The sum of 0 and any number is the same

For all real numbers a, b, and c, if a = b, climate a + c = b + c. If 2 expressions room equal to every other and also you add the exact same value come both sides of the equation, the equation will stay equal.

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additive identityThe number 0 is dubbed the additive identity because when you add it to a number, the result you get is the exact same number. Because that example, 4 + 0 = 4.additive inverseAny 2 numbers whose sum is zero, such as 3 and also -3, due to the fact that 3 + (-3) = 0.adjacent sideFor a provided acute angle in a right triangle, the nearby side to the angle is the next that, in addition to the hypotenuse, creates that acute angle.amplitudeThe distance in between the highest suggest and the rest place (zero position) in a wave.amplitudeHalf the difference between the maximum and the minimum worths of a routine function.angleA number formed by the joining of two rays v a typical endpoint.areaThe lot of an are inside a two-dimensional shape, measure in square units.arithmetic operationsThe to work of addition, subtraction, multiplication and division.associative home of additionFor three or more real numbers, the amount is the same regardless of exactly how you team the numbers. For example, (6 + 2) + 1 = 6 + (2 + 1). associative residential or commercial property of multiplication

For 3 or much more real numbers, the product is the exact same regardless of how you team the numbers. For example, (3 • 5) • 7 = 3 • (5 • 7).

asymptoteA line that a graph the a role will come nearby to, yet not cross or also touch.axisOne of 2 perpendicular currently of a coordinate location that crossing at the origin. The plural kind of axis is axes.bar graphA graph that supplies horizontal or upright bars to represent data.base

The expression the is being elevated to a power as soon as using exponential notation. In 53, 5 is the base, i m sorry is the number that is repetitively multiplied. 53 = 5 • 5 • 5. In ab, a is the base.

The expression that is being raised to a power when using exponential notation. In 53, 5 is the base, i m sorry is the number the is repeatedly multiplied. 53 = 5 • 5 • 5. In ab, a is the base.

boundary lineA line that divides the coordinate aircraft into 2 regions. If points along the boundary line are contained in the solution set, climate a solid heat is used; if points along the boundary line are not consisted of then a dotted line is used.box-and-whisker plotA graph that uses a number heat to show the distribution of a set of data.categorical dataData that details non-numerical features of an object. Instances of categorical data incorporate eye color, blood type, and types of computers.central angleAn angle whose vertex is at the facility of a circle.circle graphAlso referred to as a pie chart, a form of graph where categorical data is stood for as part of a entirety circle.circumference

The distance about a circle, calculation by the formula C =

d.

coefficientA number the multiplies a variable.cofunctionsTwo trigonometric functions, such together sine and also cosine, for which the value of the first function in ~ an acute angle equates to the worth of the second duty at the match of the angle.common logarithm
commutative residential or commercial property of additionTwo actual numbers deserve to be included in any type of order without transforming the sum. Because that example, 6 + 4 = 4 + 6.commutative residential or commercial property of multiplication

Two actual numbers deserve to be multiply in any type of order without changing the product. Because that example, 8 • 9 = 9 • 8.

completing the squareA method for solving quadratic equations by rewriting one side of the equation as a squared binomial.complex conjugate

Two complex numbers because that which the real parts are equal and the imaginary components are additive inverses. A + bi and also a – bi are complicated conjugates.

complex rational expressionA quotient of two rational expressions.compound eventAn occasion with much more than one outcome.compound inequality

A statement consisting of two inequality statements joined one of two people by words “or” or “and.” for example, 2x − 3 5 and also x + 14 > 11.

coneA solid number with a solitary circular base and also a round, smooth challenge that diminishes come a single point.congruentHaving the very same size and also shape.conjugate

One binomial in a conjugate pair. Given the binomial a + b, the conjugate is a – b; provided a – b, the conjugate is a + b.

A pair of binomials that, when multiplied, monitor the pattern:

The product the a pair of binomials that are conjugates is the difference of two squares.

consistent mechanism of linear equationsA device of straight equations that contends least one solution.constantA symbol that represents a quantity that cannot change. It have the right to be a number, letter or a symbol.constant that variation

Represented by the variable k in variation problems, the continuous of variation is a number that relates the input and the output.

