Glossary. Also available at BigIdeasMath.com: multilanguage glossary vocabulary flash cards. An equation that contains an absolute value expression


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1 Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important concepts. Also available at BigIdeasMath.com: multilanguage glossar vocabular flash cards absolute value The distance between a number and 0 on a number line; The absolute value of a number a is written as a absolute value equation An equation that contains an absolute value epression absolute value function A function that has a Vshaped graph that opens up or down; The most basic absolute value function is f. f() absolute value inequalit An inequalit that contains an absolute value epression < Addition Propert of Equalit Adding the same number to each side of an equation produces an equivalent equation. If a b, then a + c b + c Addition Propert of Inequalit If ou add the same number to each side of an inequalit, the inequalit remains true. a < b, then a + c < b + c. This propert is also true for >,, and. > > 7 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 9
2 Addition Propert of Zero The sum of an number and 0 is that number a + 0 a arithmetic sequence A sequence in which the difference between consecutive terms is the same; This difference is called the common difference., 5, 7, 9, Terms of an arithmetic sequence Common difference Associative Propert of Addition Changing the grouping of addends does not change the sum. Associative Propert of Multiplication Changing the grouping of factors does not change the product. ( + ) ( + 5) ( a + b) + c a + ( b + c) ( ) 5 ( 5) ( a b) c a ( b c) asmptote A line that a graph approaches, but never intersects 5 + ais of smmetr The vertical line that divides a parabola into two smmetric parts decreasing increasing Ais of smmetr Verte base (of a power) The base of a power is the common factor. binomial A polnomial with two terms See power Big Ideas Math Algebra Copright Big Ideas Learning, LLC
3 boandwhisker plot Displas a data set along a number line using medians; Quartiles divide the data set into four equal parts. The median (second quartile) divides the data set into two halves. The median of the lower half is the first quartile. The median of the upper half is the third quartile. least value first quartile whisker bo median third quartile whisker greatest value causation When a change in one variable results in a change in another variable; This produces a strong correlation between the two variables. time spent eercising and the number of calories burned See fivenumber summar. closed A set of numbers is closed under an operation when the operation performed on an two numbers in the set results in a number that is also in the set. The set of integers is closed under addition, subtraction, and multiplication; but not under division. coefficient The numerical factor of a term that contains a variable In the algebraic epression 5 +, 5 is the coefficient of the term 5. common difference The difference between consecutive terms of an arithmetic sequence common ratio The ratio between consecutive terms of a geometric sequence See arithmetic sequence. See geometric sequence. Commutative Propert of Addition Changing the order of addends does not change the sum. Commutative Propert of Multiplication Changing the order of factors does not change the product a + b b + a 8 8 a b b a Copright Big Ideas Learning, LLC Big Ideas Math Algebra 5
4 completing the square A method for solving quadratic equations; In this method, a constant c is added to the epression + b so that + b + c is a perfect square trinomial b b b compound inequalit An inequalit formed b joining two inequalities with the word and or the word or. and < 5 or > < < 7 compound interest Interest earned on the principal and on previousl earned interest conjugates Used to simplif radical epressions that involve a sum or difference of radicals in the denominator The balance of an account earning compound nt r interest is P +, where P is the n principal (initial amount), r is the annual interest rate (in decimal form), t is the time (in ears), and n is the number of times interest is compounded per ear. constant term A term without a variable In the epression + 8, the term 8 is a constant term. a b + c d and a b c d are conjugates. continuous domain A set of input values that consists of all numbers in an interval All numbers from to coordinate plane A coordinate plane is formed b the intersection of a horizontal number line, usuall called the ais, and a vertical number line, usuall called the ais. The horizontal number line is usuall called the ais. Quadrant II 5 5 O Quadrant III 5 Quadrant I The vertical number line is usuall called the ais. 5 The origin is at (0, 0). Quadrant IV correlation The relationship between paired data; The paired data have a positive correlation if tends to increase as increases, a negative correlation if tends to decrease as increases, and no correlation if and have no apparent relationship. Positive relationship O Negative relationship No relationship O O 5 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
