Algebra & Trigonometry (10th Edition)

Chapter 1

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; Natural numbers are elements from the set . It ... more

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The interval consists of all real numbers greater ... more

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; The values of that are less than 4 are ... more

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Terms: , 4Coefficients : -2, 4 ; In an algebraic ... more

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-5 ; Substitute 0 for in the expression to find ... more

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irrational ; An irrational number is non ... more

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Origin ; On the real number line, the positive ... more

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absolute value ; The distance between two real ... more

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Composite ; A composite number can be written as ... more

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terms ; In an algebraic expression, the parts ... more

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zero factor property ; According to the zero ... more

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Plot the numbers -8 and -4 on the real number line... more

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Plot the numbers 1 and on the real number line. ... more

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Plot the numbers and on the real number line. The ... more

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Plot the numbers and on the number line; is less ... more

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;  ; The set of nonnegative real numbers contains ... more

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;   ; is no more than implies is less than or ... more

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; is at least implies that is greater than or ... more

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  ; is no less than implies is greater than or ... more

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10 ; Using the definition of absolute value, it ... more

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0 ; Using the definition of absolute value, it can... more

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5 ; Since and , using the definition of absolute ... more

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4 ; Since and , using the definition of absolute ... more

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-1 ; Since, , using the definition of absolute ... more

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-6 ; Since, , using the definition of absolute ... more

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25 ; Since, , using the definition of absolute ... more

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-16 ; Let .Use the absolute value properties as ... more

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-1 ; Let , for .As,Substitute ; therefore, .Use ... more

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1 ; Let , for .As,Substitute ; therefore, .Use ... more

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- = - . ; - Use the absolute value property as ... more

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51. ; Let and be real numbers.Then, the distance... more

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50 ; Let and be real numbers.Then the distance ... more

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. ; Let and be real numbers.Then, the distance ... more

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; Let and be real numbers.Then, the distance ... more

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; Let and be real numbers; then, the distance ... more

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; The distance between two points and , should ... more

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; It is observed that the receipt in billions of ... more

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; It is observed that the receipts in billions of... more

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; It is observed that the receipt in billions of ... more

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; It is observed that the receipts in billions of... more

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2 terms: and 47 ; In an algebraic expression, the... more

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2 terms: and -32 ; In an algebraic expression, ... more

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2 terms: and 6, -5 ; In an algebraic expression, ... more

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3 terms: , and -54, 0.5. ; In an algebraic ... more

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2 terms: and 1 ; In an algebraic expression, the ... more

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2 terms: and -3 ; In an algebraic expression, the... more

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Multiplicative inverse property ; The algebraic ... more

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Additive inverse ; The algebraic expression ... more

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Associative property of multiplication ; The ... more

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Associative property of multiplication and ... more

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; Simplify the expression to evaluate the ... more

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; Simplify the expression to evaluate the ... more

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; Simplify the expression to evaluate the ... more

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; Simplify the expression using the property to ... more

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False, non negative numbers include both positive ... more

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False; when the positive number and the negative ... more

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True; When the negative number and the negative ... more

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; To write 45,850 in scientific notation, the ... more

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-0.002718 ; Since the exponent of 10 in is -3, ... more

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; For rationalizing the numerator or denominator ... more

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; For rationalizing the numerator of the form , ... more

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exponent ; The exponent form is used to write the... more

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Exponential form. ; The Avogadro number is written... more

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Square root. ; Each of the equal factors of a ... more

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Index. ; The expression can be written as , which... more

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Like radicals. ; For radicals to be subtracted or ... more

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Conjugates. ; For a term , the term where the ... more

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Rationalizing. ; If the denominator of the term ... more

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Power. ; The expression can further be simplified... more

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-24 ; Substitute in the expression multiply 2 ... more

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; Substitute in the expression Use the ... more

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6 ; Substitute in the expression and use the ... more

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-54 ; Substitute in the expression Multiply -3 ... more

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-48 ; Substitute in the expression Multiply -2 ... more

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; Substitute in the expression Use the property ... more

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;  The general form of the scientific notation is... more

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; The general form of the scientific notation is... more