A aircraft formed by the intersection the a horizontal number line called the x-axis and also a vertical number line referred to as the y-axis.

corresponding anglesAngles that separate numbers that room in the same position within each figure.corresponding sidesSides of separate numbers that are opposite matching angles.cosine

If A is an acute angle of a right triangle, then the cosine of angle A is the proportion of the size of the side nearby to angle A over the size of the hypotenuse.

coterminal anglesThe summary of 2 angles drawn in standard position that share your terminal side.counting numbersAlso referred to as natural numbers, the number 1, 2, 3, 4, ...cubeA six-sided polyhedron that has actually congruent squares as faces.cube root

The number which, as soon as multiplied together three times yields the original number. Because that example, the cube source of 64 is 4 due to the fact that 4 • 4 • 4 = 64.

cycleAny component of a graph that a periodic duty that is one period long.cylinderA solid figure with a pair the circular, parallel bases and a round, smooth face in between them.dataMathematical ax for info such as values or measurements.degreeThe worth of an exponent.degree the a monomial

The level of a monomial is the power to i beg your pardon the variable is raised. For example, the monomial 5y2 has actually a level of 2. If the monomial contains several variables then the degree of the monomial is the sum of the degree of all the variables. Because that example, the monomial 7x2y3 has a level of 5.

The greatest exponent or sum of exponents of a ax in a polynomial. For example, 7x2y3 + 3x2y − 8 is a fifth degree polynomial because the highest possible sum of exponents in a hatchet is 2 + 3 = 5.

dependent direct equationsEquations that graph as the same straight line.diameterThe length across a circle, passing v the center of the circle. A diameter is same to the length of two radii.direct variation

A kind of variation whereby the output varies directly with the input. Direct variation is represented by the formula y = kx.

In the Quadratic Formula, the expression underneath the radical symbol: b2 – 4ac. The discriminant have the right to be provided to recognize the number and form of services the formula will certainly reveal.

distributeTo rewrite the product that the number and a sum or difference using the distributive property.distributive residential or commercial property of multiplicationThe product of a amount (or a difference) and a number is the same as the amount (or difference) the the product of every addend (or each number gift subtracted) and the number. Because that example, 3(4 + 2) = 3(4) + 3(2), and 3(4 – 2) = 3(4) – 3(2).distributive building of multiplicationThe product of a amount (or a difference) and also a number is the same as the sum (or difference) the the product of each addend (or each number being subtracted) and also the number. For example, 3(4 + 2) = 3(4) + 3(2), and 3(4 – 2) = 3(4) – 3(2).distributive property of multiplication end additionThe product the a sum and a number is the same as the sum of the product of every addend and the number. Because that example, 3(4 + 2) = 3(4) + 3(2).divisor

The number the you are separating by in a division problem. In the problem

, 2 is the divisor.

domainThe collection of all feasible input worths for the variable in a function.domain that a function

The collection of all input worths or x-coordinates the the function.

eAn irrational number, around 2.718281828459; sometimes called Euler’s number.elimination methodA technique of solving a device of equations. Offered a system, the elimination an approach allows you to include the 2 equations in stimulate to eliminate a usual variable.equally likelyHaving the very same likelihood that occurring, such that in a huge number the trials, two equally likely outcomes would happen around the same variety of times.equationA mathematical declare that 2 expressions space equal. equilateral triangleA triangle v 3 equal sides. evaluateTo find the value of one expression.eventA collection of possible outcomes, frequently describable using a common characteristic, such together rolling an also number v a die or picking a map from a details suit.event spaceThe collection of feasible outcomes in one event: for example, the event “rolling an also number” top top a die has the event room of 2, 4, and 6.excluded valueA worth for the variable that is not contained in the domain because it would cause the function to be undefined.exponent

When a number is express in the type ab, b is the exponent. The exponent indicates how numerous times the basic is supplied as a factor. Power and exponent median the exact same thing.

When a number is to express in the type ab, b is the exponent. The exponent indicates how many times the basic is used as a factor. Power and also exponent average the exact same thing.

An exponential function of the form f(x) = bx, whereby b > 1, and b ≠ 1. The role increases as x increases.