5 correlation coefficient When a calculator uses linear regression to find a line of best fit, it often gives a value r called the correlation coefficient. This value tells whether the correlation is positive or negative, and how closel the equation models the data. Values of r range from to. Cross Products Propert The cross products of a proportion are equal. 6 6 r r 0 r Strong negative correlation No correlation Strong positive correlation data Information, often given in the form of numbers or facts degree of a monomial The sum of the eponents of the variables in a monomial; The degree of a nonzero constant term is 0. The degree of 5 is 0. The degree of is. The degree of is +. degree of a polnomial The greatest degree of the terms of a polnomial denominator The number below the fraction bar in a fraction The degree of 6 + is. 5 The degree of + 8 is 5. In the fraction, 5 the denominator is 5. dependent variable The variable that represents output values of a function direct variation Two quantities and show direct variation when k, where k is a nonzero constant. In the function, is the dependent variable. k, k > 0 k, k < 0 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 5
6 discrete domain A set of input values that consists of onl certain numbers in an interval Integers from to discriminant The epression b ac of the associated equation a + b + c 0; The epression under the radical sign, b ac, in the quadratic formula; Used to determine the number of real solutions of a quadratic equation The value of the discriminant of the equation 7 0 is b ac distance formula The distance d between an two, and points ( ) (, ) is given b the formula. d + (, ) d (, ) (, ) Distributive Propert To multipl a sum or difference b a number, multipl each number in the sum or difference b the number outside the parentheses. Then evaluate. ( + 9) + 9 ab ( + c) ab+ ac ( 9) 9 ab ( c) ab ac Division Propert of Equalit Dividing each side of an equation b the same number produces an equivalent equation. If a b, then a c b c, c Division Propert of Inequalit (Case ) If ou divide each side of an inequalit b the same negative number, the direction of the inequalit smbol must be reversed for the inequalit to remain true. If a < b and c < 0, then c >. c This propert is also true for >,, and. 5 > < 5 5 < 6 a b Division Propert of Inequalit (Case ) If ou divide each side of an inequalit b the same positive number, the inequalit remains true. a b a < b and c > 0, then <. This propert is also true for >,, and. domain c c > > > The set of all input values of a function For the ordered pairs ( 0, 6 ), (, 7 ), (, 8 ), and (, 9 ), the domain is 0,,, and. 5 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
7 equation A mathematical sentence that uses an equal sign to show that two epressions are equal 6 a + 7 equivalent equations Equations that have the same solution(s) 8 0 and 8 ecluded value A number that makes a rational function or a rational epression undefined. A number that makes the denominator equal to 0 The ecluded value of is eponent The number or variable that represents the number of times the base of a power is used as a factor See power. eponential deca When a quantit decreases b the same factor over equal intervals of time See eponential deca function. eponential deca function A function of the form a( r) a > 0 and 0 < r < See eponential deca., where t t t eponential function A function of the form ab, where a 0, b, and b > 0 eponential growth When a quantit increases b the same factor over equal intervals of time () See eponential growth function. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 55
8 eponential growth function t A function of the form a( r) a > 0 and r > 0 See eponential growth. +, where t t epression A mathematical phrase containing numbers, operations, and/or variables + 6, 8 +, 8 +, 6 a b etraneous solution A solution of a transformed equation that is not a solution of the original equation factor An integer or epression that divides an integer or epression without leaving a remainder When ou square each side of +, the resulting equation has two solutions, and. However, is an etraneous solution because it does not satisf the original equation.,, and are factors of. ( ) and ( ) + are factors of. factored completel A factorable polnomial with integer coefficients is said to be factored completel when no more factors can be found and it is written as the product of prime factors ( ) factored form A polnomial is in factored form when it is written as a product of factors factoring b grouping To factor polnomials with four terms, group the terms into pairs, factor the GCF out of each pair of terms, and look for a common binomial factor ( )( ) + + fivenumber summar The five numbers that make up a boandwhisker plot (least value, first quartile, median, third quartile, and greatest value) See boandwhisker plot. 56 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