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0.000314 ;  The negative sign of the exponent ... more

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-2,058,000 ; Here, the given number is in ... more

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;  Here, the given number is in scientific form. ... more

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; Here, the given number is in scientific form. ... more

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; To rationalize the denominator, multiply the ... more

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; Multiply the numerator and denominator both by ... more

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; The rationalizing factor is the conjugate of ... more

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; The rationalizing factor is the conjugate of ... more

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; The rationalizing factor is the conjugate of ... more

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; The rationalizing factor is the conjugate of ... more

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; For any real number and positive integer , . ... more

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; To find the rational exponential form, express ... more

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; To find the radical form, express the power as ... more

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; Apply the property of radicals .Use the ... more

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Plot the function in the interval . ; more

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The side length of package A is less than twice ... more

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Recollect the property of exponents . ; Recollect ... more

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The expression is equal to , not . Consider an ... more

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Use the distributive law , while simplifying the ... more

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The left-hand side of the expression is simplified... more

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Degree: 3.Leading coefficient: -7. ; The standard ... more

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; Simplify the expression by first distributing ... more

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; Compute the product of the given terms by first... more

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; The degree is the highest power of the variable... more

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Monomial. ; The monomial is a one-term polynomial ... more

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Like terms. ; Only terms with the same powers of a... more

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First terms. ; It refers to the product of the ... more

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; Subtract the like terms to find the difference ... more

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; Subtract the like terms to find the difference ... more

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; Add the like terms to find the sum of the ... more

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; Add the like terms to find the sum of the ... more

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; Multiply the coefficient of terms and then add ... more

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; Multiply the coefficient of terms and then add ... more

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; Multiply the coefficient of terms and then add ... more

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; To multiply with , multiply with each term of... more

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; To multiply with , use the distributive ... more

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; To multiply with , use the distributive ... more

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; To multiply with , use the distributive ... more

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; To multiply by , use the distributive property... more

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False. It depends on the degree of the factor to ... more

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False. During the addition of two binomials, the ... more

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; The highest power of the variable in a ... more

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; The highest power of the variable in a ... more

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; Let the unknown polynomial be . Subtract the ... more

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Substituting 3 for and 4 for in the expression ... more

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; First, take out four as a common factor from . ... more

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; Use the difference of squares of two numbers to... more

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; In the expression, the first term is the ... more

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; As, is a perfect cube of , use the formula to... more

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; In the trinomial , , , and . As the product is... more

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; In the trinomial , , , and . As the product is ... more

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; Simplify the expression by grouping and ... more

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; Rewrite the middle term of the equation as . ... more

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Factoring. ; Factoring is a process to split a ... more

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Completely factored. ; A polynomial that cannot be... more

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Perfect square trinomial. ; A perfect square ... more

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Grouping. ; Dividing the polynomials into smaller ... more

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; Factor and obtain . Take out the common factor... more

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; Factor the each term of and obtain . Take out ... more

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; is the common factor for both terms, so take ... more

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(x+3)(x-1) ; Factor the term of and obtain . Take... more

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FACTORING THE DIFFERENCE OF TWO SQUARES      x2−81... more

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; Express the terms of the polynomial, as their ... more

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; Express the terms of the polynomial as their ... more

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; Express the terms of the polynomial, as their ... more

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;  Express the terms of the polynomial, as their... more

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. ; Factor each term of the polynomial, to get . ... more

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. ; Factor each term of the polynomial, to get . ... more

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; Factor each term of the polynomial, to get . ... more

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. ; Factor each term of the polynomial, to get . ... more

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; Factor each term of the polynomial, to get . ... more

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; Factor each term of the polynomial, to get . ... more

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; Factor each term of to get . Then, use the sum... more

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; Factor each term of to get . Then, use the sum... more

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; Factor each term of to get . Then, use the sum... more

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; Factor each term of to get . Then, use the sum... more

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; Break the middle term, in the two terms so ... more

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; Break the middle term in the two terms in such ... more

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; Break the middle term, in the two terms in ... more

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; Break the middle term, in the two terms so ... more

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. ; Write 31 as a sum of two integers whose sum is... more

