A Graphical Approach to Algebra & Trigonometry (7th Edition)

Chapter 5

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, ; For the given function to be defined the ... more

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, ; For the given function to be defined the ... more

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Increases: Empty setDecreases: Constant: Empty set... more

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Increase: Decrease:  Constant: Empty set ; Given ... more

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, ; Given equation is . As from the left and as... more

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, ; Given equation is . As from left or right . ... more

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Even function, symmetric about -axis ; Given ... more

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Odd function, symmetric with respect to the origin... more

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The function is not defined at because as from ... more

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This function takes all values other than 0 so the... more

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This graph takes all values other than 0 so the ... more

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From the graph it is inferred that the range is . ... more

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To find the solution of the equation need to find... more

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The function takes all values other than 0 so the ... more

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As , and as , and graph does not intersect the -... more

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With respect to the vertical line , the graph is ... more

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The graph of the given function can be derived ... more

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The graph of the given function can be derived ... more

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The graph of given function can be obtained from ... more

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 Domain is Range is ; the graph can be obtained by... more

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Domain is  Range is   ; The graph is obtained by... more

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Domain is Range is ; Vertically shift the graph ... more

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Domain is Range is ; Draw the graph of by ... more

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Domain is Range is ; Draw the graph of by ... more

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Domain is Range is ; Shift the graph of ... more

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Domain is Range is ; Shift the graph of by units... more

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Domain is Range is ; Stretch the graph vertically... more

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Domain is Range is ; Extend the graph of by a ... more

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Domain is Range is   ; Shift the graph of ... more

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Domain is  Range is ; Shift the graph of ... more

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Domain is Range is ; Generate the graph of by ... more

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Domain is  Range is ; Generate the graph of by ... more

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shift horizontally the graph of towards right by... more

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Domain is Range is ; Shift horizontally the graph ... more

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Domain is Range is   ; Shift horizontally the ... more

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The given function can be written as .shift the ... more

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 The given function can be written as .shift the ... more

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The given function can be written as .shift the ... more

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The given function can be written as .shift the ... more

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Given ; Rearranging the terms ;   ; Comparing the ... more

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The rational expression is equal to . The ... more

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To find the value of vertical asymptote find value... more

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Vertical asymptote: x = 5Horizontal asymptote: y... more

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Vertical Asymptote: x = -9Horizontal Asymptote: y... more

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Vertical Asymptote: Horixontal Asymptote: Domain... more

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Vertical Asymptote: x = 4Horizontal Asymptote y = ... more

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Vertical Asymptote: x = -3Oblique Asymptote: ... more

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Vertical Asymptote: x = 1Oblique Asymptote: Domain... more

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Vertical Asymptotes: x = - , x = -2Horizontal ... more

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Vertical Asymptotes: x = , x = 5Horizontal ... more

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Vertical Asymptotes: x = -2, x  = Horizontal ... more

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Vertical Asymptotes: x = -2, x = Horizontal ... more

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Vertical Asymptote: x = -3Oblique Asymptote: y = x... more

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Vertical asymptote: x = 5Oblique asymptote: y = x+... more

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Vertical asymptote: x = 2Horizontal asymptote: y... more

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Vertical Asymptote: x = -1Horizontal Asymptote: y... more

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Vertical Asymptote: x = 2Horizontal Asymptote: y... more

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Vertical Asymptote: x = 0Horizontal Asymptote:  y... more

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where where p , q are such that N(2) 0 and N(-2... more

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where k 0 ; Given vertical asymptote = 1, thus ... more

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Highest degree of numerator is equal to the ... more

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; Vertical Asymptote occurs where Horizontal ... more

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; Vertical Asymptote occurs where Horizontal ... more

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; Vertical Asymptote occurs where ; Horizontal ... more

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; Vertical Asymptote occurs where ; Horizontal ... more

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; Vertical Asymptote occurs where ; Horizontal ... more

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; Vertical Asymptote occurs where ; Horizontal ... more

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; Vertical Asymptote occurs where ; Oblique ... more

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; Vertical Asymptote occurs where ; Oblique ... more

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; Horizontal Asymptote occurs where ; Domain of ... more

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This is because in order to find the vertical ... more

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Find the domain of the given rational function... more

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Find the domain of the given rational function... more

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Find the domain of the given rational function... more

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Find the domain of the given rational function... more

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Find the domain of the given rational function... more

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Find the domain of the given rational function... more

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Find the domain of the given rational function... more

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Find the domain of the given rational function... more