9 focus A fied point on the interior of a parabola that lies on the ais of smmetr; A parabola wraps around the focus. For functions of the form a, the focus is 0,. a function A relationship that pairs each input with eactl one output The ordered pairs ( 0, ), (, ), (, ), and (, 6 ) represent a function. Ordered Pairs ( 0, ) (, ) (, ), 6 Input 0 Output 6 geometric sequence A sequence in which the ratio between consecutive terms is the same; This ratio is called the common ratio.,, 6, 6, Terms of a geometric sequence Common ratio FOIL Method A shortcut for multipling two binomials; To multipl two binomials using the FOIL Method, find the sum of the products of the First terms, Outer terms, Inner terms, and Last terms. ( )( ) ( ) ( ) ( )( ) F + + O + + I + + L + + function notation A wa to name a function using f instead of ; The notation f is read as the value of f at or f of. 5 + can be written in function notation as f + 5. graph of an inequalit A graph that shows all of the solutions of an inequalit on a number line > 0 graph of a linear inequalit A graph in two variables that shows all of the solutions of an inequalit in a coordinate plane The graph of is the shaded halfplane. O graph of a sstem of linear inequalities A graph of all the solutions of a sstem 6 5 < + 5 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 57
10 greatest common factor (GCF) The largest of the common factors of two or more nonzero integers or epressions halfplanes In a coordinate plane, the regions on either side of a boundar line The common factors of and 0 are,, and. So the GCF of and 0 is. See graph of a linear inequalit. The common factors of and 6 are,,,, and. So the GCF of and 6 is. hpotenuse The side of a right triangle that is opposite the right angle independent variable The variable that represents input values of a function leg hpotenuse In the function 5 8, is the independent variable. leg inequalit A mathematical sentence that compares epressions; It contains the smbols <, >,, or. input A number on which a function operates < See function. integers The set of whole numbers and their opposites interest Mone paid or earned for the use of mone,,, 0,,,, See compound interest and simple interest. 58 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
11 interquartile range The difference of the third quartile of a data set and the first quartile of the data set; It represents the range of the middle half of the data. The interquartile range of the data set is 8. first quartile third quartile 5, 8,, 8, 5,, 55 inverse function When a relation and its inverse are functions, the are called inverse functions. The inverse of a function f is written as f. To find the inverse of a function represented b an equation, switch and and then solve for. 5 f 5 and f + are inverse functions. inverse relation Switches the input and output values of a relation; If a relation contains (a, b), then the inverse relation contains (b, a). inverse variation Two quantities and show inverse variation k when, where k is a nonzero constant. k k, k > 0, k < 0 irrational number A number that cannot be written as the ratio of two integers joint frequenc Each entr in a twowa table π, least common denominator (LCD) of rational epressions The least common multiple of the denominators of two or more rational epressions 5 The least common denominator of and 0 is the least common multiple of 0 and, or 60. legs The two sides of a right triangle that form the right angle See hpotenuse. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 59
12 line of best fit A precise line that best models a set of data See linear regression. line of fit A line drawn on a scatter plot that is close to most of the data points; It can be used to estimate data on a graph. Stud Time and Test Scores Test scores Stud time (minutes) linear equation An equation whose graph is a line O linear function A function whose graph is a nonvertical line; A linear function can be written in the form m + b. linear inequalit in two variables An inequalit that is the result of replacing the equal sign in a linear equation with <,, >, or. linear regression The process used to find the line of best fit for a set of data < 8 slope intercept correlation coefficient literal equation An equation that has two or more variables + 6 marginal frequencies The sums of the rows and columns in a twowa table 60 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
