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anonymous
 one year ago
What is the simplified form of ?
anonymous
 one year ago
What is the simplified form of ?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437504225310:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the common denominator of these 2 fractions: 1/x and 1/y is xy

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we can rewrite your numerator as follows: \[\frac{1}{y}  \frac{1}{x} = \frac{{x  y}}{{xy}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1similarly, we have: \[\large \frac{1}{y} + \frac{1}{x} = \frac{{...}}{{xy}}\] please complete

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1what is \[\frac{{xy}}{y}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1perfect, so we have: \[\frac{1}{y} + \frac{1}{x} = \frac{{x \cdot 1 + ...}}{{xy}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, what is: \[\frac{{xy}}{x}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1correct! so we have: \[\frac{1}{y} + \frac{1}{x} = \frac{{x \cdot 1 + y \cdot 1}}{{xy}} = \frac{{x + y}}{{xy}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1then your original expression can be rewritten as follows: \[\Large \frac{{\frac{1}{y}  \frac{1}{x}}}{{\frac{1}{y} + \frac{1}{x}}} = \frac{{\frac{{x  y}}{{xy}}}}{{\frac{{x + y}}{{xy}}}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can't we simplify that??

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! sure we can write the next step as the multiplication of the first fraction, by the inverse of the second fraction, namely: \[\Large \frac{{\frac{1}{y}  \frac{1}{x}}}{{\frac{1}{y} + \frac{1}{x}}} = \frac{{\frac{{x  y}}{{xy}}}}{{\frac{{x + y}}{{xy}}}} = \frac{{x  y}}{{xy}} \cdot \frac{{xy}}{{x + y}} = ...\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint:dw:1437504964076:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1that is a parabola whose equation is like this: \[y = a{x^2} + bx + c\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we have to determina the corfficients a, b, and c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then what would I do?? Plug in?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the coordinates of the focus, as a function of a, b, and c, are: \[F = \left( {  \frac{b}{{2a}},\frac{{1  {b^2} + 4ac}}{{4a}}} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we can write: \[\begin{gathered}  \frac{b}{{2a}} = 4 \hfill \\ \hfill \\ \frac{{1  {b^2} + 4ac}}{{4a}} = 1 \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Where would the (4,1) go?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the directrix is: \[y =  \frac{{1 + {b^2}  4ac}}{{4a}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we can write, by comparison: \[  \frac{{1 + {b^2}  4ac}}{{4a}} = 5\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now what would we do?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we have to solve this algebraic system: \[\left\{ \begin{gathered}  \frac{{1 + {b^2}  4ac}}{{4a}} = 5 \hfill \\  \frac{b}{{2a}} = 4 \hfill \\ \hfill \\ \frac{{1  {b^2} + 4ac}}{{4a}} = 1 \hfill \\ \end{gathered} \right.\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I consider the first and the third equations

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would thr answer be 1/8(x+4)^23

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1If I multiply both sides of the first equation by 4a, I get: \[1 + {b^2}  4ac =  20a\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1whereas if I multiply both sides of the third equation, by 4a, I get: \[1  {b^2} + 4ac = 4a\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1If I sum those 2 equations together, I get: \[2 =  16a\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yup! I believe in you :)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: dw:1437506094548:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now, I take the second equation: \[  \frac{b}{{2a}} = 4\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1Multiplying both sides by 2a, I can rewrite it as follows: \[b =  8a\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1substituting a, we get: \[b = \left( {  8} \right) \times \left( {  \frac{1}{8}} \right) = ...\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1correct! so we have: a= 1/8, b=1

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now I take the third equation: \[\frac{{1  {b^2} + 4ac}}{{4a}} = 1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437506420592:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is that the answer? :)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I don't know, since I solve the question now

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I substitute into the third equation, these values: a= 1/8, and b=1, so I get: \[\frac{{1  {1^2} + 4 \times \left( {  \frac{1}{8}} \right)c}}{{4 \times \left( {  \frac{1}{8}} \right)}} = 1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437506785539:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I don't understand the second fraction

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we can make these simplifications: dw:1437506923714:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so 3x^2/10y3 times 3/1

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would the answer be 9x^2/10y^3

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1that's right, since we can write our polynomial as below: \[f\left( x \right) = \left( {x + 7} \right)q\left( x \right)\] where q(x) is a appropriate polynomial