A shorter way to write repeated multiplication. For example, 24 method 2 • 2 • 2 • 2. 2 is provided as a factor 4 times.

expressionA mathematical expression that have the right to contain a mix of numbers, variables, or operations. extraneous solutionA systems of the simplified form of one equation the does not satisfy the initial equation and also must be discarded.faceThe flat surface that a solid figure.factor

A number or mathematical symbol that is multiply by one more number or mathematical price to form a product. Because that example, in the equation 4 • 5 = 20, 4 and also 5 are factors.

An equation or one expression that states a rule for a relationship amongst quantities. For example, the formula because that finding the area of a rectangle can be stood for as A = together • w, or merely l • w.

If one occasion has p feasible outcomes, and another occasion has m feasible outcomes, then there room a total of p • m feasible outcomes because that the 2 events.

greatest common factorThe largest number (or expression) that is a variable of a collection of two or an ext numbers (or expressions).greatest common factor (GCF)

The product the the prime determinants that two or much more terms have actually in common. The greatest usual factor of xyz and 3xy is xy.

grouping symbolsSymbols such together parentheses, braces, brackets, and fraction bars that show the number to be group together.half-lifeThe quantity of time it takes a problem to diminish to half its original amount.histogramA graph utilizing bars come show constant quantitative data over a collection of similar-sized intervals. The elevation of the bar reflects the frequency of the data, and also the broad of the bar represents the interval because that the data.hypotenuseThe side opposite the best angle in any type of right triangle. The hypotenuse is the longest next of any type of right triangle.hypotenuseThe side opposite the ideal angle in any kind of right triangle. The hypotenuse is the longest side of any type of right triangle.identityAn equation that is true for any possible value the the variable.identity residential property of 0When you include 0 to any type of number, the amount is the very same as the initial number. Because that example, 55 + 0 = 55.identity residential property of 1When you multiply any kind of number by 1, the product is the very same as the original number. For example, 9(1) = 9. imaginary number

A number in the kind bi, wherein b is a actual number and also i is the square root of −1.

imaginary part

The imagine term, bi, in a facility number a + bi.

inconsistent device of straight equationsA mechanism of straight equations that has no solutions.independent direct equationsEquations that graph as various straight lines.index

The little positive creature just exterior and above the radical symbol that denotes the root. Because that example,

denotes the cube root.

A mathematical declare that mirrors the relationship in between two expressions where one expression deserve to be higher than or less than the various other expression. One inequality is written by using an inequality sign (>, , ≤, ≥, ≠).

integersThe number …, -3, -2, -1, 0, 1, 2, 3…inverse functionIf you take it a duty and turning back its inputs and also outputs, climate you gain its inverse function.inverse operationsA mathematical operation that can reverse or “undo” another operation. Enhancement and subtraction room inverse operations. Multiplication and division are station operations. inverse variation

A type of variation where the calculation varies inversely v the input. Train station variation is represented by the formula

.

irrational numbersNumbers that cannot be created as the ratio of 2 integers—the decimal depiction of one irrational number is nonrepeating and also nonterminating.isolate a variableA method for addressing an equation that involves rewriting an tantamount equation in i m sorry the variable is ~ above one next of the equation and also everything rather is on the various other side the the equation.isosceles trapezoidA trapezoid through one pair that parallel sides and also another pair of opposite political parties that space congruent.isosceles triangleA triangle with 2 equal sides.joint variation

A type of variation whereby the calculation varies jointly v multiple inputs. Joint variation is stood for by the formula y = kxz.

least typical denominatorThe the smallest number (or expression) that is a lot of of every the platform in a team of fountain (or reasonable expressions).least common multipleThe smallest number (or expression) the is a multiple of a set of two or much more numbers (or expressions).legIn a ideal triangle, one of the two sides creating a best angle.like terms

Terms that contain the exact same variables increased to the exact same powers. Because that example, 3x and −8x are prefer terms, as space 8xy2 and also 0.5xy2.

lineA heat is a one-dimensional figure, i beg your pardon extends without finish in 2 directions.line graphUsed to show continuous data, a graph wherein individual data points are associated with heat segments. Line graphs are commonly used for data sets that track a quantity over time.line of reflectionThe heat that cuts a parabola into two halves (which are mirror pictures of each other).line segmentA finite section of a heat between any type of two points the lie top top the line.linear equationAn equation in two variables who ordered pairs graph as a right line.linear inequality