13 maimum value The coordinate of the verte of the graph of a + b + c when a < 0 mean The sum of the values in a data set divided b the number of data values maimum The mean of the values 7,, 8, and 9 is measure of central tendenc A measure that represents the center of a data set measure of dispersion A measure that describes the spread of a data set The mean, median, and mode are all measures of central tendenc. The range and standard deviation are measures of dispersion. median For a data set with an odd number of ordered values, the median is the middle data value. For a data set with an even number of ordered values, the median is the mean of the two middle values. minimum value The coordinate of the verte of the graph of a + b + c when a > 0 The median of the data set, 5, 9,, 8 is 9 because 9 is the middle value. minimum mode The data value or values that occur most often; Data can have one mode, more than one mode, or no mode. monomial A number, a variable, or a product of a number and one or more variables with whole number eponents The modes of the data set,,, 7, 7, 9, are and 7 because the occur most often Copright Big Ideas Learning, LLC Big Ideas Math Algebra 6
14 Multiplication Properties of Zero and One The product of an number and 0 is 0. The product of an number and is that number a a a Multiplication Propert of Equalit Multipling each side of an equation b the same number produces an equivalent equation. If a b, then a c b c. 8 8 Multiplication Propert of Inequalit (Case ) If ou multipl each side of an inequalit b the same positive number, the inequalit remains true. If a < b and c > 0, then a c < b c. This propert is also true for >,, or. < 9 < 9 < 8 Multiplication Propert of Inequalit (Case ) If ou multipl each side of an inequalit b the same negative number, the direction of the inequalit smbol must be reversed for the inequalit to remain true. If a < band c < 0, then a c > b c. This propert is also true for >,, or. < 6 6 > 6 6 > 8 negative eponent For an integer n and an nonzero number a, a n is the reciprocal of a. a n n a n negative number A number less than 0 0.5, 0, 500 nonlinear function A function that does not have a constant rate of change; The graph of a nonlinear function is not a line. nth root n When b a for an integer n greater than, b is an nth root of a. 6 n a n th root of a 6 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
15 number line A line whose points are associated with numbers that increase from left to right numerator The number above the fraction bar in a fraction In the fraction, 5 the numerator is. 0 ordered pair A pair of numbers (, ) used to locate a point in a coordinate plane; The first number is the coordinate, and the second number is the coordinate. (, ) origin The point, represented b the ordered pair ( 0, 0, ) where the ais and the ais meet in a coordinate plane See coordinate plane. O The coordinate of the point (, ) is, and the coordinate is. output A number produced b evaluating a function using a given input See function. parabola The Ushaped graph of a quadratic function perfect square A number with integers as its square roots 6, 5, 8 perfect square trinomial Trinomials of the form a + ab + b and a ab + b. () () Copright Big Ideas Learning, LLC Big Ideas Math Algebra 6
16 perpendicular lines Two lines in the same plane that intersect to form right angles; Two nonvertical lines are perpendicular if and onl if the product of their slopes is. + piecewise function A function defined b two or more equations, if 0 +, if > 0 +, > 0, 0 plane A flat surface that etends without end in all directions pointslope form A linear equation written in the form m The line passes through ; the point (, ) and the slope of the line is m. + 6 ( ) polnomial A monomial or a sum of monomials; Each monomial is called a term of the polnomial positive number A number greater than 0 0.5,, 00 power A product of repeated factors Power of a Power Propert To find a power of a power, multipl the eponents. base 5 eponent Power is used as a factor 5 times. 8 m ( a ) n a mn 6 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
17 Power of a Product Propert To find a power of a product, find the power of each factor and multipl. ( ab) m m m a b Power of a Quotient Propert To find a power of a quotient, find the power of the numerator and the power of the denominator and divide m m a a m b b prime number A whole number greater than whose onl factors are and itself prime polnomial A polnomial that cannot be factored as a product of polnomials with integer coefficients,, 5, 7,,, 7, 9,, 9,, principal An amount of mone borrowed or deposited You deposit $00 in an account that earns % compound interest per ear. The principal is $00. product The result when two or more numbers or epressions are multiplied The product of and is ( ), or. The product of + and 5 is + 5, or 0. Product of Powers Propert To multipl powers with the same base, add their eponents. Product Propert of Square Roots The square root of a product equals the product of the square roots of the factors a a a m n m+ n, where 0 and 0 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 65
