A Graphical Approach to College Algebra (7th Edition)

Chapter 3

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8i ; As the both numbers have no real parts, add ... more

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(-2+6i) ;  Add the real and imaginary parts,  ; more

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2-4i ; The complex conjugate of the denominator (i... more

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True ; All real numbers can be written as (x+iy) ... more

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True ; A pure imaginary number, has real part ... more

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True ; For a pure imaginary number, x is zero and... more

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True ; All real numbers are complex numbers. ... more

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False; All real numbers are complex numbers with ... more

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True ; All real numbers are not pure imaginary ... more

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; We know that  . Therefore . ; more

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; We know that   and . Therefore . ; more

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; We know that   and . Therefore . ; more

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. ; We know that   and . Therefore . ; more

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; We know that   and . Therefore . ; more

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; We know that   and . Therefore . ; more

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; We know that   and . Therefore ; more

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; We know that   and . Therefore ; more

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; We know that   and . Therefore The last ... more

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; We know that   and . Therefore The last ... more

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; We know that  . Therefore The last equality is ... more

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; We know that  . Therefore ; more

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; We know that  \(\sqrt{-1}= i. Therefore \[\... more

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; We know that  . Therefore The last equality is ... more

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; Since here the radicands are negative so use ... more

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; Since here the radicands are negative so use ... more

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-2 ; Since here the radicands are negative so use ... more

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-3 ; Since here the radicands are negative so use ... more

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; In the complex numbers addition operation, the ... more

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; In the complex number's addition, the real ... more

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2 ; In the subtraction of complex numbers, the ... more

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1 ; In the subtraction of complex numbers, the ... more

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; In the complex number's addition operation, the... more

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; In the subtraction of complex numbers, the ... more

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; In the subtraction of complex numbers, the ... more

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; In case of complex numbers, the addition and ... more

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0 ; In the complex number's addition, the real ... more

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0 ; In the complex number's addition, the real ... more

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; Steps to be followed in multiplying the complex... more

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; Steps to be followed in multiplying the complex... more

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; Steps to be followed in multiplying the complex... more

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; Steps to be followed in multiplying the complex... more

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; Steps to be followed in multiplying the complex... more

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; Steps to be followed in multiplying the complex... more

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; Apply FOIL method or distributive property then... more

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; Apply the FOIL method or distributive property ... more

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  ; Apply formula of product of sum of two terms ... more

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; Apply formula of product of sum of two terms ... more

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; Apply formula of product of sum of two terms ... more

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; Apply formula of product of sum of two terms ... more

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; Apply formula of product of sum of two terms ... more

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; Apply formula of product of sum of two terms ... more

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; Apply formula of square of difference of two ... more

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; Apply formula of square of difference of two ... more

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; Apply formula of product of sum of two terms ... more

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  ; Apply formula of product of sum of two terms ... more

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; Value of is and now square on both sides. ... more

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1 ; Value of is and now square on both sides. ... more

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; Value of is and now square on both sides. ... more

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; Value of is and now square on both sides. ... more

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1 ; Value of is and now square on both sides. ... more

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-1 ; Value of is and now square on both sides. ... more

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-1 ; Value of is and now square on both sides. ... more

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; Value of is and now square on both sides. ... more

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; Taking the powers in numerator. ; Using the ... more

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Shifting powers in the numerator.Using the ... more

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Shifting the powers in the numerator.      Using ... more

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Shifting the powers in the numerator.      Using ... more

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Shifting the powers of the expression in the ... more

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Shifting the powers of the expression in the ... more

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Shifting the powers of the expression in the ... more

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; If for any expression of the form , the complex... more

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; If for any expression of the form , the complex... more

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; If for any expression of the form , the complex... more

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; If for any expression of the form , the complex... more

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  ; If for any expression of the form , the ... more

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; If for any expression of the form , the complex... more

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; Taking the conjugate of denominator and ... more

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; Taking the conjugate of denominator and ... more

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; Taking the conjugate of denominator and ... more

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; Taking the conjugate of denominator and ... more

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; Taking the conjugate of denominator and ... more

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\(\frac{7i}}{4}\} ; Taking the conjugate of ... more

