common ratio

compound interest

decay factor

exponential decay

The fixed number added to each term of an arithmetic sequence

Interest paid on both the principal and the interest that has…

The base b in the exponential function y = ab^x, where 0<b<1

A situation modeled with a function of the form y = ab^x, whe…

common ratio

The fixed number added to each term of an arithmetic sequence

compound interest

Interest paid on both the principal and the interest that has…

equation

solution of an equation

inverse operations

subtraction property of equality

an algebraic or numerical sentence that shows that two quanti…

a value of a variable that makes an equation true

operations that undo each other; multiplication and division…

if you subtract the same number from both sides of an equatio…

equation

an algebraic or numerical sentence that shows that two quanti…

solution of an equation

a value of a variable that makes an equation true

Monomial

degree of a monomial

Polynomial

Standard form of a polynomial

A real number, a variable, or a product of a real number and…

The sum of the exponents of the variables of a monomial.

A monomial or the sum or difference of two or more monomials.…

The form of a polynomial that places the terms in descending…

Monomial

A real number, a variable, or a product of a real number and…

degree of a monomial

The sum of the exponents of the variables of a monomial.

Factoring by Grouping

Trinomial

Standard Form of a Polynomial

Polynomial

A method of factoring that uses the Distributive Property to…

A polynomial of three terms.

The form of a polynomial that places the terms in descending…

A monomial or the sum or difference of two or more monomials.

Factoring by Grouping

A method of factoring that uses the Distributive Property to…

Trinomial

A polynomial of three terms.

Factor

Common Factors

Greatest Common Factor (GCF)

Prime (number)

Whole numbers multiplied together forming a product.

Factors that are shared by 2 or more whole numbers.

The largest factor shared by two whole numbers.

A number is called "prime" if it's factors are ONLY "1" and "…

Factor

Whole numbers multiplied together forming a product.

Common Factors

Factors that are shared by 2 or more whole numbers.

Center (of a Circle)

Circle

Circumference

Composite Figure

The point inside a circle that is the same distance from all…

The set of all points in a plane that are the same distance f…

The distance around a circle.

A figure made up of triangles, squares, rectangles, semicircl…

Center (of a Circle)

The point inside a circle that is the same distance from all…

Circle

The set of all points in a plane that are the same distance f…

binomial

degree of a monomial

degree of a polynomial

difference of two squares

the sum of 2 monomials. [p. 503]

the sum of the exponents of the variables of a monomial. [p.…

the greatest degree of any term in the polynomial. [p. 503]

the difference of two perfect square monomials. [p. 547]

binomial

the sum of 2 monomials. [p. 503]

degree of a monomial

the sum of the exponents of the variables of a monomial. [p.…

Exponential function

Scientific notation

Exponential growth

Growth factor

A function of the form y= abx where x is a real number

A number expressed in the form c x 10 n,

A quantity that is increasing by the same percent in each uni…

The expression 1+ r in the exponential growth model where r i…

Exponential function

A function of the form y= abx where x is a real number

Scientific notation

A number expressed in the form c x 10 n,

binomial

constant

degree of a monomial

degree of a polynomial

the sum of 2 monomials

a monomial that is a real number

the sum of the exponents of all of its variables

the greatest degree of any term in the polynomial

binomial

the sum of 2 monomials

constant

a monomial that is a real number

zero as an exponent

negative exponent

scientific notation

multiplying powers with the same base

for any nonzero number, a to the zero power = 1

for every nonzero number a and integer n, a to the -n power =…

the product of two factors in the form a X 10 to the n power…

keep the base and add the exponents

zero as an exponent

for any nonzero number, a to the zero power = 1

negative exponent

for every nonzero number a and integer n, a to the -n power =…

Common Ratio

Compound Interest

Decay Factor

Exponential Decay

The fixed number used to find terms in a geometric sequence.

Interest paid on both the principal and the interest that has…

The base b in the exponential function y=ab^x, where 0 < b < 1

A situation modeled with the function of the form y = ab^x, w…

Common Ratio

The fixed number used to find terms in a geometric sequence.