A mathematical statement in 2 variables making use of the inequality icons , >, ≤, or ≥ to present the relationship between two expressions. As soon as the inequality prize is changed by an same sign, the resulting related equation will certainly graph as a directly line.

linear relationshipA direct relationship exists between two variables if, as soon as you plot their worths on a name: coordinates system, you obtain a directly line.logarithm

A calculation in i m sorry the exponent y in x = through is uncovered when offered x and also b; the equivalent notation is logbx = y.

A role using a logarithm, in the that the kind

. A calculate in i beg your pardon the exponent y in x = by is found when given x and b; the matching notation is logbx= y.

meanThe amount of all the data worths in a data collection divided by the number of items in the data set; additionally called the average.medianThe middle number or the average of the two center numbers of a set of ordered data.midrangeThe typical of the greatest and also least values of a data set.modeThe number that shows up most frequently in a data set.monomial
multi-step equationAn equation the requires more than one action to solve.multiplication building of equality

For all real numbers a, b, and also c, c ≠ 0: If a = b, then ac = bc. If 2 expressions are equal to each other and also you multiply both political parties of the equation by the exact same non-zero number, the equation will stay equal.

Two numbers are multiplicative inverses if your product is 1. Because that example,

.

natural numbersAlso called counting numbers, the number 1, 2, 3, 4, … negative numbersNumbers much less than 0.nonrepeating decimalsNumbers who decimal parts proceed without repeating—these space irrational numbers.nonterminating decimalsNumbers who decimal parts continue forever (without finishing in an unlimited sequence that zeros)—these decimals deserve to be reasonable (if they repeat) or irrational (if they space nonrepeating).obtuse angle

An edge measuring more than 90º and also less than 180º.

obtuse triangle

A triangle v one angle that measures in between 90º and 180º.

one-step equationAn equation that requires just one action to solve.oppositeAn the opposite of a number is the number with the the opposite sign, but same absolute value. Because that example, the opposite of 72 is -72. A number plus its opposite is constantly 0.opposite sideFor a provided acute edge in a appropriate triangle, the opposite side to the angle is the side the is not among the two sides that form that acute angle.order that operationsThe rule that identify the succession of calculations in one expression with more than one form of computation.ordered pairA pair of number that shows a suggest on a coordinate plane.origin
outcomeA result of a trial.parabolaA u-shaped graph which is produced by a quadratic function.parallel linesTwo or much more lines the lie in the same plane but which never ever intersect.parallel linesTwo or more lines that lie in the same airplane but which never ever intersect.parallelogramA quadrilateral through two bag of parallel sides.perfect cubeA number who cube source is one integer.perfect square

A trinomial the is the product of a binomial times itself, such together a2 + 2ab + b2 (from (a + b)2), and also a2 – 2ab + b2 (from (a – b)2).

A trinomial that is the product the a binomial time itself, such as a2 + 2ab + b2 (from (a + b)2), and a2 – 2ab + b2 (from (a – b)2).

perimeterThe distance around a two-dimensional shape.periodThe length of the smallest interval that includes exactly one copy the the repeating sample of a periodic function.periodic functionA duty whose graph has a pattern the repeats forever in both directions.perpendicular lines

The proportion of a circle’s circumference come its diameter. Pi is denoted by the Greek letter

. The is often approximated as 3.14 or.

pictographA graph that uses little icons or images to represent data.planeIn geometry, a two-dimensional surface ar that continues infinitely. Any three separation, personal, instance points the don"t lie on the very same line will certainly lie on precisely one plane.pointA zero-dimensional object that specifies a particular location top top a plane. The is stood for by a tiny dot.polygonA closed plane figure with 3 or more straight sides.polyhedronA hard whose deals with are polygons.polynomialA monomial or the sum or distinction of two or much more monomials.positive numberNumbers better than 0.power

In an exponent ab, the strength is stood for by b. The power suggests how countless times the basic is supplied as a factor. Power and also exponent average the exact same thing.

power dominance for exponents

To advanced a strength to a power, main point the exponents. (xa)b = xa•b

prime factorA element that only has actually itself and also 1 together factors.prime factorization

The procedure of breaking down a number (or expression) right into its element multiplicative factors. For example, the prime factorization the 12xy is 2 • 2 • 3 • x • y.