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; Using the conjugate of denominator multiply ... more

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;  Using the conjugate of denominator multiply ... more

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; Using the conjugate of denominator multiply ... more

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; Using the conjugate of denominator multiply the... more

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; Using the conjugate of denominator multiply the... more

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; Using the conjugate of denominator multiply the... more

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In this process denominator becomes a real number... more

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If exponent is where is remainder. So when it is ... more

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Since vertex and parabola is upward as . ; Since ... more

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(original equation)comparing the standard form ... more

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(standard form) (original equation)Its vertex is... more

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; For the function , by the vertex formula the ... more

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3 ; The graph of quadratic function increasing on ... more

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-3 ; The graph of quadratic function increasing on... more

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No real solution ; f(x) has minimum value 3 at x=-... more

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One ; (-3,3) is the vertex for the graph of the ... more

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; Quadratic model is appropriate for the data ... more

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; Linear model is appropriate for the data ... more

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; Quadratic model is appropriate for the data ... more

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; Quadratic model is appropriate for the data ... more

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; Linear model is appropriate for the data ... more

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; Linear model is appropriate for the data ... more

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; Given that, quadratic function has vertex is (-... more

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; Given that, quadratic function has vertex is (-... more

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; Given that, quadratic function has vertex is (8... more

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; Given that, quadratic function has vertex is (-... more

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; Given that, quadratic function has vertex is (-... more

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; Given that, quadratic function has vertex is (5... more

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B ; Given the center radius equation of the circle... more

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Circle equation is ; Given center of the radius is... more

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Circle equation is ; Given center of the radius is... more

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Circle equation is ; Given, the center of the ... more

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Circle equation is ; Given, the center of the ... more

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Circle equation is ; Given, the center of the ... more

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Circle equation is ; Given, the center of the ... more

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Circle equation is ; Given, the center of the ... more

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Circle equation is ; Given, the center of the ... more

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Circle equation is Center of the circle is Radius ... more

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Circle equation is Center of the circle is Radius ... more

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Circle equation is Center of the circle is Radius ... more

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Circle equation is Center of the circle is Radius ... more

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Circle equation is Center of the circle is Radius ... more

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Circle equation is Center of the circle is Radius ... more

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Circle equation is Center of the circle is Radius ... more

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Circle equation is Center of the circle is Radius ... more

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; Given equation is Now add or subtract real ... more

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; Given equation is Since and also substitute . ... more

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

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0 ; The is called as imaginary in complex number... more

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The graph is plotted by using the function of . In... more

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Minimum point ; Rewrite the given function in the ... more

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; To find roots of the equation, use the ... more

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Domain: Range: ; The given function is in the ... more

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Center: (-7,0)Radius: 25 ; Convert the given ... more

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Center: (-8,3)Radius: 3 ; Convert the given ... more

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No ; The represents the parabola and represents ... more

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To understand that how many points, the line ... more

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From given equation, substract 4 from both sides ... more

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By the zero property, when the and are complex ... more

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Square root property is applicable only for form ... more

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In given equation the leading coefficient of is 3... more

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and the solution set of the equation is . ; ... more

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The solution set is . ; In the equation , 16 is a ... more

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The solution set is . ; In the equation , 144 is a... more

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The solution set is . ; First divide by 2 on both ... more

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The solution set is . ; First divide by 2 on both ... more

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; In the equation , -16 is a negative number, so ... more

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; In the equation , -100 is a negative number, so... more

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; In the equation , -18 is a negative number, so ... more

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; In the equation , -32 is a negative number, so ... more

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The solution set is . ; First use square root ... more

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The solution set is . ; First use square root ... more

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; First use square root property, the square root... more

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; First use square root property, the square root... more

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The solution set is . ; First write the quadratic ... more

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The solution set is . ; First write the quadratic ... more

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The solution set is . ; Write the factors of ... more

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The solution set is . ; Write the factors of ... more

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The solution set is . ; Write the quadratic ... more

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The solution set is . ; Write the quadratic ... more

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The solution set is . ; Rearrange the terms of the... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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; In order to solve the equation, follow the ... more