Compound Interest

Interest paid on both the principal and the interest that has…

Common Ratio

Compound Interest

Decay Factor

Exponential Decay

The fixed number used to find terms in a geometric sequence.

Interest paid on both the principal and the interest that has…

The base b in the exponential function y=ab^x, where 0 < b < 1.

A situation modeled with a function of the form y=ab^x, where…

Common Ratio

The fixed number used to find terms in a geometric sequence.

Compound Interest

Interest paid on both the principal and the interest that has…

Scientific Notation

Geometric Sequence

Common Ratio

Exponential Function

A method of writing or displaying numbers in terms of a decim…

a sequence in which the ratio of successive terms is a consta…

The ratio of successive terms of a geometric sequence

a function of the form f(x) = ab^x, where a and b are real nu…

Scientific Notation

A method of writing or displaying numbers in terms of a decim…

Geometric Sequence

a sequence in which the ratio of successive terms is a consta…

difference of two squares

factored form

factoring

factoring by grouping

Two perfect squares separated by a subtraction sign.

A monomial expressed as a product of prime numbers and variab…

To express a polynomial as the product of monomials and polyn…

The use of the Distributive Property to factor some polynomia…

difference of two squares

Two perfect squares separated by a subtraction sign.

factored form

A monomial expressed as a product of prime numbers and variab…

Angle of rotation

Center of rotation

Dilation

Enlargement

The angle of rotation is the number of degrees that a figure…

The center of rotation is a fixed point about which a figure…

A dilation is a transformation where the original figure and…

A dilation with a scale factor greater than 1 is an enlargeme…

Angle of rotation

The angle of rotation is the number of degrees that a figure…

Center of rotation

The center of rotation is a fixed point about which a figure…

power

base

exponent

scientific notation

An expression where a base is raised by an exponent

The number or variable that is used as a factor in repeated m…

Tells how many times a number (the base) is multiplied by its…

The method of expressing a very large or very small number nu…

power

An expression where a base is raised by an exponent

base

The number or variable that is used as a factor in repeated m…

"Fractional equations" are equations w…

What is the first step in solving a fr…

The process called "clearing the fract…

In more complicated equations, multipl…

an X in the bottom.

getting the X out of the bottom of the fraction; then the ope…

eliminating a fraction from an equation by multiplying by the…

checking your answer by putting it back in the original equat…

"Fractional equations" are equations w…

an X in the bottom.

What is the first step in solving a fr…

getting the X out of the bottom of the fraction; then the ope…

inverse variation

combined variation

joint variation

reciprocal function

y=k/x

one variable varies with 2 or more other variables

one variable varies directly with 2 or more other variables

y= a/x-h + k

inverse variation

y=k/x

combined variation

one variable varies with 2 or more other variables

Rational expression

Simplest form

Scientific notation

Least common multiple

Any expression that can be written as the quotient of two pol…

Any fraction whose numerator and denominator are integers or…

A form of writing numbers that is provides an efficient way t…

...

Rational expression

Any expression that can be written as the quotient of two pol…

Simplest form

Any fraction whose numerator and denominator are integers or…

Binomial

Degree of a monomial

Degree of a polynomial

Monomial

a polynomial with two terms

the sum of the exponents of its variables

the degree of the monomial with the greatest exponent

a real number, a variable, or a product of a real number and…

Binomial

a polynomial with two terms

Degree of a monomial

the sum of the exponents of its variables

Mixture Equations

Distance Equation

Work Equation

Vertical Asymptote is found in

(% / 100) = (amount of ____ / total solution)

d=rt and [ .5d / constant rate - current (r) ] + [ .5d / cons…

[ # of total people / # of ____ built ] + [ # of other people…

the denominator

Mixture Equations

(% / 100) = (amount of ____ / total solution)

Distance Equation

d=rt and [ .5d / constant rate - current (r) ] + [ .5d / cons…

Completing the square

Cubic equation

Discriminant

Double root

is a method for solving any quadratic equation

a polynomial equation in which the highest sum of exponents o…

If discriminant (D) is equal to 0 then the equation has one r…

a root that appears twice in the solution of an algebraic equ…

Completing the square

is a method for solving any quadratic equation

Cubic equation

a polynomial equation in which the highest sum of exponents o…