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; Write the middle term as a sum of two terms ... more

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; Break the middle term into two terms such that ... more

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; Break the middle term as a sum of two terms ... more

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; Group the polynomial as .Factor each group ... more

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. ; Group the polynomial as .Factor each group ... more

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; Group the polynomial as .Factor each group ... more

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; Group the polynomial as .Factor each group ... more

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; Group the polynomial as .Factor each group ... more

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; Group the polynomial as .Factor each group ... more

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. ; Follow these steps to factor the trinomial .... more

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; Follow below steps to factor the trinomial :... more

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; Follow below steps to factor the trinomial :... more

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; To factor the the polynomial by grouping, ... more

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; To factor the expression completely, follow ... more

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; To factorize the expression completely, follow... more

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; To factorize the expression , completely factor... more

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. ; To factorize the expression completely, ... more

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; To factor the expression completely follow the... more

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; To factorize the expression completely follow ... more

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The factors will be (2x+1)(x+2)(x-2) If u still ... more

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; To factorize the expression completely, follow... more

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; To factorize the expression follow the ... more

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. ; Factor out from the terms and , and use the ... more

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True, as the difference of the perfect squares ... more

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The number 3 is factored from both the factors. ... more

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; The polynomial is not reducible over the ... more

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; Follow the steps below to obtain the result.... more

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; Follow the steps to obtain the result:Factor ... more

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; Follow the steps below to obtain the result.... more

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; Follow the steps below to perform the division.... more

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; Follow the steps below to perform the ... more

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; Use the factored denominators , and .The least ... more

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; Combine the fraction in numerator and ... more

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; Solve the given expression with a negative ... more

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; Multiply and divide with a suitable expression ... more

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; Multiply and divide the expression with a ... more

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domain ; The domain is the set of all values that ... more

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rational expression ; A polynomial cannot contain ... more

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complex ; Complex fractions have fractions within ... more

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equivalent ; Different algebraic expressions are ... more

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The set of all real numbers of ; Polynomial ... more

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The set of all positive real numbers for . ; The ... more

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All real numbers of such that . ; The expression ... more

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All real numbers of such that ; The expression ... more

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All real numbers of such that ; The expression ... more

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All real numbers of such that ; The expression ... more

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All real numbers of such that ; The denominator ... more

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All real numbers of such that ; The denominator ... more

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The set of all real numbers such that ; The ... more

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The set of all real numbers such that ; The ... more

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The set of all real numbers such that ; The ... more

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All real numbers such that, ; The domain of the ... more

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; Follow the steps below to perform the ... more

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; Follow the steps below to perform the ... more

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; Follow the steps below to perform the ... more

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; Follow the steps below to perform the ... more

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. ; Apply the formula to write the expression ... more

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; Apply the formula to write the expression ... more

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; Factorize the numerator and denominator both in... more

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; Factorize the numerator and denominator both in... more

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. ; Factorize the numerator and denominator of the... more

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; Factorize the numerator and denominator of the ... more

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. ; Factorise the numerator and denominator of the... more

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; Factorize the numerator and denominator of the ... more

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; Factorize the denominator of the given rational... more

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; Factorize the denominator of the given rational... more

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Non-common factor has been cancelled out from the ... more

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 x012345So, from the completed table, the ... more

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; Multiply the rational expressions. ; Cancel the... more

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; To divide the rational expression, multiply the... more

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. ; To divide the rational expression, multiply ... more

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  ; Factorize the terms in the given rational ... more

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; Factorize the terms in the given rational ... more

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; Factorize the terms in the given rational ... more

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; Take the least common multiple in the given ... more

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; Take the least common multiple in the given ... more

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. ; Take the least common multiple in the given ... more

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; Take the least common multiple in the given ... more

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; Take the least common multiple in the given ... more

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. ; Take the least common multiple in the given ... more

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; Simplify the given rational expression with the... more

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; Simplify the given rational expression with the... more

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should be written instead of ; Simplify the given... more

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The least common multiple results in the ... more

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; Take the least common multiple in the numerator... more

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; Take the least common multiple in the ... more

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. ; Revert the denominator term of the given ... more