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In the first step, find the domain of the given ... more

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Simplify the function and bring it to its lowest ... more

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Simplify the function and bring it to its lowest ... more

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Start solving by simplifying the given function to... more

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Start solving by reducing the given function to ... more

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Start solving by reducing the given function to ... more

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Start solving by writing down the Domain of the ... more

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Find the domain of the function since it is ... more

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Simplifying the given equation, we get Since the ... more

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Simplifying the given equation, we get Since the ... more

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Start solving by simplifying the function to its ... more

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Start solving by simplifying the function to its ... more

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Since the given function is already in its lowest ... more

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Since the function is already given in its lowest ... more

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Start solving by simplifying the function to its ... more

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Since the given function is already in its lowest ... more

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Since the given function is already in its lowest ... more

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Calculate vertical asymptotes,  ; are the ... more

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The vertical asymptotes and the domain are: ; The ... more

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Obtain the vertical asymptote by equating ... more

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Obtain the vertical asymptote by equating ... more

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To determine the vertical asymptotes, equate the ... more

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To determine the vertical asymptotes, equate the ... more

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To determine the vertical asymptotes, equate the ... more

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To determine the vertical asymptotes, equate the ... more

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To determine the vertical asymptote for the ... more

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The vertical asymptote for the given function is ... more

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The vertical asymptote of the graph is found by ... more

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The vertical asymptote is found by equating the ... more

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The vertical asymptote is found by equating the ... more

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The vertical asymptote is found by equating the ... more

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Factorise numerator and denominator in the given ... more

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The points of discontinuity is found by ... more

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The given expression is not in the lowest terms. ... more

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The given function can be converted into lower ... more

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The vertical asymptote is found by equating the ... more

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The domain is and the range is (0,  ]. The x ... more

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The domain is and the range is (0,  ]. The \(x\) ... more

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The domain is and the range is (0, 0]. The x ... more

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The domain is and the range is { All real numbers... more

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The domain is and the range is {all real numbers ... more

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The domain is and the range is {all real numbers ... more

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p=4, q=2 ; from the table X=0; Y1=2from the table ... more

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p=3,q=1 ; from the table X=0; Y_1=3from the table ... more

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p=-2; q=-0.5 ; from the table X=-3; Y1=0.5from the... more

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p=-4; q=3 ; from the table X=-7; Y1=0.75from the ... more

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; From the knowledge of geometry if denominator ... more

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; From the knowledge of geometry and rational ... more

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; From the knowledge of geometry and rational ... more

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; From the knowledge of geometry and rational ... more

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By  long division method we have to oblique ... more

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By  long division method we have to oblique ... more

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y=3-x ; Divide the numerator by the denominator ... more

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; Divide the numerator by the denominator ... more

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y=x-5; x=0.5 ; Divide numerator by the denominator... more

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Divide numerator by the denominator and check ... more

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No; at x=-5, the graph is discontinuous. ; Divide ... more

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; Find the zeros of the function . ; Tabulate the... more

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; Find the zeros of the polynomial by equating... more

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The length of the line increases when the ... more

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x=-3 ; Multiply with the least common denominator... more

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x=0 ; Multiply by least common denominator (LCD... more

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x=3 ; x=-4 ; Multiply with the least common ... more

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x=4 ; Multiply the equation with the least common ... more

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x=9 ; x=4 ; Multiply the right side of the ... more

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x=5 ; x=-2 ; Multiply the right hand side of the ... more

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x= \frac{-3\pm\sqrt{29}}{2} ; Subtract the Right ... more

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x=\frac{-7\pm\sqrt{33}}{8} ; Multiple the equation... more

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x=1\pm\frac{1}{\sqrt{3}} ; Multiply the equation ... more

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x=\frac{1\pm\sqrt{7}}{2} ; Multiply the equation ... more

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; Multiply the left hand side of the equation ... more

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; Multiply the equation with the least common ... more

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-2 ; Multiply the left side of the equation with ... more

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-3-5 ; Simplifying the LHS of equation ; Rewriting... more

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-10 ; The given equation is ; Making denominator ... more

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2.42443-7.42443 ; The given equation is ; Making ... more

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-13.5 ; Simplifying the given equation ; Making ... more

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1-1 ; Simplifying the given equation ; Making ... more

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The solution set is ; The numerator of the ... more

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There exists no which satisfies the given ... more

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There exists no which satisfies the given ... more

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The solution set is ; The numerator of the ... more

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No value of satisfy the given inequality. ; The ... more