18 Pthagorean Theorem In an right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hpotenuse. a + b c cm 5 cm quadratic equation A nonlinear equation that can be written in the standard form a + b + c 0, where a cm 5 + quadratic formula The formula below that can be used to find the real solutions of the quadratic equation a + b + c, where a 0 and b ac 0: b ± b ac a To solve + 7 0, substitute for a, for b, and 7 for c in the quadratic formula. ± 7 or 7 quartile Divides a data set into four equal parts See boandwhisker plot. quadratic function A nonlinear function that can be written in the standard form a + b + c, where a 0 quotient The result of a division The quotient of 0 and 5 is 0 ( 5 ), or. Quotient of Powers Propert To divide powers with the same base, subtract their eponents. Quotient Propert of Square Roots The square root of a quotient equals the quotient of the square roots of the numerator and denominator a a m n m n a, where a , where 0 and > 0 66 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
19 radical sign The smbol square root which is used to represent a ± 00 ± 0 radicand The number or epression under a radical sign The radicand of 5 is 5. The radicand of + is +. range The set of all output values of a function For the ordered pairs ( 0, 6 ), (, 7 ), (, 8 ), and (, 9 ), the range is 6, 7, 8, and 9. range (of a data set) The difference between the greatest value and the least value of a data set; The range describes how spread out the data are. The range of the data set, 6, 8,, 7, 5 is 5. rate A ratio of two quantities with different units You read books ever weeks. ratio A comparison of two quantities using division; The ratio of a to b ( where b 0) can be written a as a to b, a : b, or. b to, :, or rational equation An equation that contains one or more rational epressions rational eponents The nth root of a positive number a can be written as a power with base a and an eponent of /n. 5 + n 8 8 a a n Copright Big Ideas Learning, LLC Big Ideas Math Algebra 67
20 rational epression An epression that can be written as a fraction whose numerator and denominator are polnomials + rational function A function of the form polnomial, where polnomial the denominator does not equal 0; The most basic rational function is + 6. rational number a A number that can be written as, b a and b are integers and b 0, , where rationalizing the denominator The process of eliminating a radical from the denominator of an epression b multipling the epression b an appropriate form of real numbers The set of all rational and irrational numbers, 6.5, π, recursive rule Gives the beginning term(s) of a sequence and an equation that indicates how an term a n in the sequence relates to the previous term a a + d where d is the common difference n n, a, an an + an r an, where r is the common ratio a, a a n n relation Pairs inputs with outputs; A relation that pairs each input with eactl one output is a function. Input 9 5 Output residual The difference between the value of a data point and the corresponding value found using the line of fit; A residual can be positive, negative, or zero. positive residual data point line of fit negative residual data point 68 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
21 right angle An angle whose measure is 90 right triangle A triangle that has one right angle rise The change in between two points on a line See slope. roots The solutions of a polnomial equation The roots of the equation ( )( ) 9 and are run The change in between two points on a line See slope. scatter plot A graph that shows the relationship between two data sets using ordered pairs in a coordinate plane Stud Time and Test Scores Test scores Stud time (minutes) sequence An ordered list of numbers simple interest Mone paid or earned onl on the principal 5, 0, 5, 0,, a,,, 8, 6,, a, n n Simple interest Principal I Prt Annual interest rate (in decimal form) Time (in ears) You put $00 into an account. The account earns 5% simple interest per ear. The interest earned after ears is $ , or $0. The account balance is $00 + $0 $0 after ears. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 69