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we have to solve this equation: \[{x^2} + 2x  15 = 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then you get (x5)(x+3)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the solutions are: \[\begin{gathered} x = \frac{{  2 \pm \sqrt {{2^2}  4 \times 1 \times \left( {  15} \right)} }}{{2 \times 1}} = \hfill \\ \hfill \\ = \frac{{  2 \pm \sqrt {4 + 60} }}{2} = \frac{{  2 \pm 8}}{2} = \begin{array}{*{20}{c}} {\frac{{  2  8}}{2} =  5} \\ {\frac{{  2 + 8}}{2} = 3} \end{array} \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would those be the discontuiny?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the factorization is: \[{x^2} + 2x  15 = \left( {x + 5} \right)\left( {x  3} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! your discontinuities are located at x=5 and x=3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Which polynomial identity will prove that 16 = 25 − 9?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Difference of Squares Difference of Cubes Sum of Cubes Square of a Binomial

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think difference of squares, since I can write: \[\left( {x  y} \right)\left( {x + y} \right) = {x^2}  {y^2},\quad x = 5,y = 3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no. For the equation 16= 259

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1yes! please substitute x=5 and y=3, what do you get?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: we have the subsequent steps: \[\begin{gathered} \left( {5  3} \right)\left( {5 + 3} \right) = {5^2}  {3^2} \hfill \\ 2 \times 8 = 25  9 \hfill \\ 16 = 25  9 \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yay! Solve 3x2 + 13x = 10.

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I rewrite your equation as follows: \[3{x^2} + 13x  10 = 0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0use the quad. formula

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so I get: \[\begin{gathered} x = \frac{{  13 \pm \sqrt {169 + 4 \times 3 \times 10} }}{{2 \times 3}} = \hfill \\ \hfill \\ = \frac{{  13 \pm \sqrt {289} }}{6} = \begin{array}{*{20}{c}} {\frac{{  13 + 17}}{2} = 2} \\ {\frac{{  13  17}}{2} =  15} \end{array} \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1oops.. I have made an error

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1\[\begin{gathered} x = \frac{{  13 \pm \sqrt {169 + 4 \times 3 \times 10} }}{{2 \times 3}} = \hfill \\ \hfill \\ = \frac{{  13 \pm \sqrt {289} }}{6} = \begin{array}{*{20}{c}} {\frac{{  13 + 17}}{6} = \frac{2}{3}} \\ {\frac{{  13  17}}{6} =  5} \end{array} \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0just factor instead of using the formula bc that diddn't work for me

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What are the zeros of the polynomial function f(x) = x3 + x2 − 20x?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we have to factor out x, so we can write: \[{x^3} + {x^2}  20x = x\left( {{x^2} + x  20} \right)\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1now I solve the quadratic equation with the standard formula: \[\begin{gathered} {x^2} + x  20 = 0 \hfill \\ x = \frac{{  1 \pm \sqrt {1 + 4 \times 1 \times 20} }}{{2 \times 1}} = \frac{{  1 \pm 9}}{2} = \hfill \\ \hfill \\ = \begin{array}{*{20}{c}} {\frac{{  1  9}}{2} =  5} \\ {\frac{{  1 + 9}}{2} = 4} \end{array} \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1437508513154:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1the common denominator is: (x5)(x+5)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1so we can simplify your expression as follows: \[\frac{{\left( {4x + 2} \right)\left( {x + 5} \right)  \left( {3x  1} \right)\left( {x  5} \right)}}{{\left( {x + 5} \right)\left( {x  5} \right)}} = ...\] please complete my computation

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I got a different result

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1we can write this: \[\begin{gathered} \frac{{\left( {4x + 2} \right)\left( {x + 5} \right)  \left( {3x  1} \right)\left( {x  5} \right)}}{{\left( {x + 5} \right)\left( {x  5} \right)}} = \hfill \\ \hfill \\ = \frac{{4{x^2} + 22x + 10  3{x^2} + 16x  5}}{{\left( {x + 5} \right)\left( {x  5} \right)}} = ... \hfill \\ \end{gathered} \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x^2+38x+5/(x5)(x+5)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now what do we do?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1I think that we have completed our exercise

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0KK :) tHANKS SO MUCH FOR ALL YOU HELP!!!!!!! <3 <3 <3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0<3 dOZENS OF HEARTS BECAUSE YOU'RE AWESOME!!!!!!! :D
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