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No value of satisfies the given inequality. ; The... more

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The solution set is ; The numerator of the ... more

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; The Numerator is always positive, thereby it ... more

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; The denominator of the inequality is always ... more

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; Solve the Numerator which is less than . ; ... more

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; Solve for Numerator ; Equate Denominator  ; ... more

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and ; Solve for Numerator. If is greater than ... more

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; In order to satisfy the given equation, one of ... more

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; The Numerator } is always a positive number... more

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; The numerator is a square of a function which ... more

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; Evaluate the numerator ; After evaluating the ... more

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; Evaluate the numerator. It is analysed that the... more

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; Evaluate the given function. ; To satisfy the ... more

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; Evaluate the function ; The deduced function ... more

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; Evaluate the function ; Analyse the numerator ... more

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; Evaluate the function ; From the evaluated ... more

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The Traffic Intensity is approximately 0.8730. ; ... more

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The Dimension of the Cube is . ; Let length of ... more

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; Volume of a cylinder is given by Surface area ... more

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; Here, is directly proportional to the square ... more

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1 ; Here, is directly proportional to the square ... more

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; Here, is directly proportional to and (joint... more

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; Here, is directly proportional to and ... more

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increases ; From the definition of directly ... more

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decreases ; From the definition of inversely ... more

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becomes half. ; Here, is inversely proportional ... more

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becomes one-fourth as much. ; Here, is inversely... more

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increases by 27 times. ; As proportional to , ... more

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It becomes times as much. ; As proportional to... more

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21 ; The constant for the proportionality is ... more

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; The constant for the proportionality is ... more

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; The constant for the proportionality is ... more

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4.94 ; The constant for the proportionality is ... more

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about   ; The constant for the proportionality is ... more

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about 50 times. ; Intensity is inversely ... more

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; The constant for the proportionality is ... more

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; The constant for the proportionality is ... more

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; Rate of work if work together is determined by ... more

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; Rate of work to work together is determined by ... more

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; Rate of work of student teacher is determined ... more

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; Rate of work of other one is determined by ... more

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; Rate of work to fill the tank is determined by ... more

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; To fill the tank the rate of work be hours is ... more

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Inlet pipe and outlet pipe ; Rate of work to fill... more

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hot water tap and cold water tap ; Rate of work ... more

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In the graphing calculator, check the graph of ; more

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; The set of the input values for which the ... more

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; To solve follow these stepsFirst equate the ... more

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; To solve follow these stepsFirst divide each ... more

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; To solve follow these stepsFirst divide the ... more

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The graph is accurate ; To solve follow these ... more

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; To solve follow these stepsFirst subtract 1 ... more

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Inversely ; The base is inversely proportional to ... more

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; To solve follow these stepsUse to find the ... more

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13 ; To solve follow these stepsUse to ... more

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-4 ; To solve follow these stepsUse to ... more

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-2 ; To solve follow these stepsFirst apply the ... more

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2 ; To solve follow these stepsUse to ... more

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729 ; To solve follow these stepsFirst apply the ... more

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81 ; To solve follow these stepsFirst apply the ... more

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; To solve follow these stepsFirst apply the ... more

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9 ; To solve follow these stepsFirst apply the ... more

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100 ; To solve follow these stepsFirst apply the ... more

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; To solve follow these stepsFirst apply the ... more

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4 ; For evaluating the expression we first ... more

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-64 ; For evaluating the expression we first ... more

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; For evaluating the expression we first express... more

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; For evaluating the expression we first express... more

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-9 ; For evaluating the expression we first ... more

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2 ; For evaluating the expression we first ... more

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2 ; For evaluating the expression we first ... more

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; For evaluating the expression we first express... more

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27 ; For evaluating the expression we express 9 ... more

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16 ; For evaluating the expression we express 4 ... more

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; The expression represents the cube root of . ... more

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; The expression represents the square root of... more

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; The expression is obtained by simplifying the ... more

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; The expression is obtained by simplifying the ... more

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; The expression is obtained by simplifying the ... more

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; The expression is obtained by simplifying the ... more

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; The expression has to be simplified in terms ... more

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; The expression is obtained by simplifying the ... more

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; The expression is obtained by simplifying the ... more

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; The expression is obtained by simplifying the ... more

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-1.587401052 ; The given function is computed by ... more

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-1.2457309396 ; The given function is computed by... more

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-5 ; The given function is computed by using a ... more

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-3 ; The given function is computed by using a ... more

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-2.5712815907 ; The given function is computed by... more