The procedure of breaking down a number (or expression) into its element multiplicative factors. Because that example, the prime factorization of 12xy is 2 • 2 • 3 • x • y.

prime numberA prime number is a herbal number with specifically two distinctive factors, 1 and itself. The number 1 is not a element number because it does not have actually two distinct factors.principalIn finance, the quantity of money ~ above which attention is calculated.principal root

The hopeful square root of a number, together in

. By definition, the radical price always method to find the primary root. Note that zero has only one square root, chin (since 0 • 0 = 0).

Principle that Zero Products

If abdominal muscle = 0, then either a = 0 or b = 0, or both a and b are 0.

probabilityA measure of exactly how likely that is the something will certainly occur.product elevated to a strength rule

The product of 2 or more non-zero numbers increased to a power amounts to the product of every number elevated to the exact same power: (ab)x = ax • bx

The product of 2 or much more non-zero numbers increased to a power equals the product of each number increased to the exact same power: (ab)x = ax • bx

pyramidA polyhedron through a polygonal base and also a repertoire of triangular deals with that satisfy at a point.PythagorasA Greek philosopher and also mathematician who resided in the sixth Century B.C.Pythagorean Theorem

The formula the relates the lengths the the political parties of any right triangle:

, whereby c is the hypotenuse, and a and b room the foot of the right triangle.

The x- and also y-axes division the coordinate airplane into four regions. These areas are dubbed quadrants.

An equation that have the right to be created in the type ax2 + bx + c = 0, wherein x is a variable, and a, b and also c room constants with a ≠ 0.

quadrilateralA four-sided polygon.quantitative dataNumerical data. Instances of quantitative data include height, weight, and test scores.quartileThe name of 4 minutes 1 sections of an ordered set of data.quotient

The result of a department problem. In the problem

, 4 is the quotient.

For any kind of real numbers a and b (b ≠ 0) and any optimistic integer x:

For any type of real numbers a and b (b ≠ 0) and any optimistic integer x:

For any non-zero number x and any integers a and b:

radian measureA measure of a central angle provided by the proportion of the arc size to the radius.radical equationAn equation that includes a radical expression.radical expressionAn expression that consists of a radical.radical symbol

The symbol,

, provided to signify the procedure of taking a source of a quantity.

radicandThe number or value under the radical symbol.radiusThe distance from the facility of a circle to any allude on the circle.rangeThe collection of all possible outputs in a function. Also the difference between the best value the a data collection and the the very least value.rangeThe collection of all feasible outputs in a function. Additionally the difference in between the best value the a data collection and the the very least value.range the a function
rational equationAn equation that has one or much more rational expressions.rational exponentAn exponent the is a fraction.rational expressionA fraction that has a polynomial as the numerator, denominator, or both.rational formulaA formula expressed together a rational equation.rational numbersNumbers that can be composed as the ratio of two integers, wherein the denominator is not zero. rationalizing a denominatorThe procedure by which a fraction containing radicals in the denominator is rewritten to have actually only rational numbers in the denominator.rayA half-line that begins at one point and goes on forever in one direction. real numbersAll rational or irrational numbers.real part

A number that when multiplied through a provided number provides a product of 1. For example,

 and  are reciprocals of each other.

rectangleA quadrilateral with two bag of parallel sides and also four best angles.rectangular prismA polyhedron that has three pairs of congruent, rectangular, parallel faces.reference angle

The angle formed by the terminal next of an edge in standard position and also the x-axis, whose measure is in between 0° and 90°.