22 simplest form of a radical epression A radical epression that has no perfect square factors other than in the radicand, no fractions in the radicand, and no radicals appearing in the denominator of a fraction simplest form of a rational epression A rational epression whose numerator and denominator have no common factors ecept The simplest form of is slope A ratio of the change in (the rise) to the change, and in (the run) between an two points, ( ) (, ) on a line; It is a measure of the steepness of a line. rise change in slope run change in solution of an equation A value that makes an equation true (, ) (, ) Rise Run O slopeintercept form A linear equation written in the form m + b; The slope of the line is m and the intercept of the line is b. The slope is and the intercept is. (, 5) 5 (, ) + (, ) (0, ) solution of an inequalit A value that makes an inequalit true 6 is the solution of the equation. A solution of the inequalit + > 9 is. solution of a linear equation An ordered pair (, ) that makes a linear equation true; All of the points on the line are solutions. (, ) is a solution of + 6 solution of a linear inequalit An ordered pair (, ) that makes a linear inequalit true; All of the points in the shaded halfplane are solutions., is a solution of + >. See graph of a linear inequalit. 70 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
23 solution set The set of all solutions of an inequalit solution of a sstem of linear equations An ordered pair that is a solution of each equation in a sstem (, ) is the solution of the following sstem of linear equations solution of a sstem of linear inequalities An ordered pair that is a solution of each inequalit in a sstem (, 5) is a solution of the following sstem of linear inequalities. < 9 square root If b a, then b is a square root of a. The radical sign,, represents a nonnegative square root. The square roots of 5 are 5 and 5 because 5 5 and 5 5. So, 5 5 and 5 5. square root equation An equation that contains a square root with a variable in the radicand square root function A function that contains a square root with the independent variable in the radicand; The most basic square root function is standard deviation A measure of how much a tpical value in a data set differs from the mean; It is given b standard deviation ( ) + ( ) + + ( ) n n where n is the number of values in the data set. The smbol represents the mean. It is read as bar. standard form A linear equation written in the form a + b c, where a and b are not both zero + 6 Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
24 step function A piecewise function defined b constant values over its domain f 50, if 0 < 75, if < 00, if < 5, if < 50, if < 5 Subtraction Propert of Equalit Subtracting the same number from each side of an equation produces an equivalent equation. If a b, then a c b c Subtraction Propert of Inequalit If ou subtract the same number from each side of an inequalit, the inequalit remains true. If a < b, then a c < b c. This propert is also true for >,, and. + 7 > > 7 sstem of linear equations A set of two or more linear equations in the same variables; also called a linear sstem + Equation 7 Equation sstem of linear inequalities A set of two or more linear inequalities in the same variables term (of a sequence) Each number in a sequence; Each term a n has a specific position n in the sequence. < + Inequalit Inequalit 5, 0, 5, 0, 5,, a, st position rd position nth position n terms (of an epression) The parts of an epression that are added together theorem A rule in mathematics The terms of + are,, and. The Pthagorean Theorem 7 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
25 trinomial A polnomial with three terms twowa table Displas two categories of data collected from the same source variable A smbol, usuall a letter, that represents one or more numbers is a variable in +. verte (of a parabola) The lowest or highest point on a parabola Function is decreasing Function is increasing. Ais of smmetr: Verte: (, ) verte form A quadratic function of the ( h) + k, where a 0; The verte of the parabola is ( h, k ). Vertical Line Test A graph represents a function when no vertical line passes through more than one point on the graph. Function Not a function ( ) ( ) + + whole numbers The numbers 0,,,,, ais The horizontal number line in a coordinate plane See coordinate plane. Copright Big Ideas Learning, LLC Big Ideas Math Algebra 7
26 coordinate The first coordinate in an ordered pair, which indicates how man units to move to the left or right from the origin In the ordered pair (, 5 ), the coordinate is. intercept The coordinate of the point where a line crosses the ais (0, b) intercept b intercept a O (a, 0) ais The vertical number line in a coordinate plane See coordinate plane. coordinate The second coordinate in an ordered pair, which indicates how man units to move up or down from the origin In the ordered pair (, 5 ), the coordinate is 5. intercept The coordinate of the point where a line crosses the ais See intercept. zero (of a function) An value for which f( ) 0; A zero is located at the intercept of the graph of the function. The zero of f f 6 is because 0. zero eponent 0 For an nonzero number a, a , where 0 ZeroProduct Propert If the product of two real numbers is 0, then at least one of the numbers is 0. If a and b are real numbers and ab 0, then a 0 or b 0. ( )( ) or or 5 7 Big Ideas Math Algebra Copright Big Ideas Learning, LLC
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