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-1.5157165665 ; The given function is computed by... more

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1.46459188756 ; The given function is computed by... more

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0.82630748711 ; The given function is computed by... more

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0.42529037028 ; The given function is computed by... more

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0.63677321947 ; The given function is computed by... more

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2 ; The given function is computed by using a ... more

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3 ; The given function is computed by using a ... more

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1.26746396213 ; The given function is computed by... more

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1.39901647623 ; The given function is computed by... more

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0.03225153443 ; The given function is computed by... more

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11.5941742857 ; The given function is computed by... more

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1.34 ; The required solution is obtained on ... more

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0.39 ; The required solution is obtained on ... more

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346.48 ; The required solution is obtained on ... more

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11.15 ; The required solution is obtained on ... more

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Substitute , , and in the function with the ... more

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Substitute , and in the function with the help ... more

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Substitute , and in the function with the help ... more

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Substitute , and in the function with the help ... more

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2.13066858 ; Use the calculator to evaluate the ... more

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2.08008382 ; Radical expression is an expression ... more

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; Graph has been plotted for till required value... more

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; Substitute 4 for in the right hand side of the... more

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; Substitute 5.2 for in the right hand side of ... more

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; Substitute 15 for in the equation to find the... more

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; Substitute 30,000 for in the equation to find... more

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; The weight if claw of a crab weighing over ... more

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; Average weight of a man is modelled by the ... more

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; Finding the value of and in the model . Here... more

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; According to the model given in question 69, ... more

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; Approximating in the model where is the ... more

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Determining the domain of the function of the form... more

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Domain of is : ; The given equation can be ... more

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Domain of is : ; The given equation can be ... more

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Domain of is : ; The given equation is  . Now ... more

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Domain of is : ; The given equation is  . Now ... more

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Domain of is: ; The given equation is  . Now ... more

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Domain of is : ; The given equation is  . Now ... more

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Domain of is : ; The given equation can be ... more

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 Domain of is : ; The given equation can be ... more

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Domain of f is : ; The given equation can be ... more

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The given equation can be written as . Now ... more

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 Transform the given equation by taking the factor... more

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The basic form of given function is Graph by ... more

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The basic form of given function is Graph by ... more

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The basic form of given function is Graph by ... more

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The basic form of given function is Graph by ... more

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The basic form of given function is Graph by ... more

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Given equation is in the general form of circle ... more

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Given equation is in the general form of circle ... more

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Given equation is in the general form of circle ... more

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Given equation is in the general form of circle ... more

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The equation gives a circle with a radius 4 and ... more

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The equation gives a circle with a radius 1 and ... more

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The equation gives a parabola with a opening on ... more

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The equation gives a parabola with a opening on ... more

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The equation gives a parabola with a opening on ... more

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The equation gives a parabola with a opening on ... more

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The equation gives a parabola with a opening on ... more

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The equation gives a parabola with a opening on ... more

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The equation results in a circle.  ; The functions... more

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This is an equation of a circle. ; The functions ... more

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This is an equation of a circle. ; The functions ... more

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This is an equation of a circle. ; The functions ... more

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This is an equation of a circle. ; The functions ... more

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This is an equation of a circle. ; The functions ... more

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This is an equation of a parabola. ; The functions... more

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This is an equation of a parabola. ; The functions... more

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This is an equation of a parabola. ; The functions... more

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This is an equation of a parabola. ; The functions... more

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The person did not distribute the negative sign. ... more

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The equation have two solutions. ; The roots are... more

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; Squaring both the side and simplifying using ... more

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approximately ; Squaring both the side and ... more

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; Cubing both the side and using exponent ... more

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; Cubing both the side and simplifying to obtain ... more

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First squaring both the side of the equation and ... more

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solution is correct. ; Converting the negative ... more

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are correct solutions. ; Sustitude in the ... more

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; Squaring both the side and simplifying using ... more

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; Squaring both the side and simplifying using ... more

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; Squaring both the side and simplifying using ... more

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; Squaring both the side and simplifying using ... more

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; Squaring both the side and simplifying using ... more

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; Squaring both the side and simplifying using ... more

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; Cubing both the side to get equation in and ... more

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; Cubing both the side to get equation in and ... more

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  ; Cubing both the sides and simplify to get ... more

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; Cubing both the side and simplify by moving ... more

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; Raising power of four on both the sides of to ... more

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approximately ; Raising power of four on both the... more

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; Raising power of five on both the sides of to ... more

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The solution is ; To solve this equation, first ... more

