A Graphical Approach to College Algebra (7th Edition)
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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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7-7i ; 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 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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From the equation ; more
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From the equation ; more
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From the equation ; 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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