A mirror-image that a graph. If the enjoy is end the x-axis, then the part of the initial graph the was listed below the x-axis will be above the x-axis, and also vice versa.

relationA correspondence between sets of worths or information.repeating decimalsNumbers who decimal parts repeat a sample of one or an ext digits—these space all rational numbers.rhombusA square with four congruent sides.right angle
right triangleA triangle containing a ideal angle.riseThe vertical readjust between two points ~ above a line.runThe horizontal adjust between two points top top a line.sample spaceThe set of all feasible outcomes.scalene triangleA triangle in which all three sides space a various length.scientific notation

A optimistic number is created in scientific notation if the is created as a x 10n where the coefficient a has a value such the 1 ≤ a 10 and n is one integer.

setA collection or team of things such as numbers.similarHaving the same shape yet not have to the very same size.simple eventAn event with just one outcome.sine

If A is one acute angle of a right triangle, climate the sine of angle A is the proportion of the length of the next opposite angle A over the length of the hypotenuse.

slope

The ratio of the vertical change to the horizontal change of 2 points ~ above a line.

slope-intercept form

A straight equation composed in the kind y = mx + b, where m to represent the steep of the line, and also b represents the y-value of the y-intercept, (0, b).

sphereA solid, round figure where every point on the surface is the same distance indigenous the center.squareA quadrilateral whose sides space all congruent and which has four right angles.square root

A number that when multiplied through itself provides the initial nonnegative number. Because that example, 6 • 6 = 36 and −6 • −6 = 36 so 6 is the optimistic square of 36 and −6 is the an unfavorable square root of 36.

square source property

If x2 = a2, climate x = a or x = −a.

standard position

The location of an angle upon a collection of name: coordinates axes with its vertex in ~ the origin, its initial side inserted along the confident x-axis, and also a directional arrowhead pointing to the angle’s terminal side.

stem-and-leaf plotA kind of graph supplied to visualize quantitative data. In a stem-and-leaf plot the digits of each number are organized separately to screen a collection of data.straight angle
substituteThe replacement of a variable with a number.substitution methodA an approach of addressing a mechanism of equations. Provided a system, the substitution technique allows girlfriend to create a simpler, one-variable equation through substituting one quantity in because that an equivalent quantity.supplementary angles

Two angles whose measurements include up to 180º.

symmetric about the y-axis

The left and right halves of the graph space mirror photos of each other over the y-axis.

system of linear equationsTwo or more linear equations v the same variables.system of linear inequalitiesTwo or more linear inequalities with the same variables. tangent

If A is one acute edge of a right triangle, then the tangent of angle A is the ratio of the size of the next opposite angle A over the size of the side surrounding to A.

A number or product of a number and variables elevated to powers. 4x, −5y2, 6, and also x3y4 room all instances of terms.

terminal sideThe beam that has actually been rotated roughly the origin to kind an angle through the stationary ray that is the initial next of the angle.terminating decimalsNumbers who decimal components do not continue indefinitely yet end eventually—these are all rational numbers.trapezoidA quadrilateral through one pair that parallel sides.tree diagramA chart that mirrors the choices or random outcomes native multiple trials, using branches because that each brand-new outcomes.trialA random activity or series of actions.triangleA polygon with three sides.trigonometric functionsA role of an edge expressed as the ratio of two of the sides of a ideal triangle that has that angle; the sine, cosine, tangent, cotangent, secant, cosecant.trinomial
unit circleA circle focused at the beginning that has radius 1.variableA letter or symbol provided to stand for a amount that deserve to change. vertexA turning point in a graph. Additionally the endpoint the the 2 rays that kind an angle.vertexA transforming point in a graph. Additionally the endpoint that the two rays that form an angle.volumeA measure up of just how much the takes to fill up a three-dimensional figure. Volume is measured in cubic units.whole numberThe number 0, 1, 2, 3, …., or all organic numbers add to 0.x-axisThe horizontal axis that a coordinate plane. Also the horizontal axis the a bar graph or histogram.x-axisThe horizontal axis the a coordinate plane. Likewise the horizontal axis of a bar graph or histogram.x-coordinateThe first number in an bespeak pair, which speak the street to the best or left native the origin once graphing in a coordinate plane. x-intercept
y-axisThe vertical axis of a coordinate plane. Likewise the upright axis the a bar graph or histogram.y-axisThe vertical axis of a name: coordinates plane. Additionally the vertical axis that a bar graph or histogram.

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y-coordinateThe 2nd number in an notified pair, which tells the distance to move up or under from the origin once graphing in a coordinate plane.y-intercept