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So, the solution of the equation is ; To solve ... more

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The solution of the equation is ; To solve this ... more

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; To solve this equation, reduce this equation to... more

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; To solve this equation, reduce this equation to... more

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; To solve this equation, reduce this equation to... more

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; To solve this equation, reduce this equation to... more

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; To solve this equation, reduce this equation to... more

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; To solve this equation, reduce this equation to... more

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is the solution of the equation.  ; To solve this... more

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is the solution of the equation.  ; To solve this... more

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; Let us solve the equation Firstly squaring on ... more

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   ; Let us solve for  Firstly squaring on both ... more

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; Let us solve Subtracting on both sides and ... more

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; Let us solve Subtracting on both sides and ... more

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; Let us solve Cubing on both sides  and ... more

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; Let us solve Cubing on both sides and ... more

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; Let us solve the equation Squaring on both ... more

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  ; Let us solve the inequality Squaring on both ... more

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 No solution ; Since the term in sqaure root must ... more

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No solution  ; In the given inequality, ... more

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; Let us solve the inequality Adding on both ... more

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; Let us solve the inequality Subtracting on ... more

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; Let us simplify the equation by squaring both ... more

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; Let us simplify the equation by squaring both ... more

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; Let us simplify the equation by squaring both ... more

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; Let us simplify the equation by squaring both ... more

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; Let us simplify the equation by emoving roots ... more

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; Let us simplify the equation by squaring both ... more

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; Velocity of the particle is given by the ... more

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(approx) ; substitute the given values in the ... more

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foot ; find the derivative of the function ; find... more

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; The equation  involving roots can be converted ... more

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6 ; The cube roots and square roots can be written... more

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; The cube roots and square roots can be written ... more

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       The equation is simplified to the form of... more

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The number of real solution for the equation is 3... more

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The proposed zero of the function is 3. In ... more

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;          The polynomial has a zero for the 3. ... more

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; The polynomial is equal to . As the quadratic ... more

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; The cube roots and square roots can be written ... more

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The real solution are and . ; The graphing the ... more

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; The cube roots and square roots can be written ... more

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The solution for the equation is and is a ... more

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; The equation for calculating surface area with ... more

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            The given equation is a equation of ... more

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                       The given equation is a ... more

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and ;                   The given equation is a ... more

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Equation is . Thus, solve the equation by moving ... more

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First, stretch the graph of vertically by a ... more

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The rational function has degree 2 as its highest... more

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{-2} ; Here, the question looks for point where f(... more

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(-2,-1) ; Here the question looks for the range of... more

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2 ; We are given that y is inversely proportional ... more

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1.25 ; It is given that ; Converting it into an ... more

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847 ; It is given that, ; Converting it into an ... more

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Inversely ; Looking at the formula given we can ... more

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12.15 candela ; Denoting illumination with the ... more

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0.04 ohm ; Denoting resistance with r, diameter ... more

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1375 ; Denoting Simple Interest with S, Principal ... more

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7470 pounds ; Denoting the force with F, the ... more

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0.75 metric tons ; Denoting load with L, diameter ... more

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113.28 kilograms ; Denoting load with L,length ... more

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71.1 Kg ; Given in the question   Radius of the ... more

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2 Hours 55 Minutes ; Worker A takes 7 hours to ... more

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hours. ; The cleaning done by individual T and C ... more

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26.25 minutes. ; Work done by person in 1 minute ... more

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The solution is 12. Insert the number 144 under ... more

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The solution is -4. Insert the number -64 under ... more

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The solution is . Insert the number under the ... more

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The solution is 3. Insert the number 81 under the ... more

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The solution is . Insert the fraction under the ... more

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The solution is 2. Insert the number -32 under the... more

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The solution is . Insert the number 36 with the ... more

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The solution is 100. The calculator check gives ... more

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The solution is . The calculator check gives the ... more

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The solution is 8. The calculator check gives the ... more

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; By use of scientific calculator find the 5th ... more

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; By using scientific calculator find the 4th ... more

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Domain of the given function is ; given function... more

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At first using the given equation we need to find ... more

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4 ; Writing 1024 in terms of its factors such that... more

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64 ; Writing of the equation as power equal to ; ... more

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3,6 ; Squaring both sides of the equation.  ; ... more

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;   ; Separating constants and variables. ; ... more

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; Eliminate root function on of the equation. ; ... more

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; The equation can be written as :Rearranging the... more

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92. Undernourished. ; From the quesion, pelidisi ... more

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