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{} ; To solve follow these stepsFirst subtract 4 ... more

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{} ; To solve follow these stepsFirst add on both... more

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{} ; To solve follow these stepsFirst subtract on... more

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{} ; To solve follow these stepsUse quadratic ... more

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{} ; To solve follow these stepsUse quadratic ... more

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{} ; To solve follow these stepsUse quadratic ... more

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{} ; To solve follow these stepsUse quadratic ... more

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{} ; To solve follow these stepsFirst expand the ... more

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{} ; To solve follow these stepsFirst expand the ... more

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{} ; To solve follow these stepsFirst substitute ... more

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{} ; To solve follow these stepsFirst substitute ... more

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{} ; To solve follow these stepsFirst add 3 on ... more

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{} ; To solve follow these stepsFirst add 1 on ... more

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{} ; To solve follow these stepsFirst expand the ... more

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{} ; To solve follow these stepsFirst expand the ... more

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{} ; To solve follow these stepsFirst divide with ... more

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{} ; To solve follow these stepsFirst substitute ... more

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{} ; To solve follow these stepsFirst expand . ... more

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0One real solutionRational ; To solve follow these... more

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100,There are two real solutions of the equation.... more

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84,There are two real solutions.Both solutions are... more

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8,There are two real solutions.Both solutions are ... more

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-23, There are two non real or complex solutions ... more

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-44, There are two non real or complex solutions ... more

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; There are two solutions and hence is a ... more

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; There are two solutions and hence is a ... more

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; There are two solutions and hence is a ... more

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; There are two solutions and hence is a ... more

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; There are two solutions and hence is a ... more

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; There are two solutions and hence is a ... more

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; There are two solutions and hence is a ... more

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; There are two solutions and hence is a ... more

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The discriminant is equal to zero. This means ... more

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The discriminant is less than zero. This means ... more

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The discriminant is less than zero. This means ... more

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The discriminant is greater than zero. This means... more

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The discriminant is greater than zero. This means... more

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The discriminant is equal to zero. This means ... more

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; The solution set of is the set of x-values ... more

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; A parabola opening upwards and having vertex in... more

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; A parabola opening upwards and having vertex in... more

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; A parabola opening downwards and having vertex ... more

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; A parabola opening downwards and having vertex ... more

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; A parabola opening downwards and having vertex ... more

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; A parabola opening upwards and having vertex in... more

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; A parabola opening upwards and having vertex in... more

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; A parabola is a function of degree 2 and thus ... more

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0 ; The parabola opens downward, is located in ... more

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3 ; The x-coordinate of the vertex of the parabola... more

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; For a parabola in the standard form , where the... more

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Yes.The y-coordinate of the vertical intercept is ... more

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The parabola opens upward and has its vertex in ... more

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; To solve the inequality , bring all the ... more

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; Solving for the indicated variable by ... more

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; Solving for the indicated variable by ... more

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; Solving for the indicated variable by ... more

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; Square root property: If then .To solve for , ... more

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;  First rewrite the given equation as and then ... more

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; First, rewrite the given equation as and then ... more

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; To solve for , first rewrite the given equation... more

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; First, rewrite the given equation as and then ... more

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; First, rewrite the given equation as and then ... more

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; Subtract from both sides. ; Divide both sides ... more

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; Multiply both sides by . ; Expand the using ... more

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; First rewrite the given equation as . Then ... more

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No solution exists ; Give equation is quadratic ... more

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; ; Subtract 2 from both sides. ; Equation is ... more

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; ; Add 1 to both sides. ; Equation is quadratic ... more

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; Given equation is quadratic in .Here, , , and .... more

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116 ; Vertex formula for the is If , then the ... more

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3 ; Vertex formula for the is If , then the ... more

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2 ; Given function is a quadratic function with... more

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-28 ; Given function is a quadratic function with... more

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; Subtract 1 from both sides. ; Equation is ... more

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7, -1 ; Subtract 7 from both sides. ; Equation is... more

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, ; First, multiply both sides of the given ... more

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Values of are   ; Given, ; Multiplying both the ... more

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It is known that the area of a rectangle is the ... more