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; Revert the denominator term of the given ... more

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; Take the least common multiple in the numerator... more

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; Take the least common multiple in the numerator... more

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. ; Simplify the given expression with the help of... more

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; Since is less than , take the common factor ... more

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; Since is less than , take the common factor ... more

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; Let the first factor be and the second factor ... more

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; Take the common factor from both the terms of ... more

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; Take the common factor from both the terms of ... more

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; Solve the numerator by taking the using the ... more

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; Solve the numerator by taking the using least ... more

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; Solve the numerator by taking the least common ... more

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; Solve the numerator by taking the least common ... more

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; To rationalize the numerator, multiply and ... more

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; To rationalize the numerator, multiply and ... more

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; To rationalize the numerator, multiply and ... more

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; To rationalize the numerator, multiply and ... more

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; To rationalize the numerator, multiply and ... more

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; To rationalize the numerator, multiply and ... more

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; The dimensions of the shaded area are the ... more

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; The object is tossed such that its shaded area ... more

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; First, simplify the denominator terms and then ... more

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When there is no organic waste, then the oxygen ... more

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FalseFor simplification, its domain should be ... more

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TrueThis is a quadratic equation in which the ... more

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Each point is plotted on a graph by measuring a ... more

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Let the x axis represent the years and the axis ... more

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6.08 ; The distance between the points and can ... more

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The distance between two points and can be ... more

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; The midpoint of the coordinates and can be ... more

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; Let the sideline be the axis. The footballer ... more

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; As 2013 comes in the middle of the years 2012 ... more

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, , and . ; To shift the parallelogram that is ... more

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Cartesian ; The plane on which the graph of a ... more

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distance formula ; The distance between the two ... more

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midpoint ; The coordinates of the middle point of ... more

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Each point is plotted on a graph by measuring a ... more

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Each point is plotted on a graph by measuring a ... more

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; Assume that the point is at the origin . Now, ... more

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; Assume that the point is at the origin . Now, ... more

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4th quadrant. ; As , the point is to the right ... more

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3rd quadrant ; As , the point is to the left side ... more

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2nd quadrant ; As , which is negative, the point ... more

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2nd quadrant. ; As , the point is in the left side... more

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Either the 2nd quadrant or the 4th quadrant ; For... more

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Either the 1st quadrant or the 3rd quadrant. ; For... more

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Let axis represent the months and axis represent... more

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13 units ; The distance between the points andcan... more

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17 units ; The distance between the points and ... more

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units  ; The distance between the points and ... more

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units  ; The distance between the points and is... more

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units  ; The distance between the points and ... more

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17.21 ; The distance between the points and can ... more

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The distance between the two points and can be ... more

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The distance between the two points and can be ... more

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The distance between the two points and can be ... more

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Distance between two points and can be ... more

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; Assume the positive y axis represents the ... more

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; The points at which the players are standing ... more

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; Sales in the years 2010 and 2014 can be written... more

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; Revenue per share in the years 2013 and 2015 ... more

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; Add 2 to the coordinates of each original ... more

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; Add 6 to the coordinates of each of the ... more

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; Add 4 to the coordinates of each of the ... more

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; Subtract 10 from the coordinates of each of the... more

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True; in quadrant II, and . Hence, and , which ... more

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False; the midpoint formula is used once to divide... more

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True, two sides of the triangle are each and one ... more

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False. The polygon could be a rhombus. ; Consider ... more

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Whenever the difference between the values of the ... more

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On the x axis, the y coordinate is always zero.... more

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; For a line segment with the end points and , ... more

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; For a line segment with the end points and , ... more

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Use the midpoint formula to obtain the midpoint ... more

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The and distance of the point from the origin is... more

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Draw the and axes. Then label for the axis and... more

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Draw the and axes. Then label for the axis and... more

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Quadrant IV. ; As the value is positive and the ... more

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Quadrant 1 and Quadrant 3. ; It is clear from the ... more

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. ; The annual sale in 2013 was , and in 2015 it ... more

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The company's total cost for producing 225 T-... more

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Detailed explanation: more

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The weight of one golf ball is approximately 0.1 ... more

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