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If the width of frame is , then the original ... more

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; Length of the fence is equal to the perimeter ... more

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400 ; Given, perimeter of the rectangular fence is... more

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2.1 ; s(t)= 75 - 16t2 ; Given ; 0 = 75 - 16t216t2... more

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1.49 ; 28 = π * r² * 4  ; the volume of a cylinder... more

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; Let consider the radius of cylinder is and ... more

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The length is and width is ; Let, the length of ... more

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feet ; From the area we can get the side of the ... more

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40ft ; Let, the kite's height from ground given,... more

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5 ft ; Let the height of the dock given , the ... more

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1300 yards ; let,the smaller leg ; as given the ... more

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4.04 ft ; let,the height of the ladder is given ,... more

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; let,the length of one leg other leg given the ... more

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The height of the frame and the width of the ... more

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   ; Length of runway in is given as a function ... more

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; To find the minimum or maximum value of a ... more

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f(0) = 160 and f(2)= 131.2 ; Equation for the ... more

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The inequality only holds in interval . The graph ... more

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The inequality only holds in interval  . The graph... more

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The inequality does not hold true. The graph shows... more

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; Separate the negative and positive under the ... more

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; Separate the negative and positive under the ... more

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-6 ; Separate the negative and positive under the ... more

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3 ; Separate the negative and positive under the ... more

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; Separate the negative and positive under the ... more

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-6 ; Separate the negative and positive under the ... more

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; Plug in the values of and .Add the imaginary ... more

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; Add or subtract real and imaginary parts ... more

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; Plug in the values of and .Multiply 17 by 1, ... more

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. ; Plug in the values of .Multiply 17 by 17, 17 ... more

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; Plug in the value .Multiply the denominator and... more

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; Substitute values of and as and ... more

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; Consider the identity of iota . Writing the ... more

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; Consider the identity of iota . Writing the ... more

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; Consider the identity of iota . Writing the ... more

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; Consider the identity of iota . Writing the ... more

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  ; The domain of function is that set of inputs (... more

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; Firstly calculating the coordinate of vertex ... more

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; To find the value of - intercept substitute ... more

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; To find the value of - intercept substitute ... more

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; Firstly calculating the coordinates of vertex ... more

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Increasing under the interval : ; Decreasing under... more

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   ; It can be seen from the graph of that the ... more

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; To find the value of - intercept substitute ... more

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Firstly calculating the coordinate of vertex ... more

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  ; Firstly calculating the coordinate of vertex... more

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; Firstly calculating the coordinate of vertex ... more

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; From the graph it can be seen that the parabola... more

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At x=1, f(x) will be maximum.  ; The vertex of the... more

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Two real solutions will be there.  ; f(x)=2 means ... more

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No real solution.  ; f(x)=6 means the intersection... more

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To graph this equation consider the general ... more

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To graph this equation consider the general ... more

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Since maximum value is 1 at x=3, (3,1 ) is the ... more

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The minimum value is -4 at x=-3 hence the point (-... more

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The centre radius form of a circle is   where (h,k... more

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The centre radius form of a circle is   where (h,k... more

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The centre radius form of a circle is   where (h,k... more

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The centre radius form of a circle is   where (h,k... more

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; This is a parabola with axis on y-axis.The ... more

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; To evaluate the altitude, substitute 1 for in... more

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; Minus thirty-six can be written as a factor of ... more

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-10 ; Minus five can be written as a factor of ... more

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; The actual part of a complex number is added ... more

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; Multiply with each element of and with each ... more

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; The expansion of is equal to .Expand by using... more

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; To simplify the expression , multiply conjugate... more

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; Sixty-five can be written as the sum of sixty-... more

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1 ; Negative property of exponent- If is real ... more

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The center of the circle is and the radius is 4 ... more

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The solution set is ; Let the function be denoted ... more

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; The given equation is Add 4 on both sides of ... more

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The solution set of the equation is ; The given ... more

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The function when equated to 0 forms an equation ... more

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Solve the equation And find the points where the ... more

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Solve the equation And find the points where the ... more

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The length of one of the leg is The length of the ... more

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