11

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=24 BGCOLOR="#000000" TEXT="#F7F7FF"> <div> <FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>M</B></FONT><FONT SIZE="4" COLOR="#FFFFFF" FACE="Georgia" ><B>atemáticas de la U</B></FONT><B> (MatU)  | </B><A HREF="http://www.jcbmat.com/" TARGET="_top" TITLE="http://www.jcbmat.com/"><U><B>Home</B></U></A><B> | </B><A HREF="index.htm" TARGET="_top" TITLE="Álgebra de Baldor"><U><B>Algebra de Baldor</B></U></A><B> |  </B><A HREF="id1076.htm" TARGET="_top" TITLE="Índice temático"><U><B>Índice temático</B></U></A><B>  |  </B><A HREF="id1073.htm" TARGET="_top" TITLE="Lista"><U><B>Lista de Ejercicios</B></U></A><B> |</B></div> <div> </div> </td> </tr><tr> <td valign="top" rowspan="2" width=165 BGCOLOR="#FFFFFF" TEXT="#080000"> <bR> <div> <B> <script async src="//pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:160px;height:600px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="3073775660"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </B></div> </td> <td valign="top" height=432 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <B>11</B></div> <div> <B>V a l o r   n u m é r i c o </B></div> <div> <B>Valor numérico de expresiones simples</B></div> <bR> <div>  <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js"></script>  <ins class="adsbygoogle" style="display:inline-block;width:970px;height:250px" data-ad-client="ca-pub-1578463498418701" data-ad-slot="8553279920"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script>  </div> <div>        El valor numérico de una expresión algebraica es el número resultante cuando se sustituyen los valores numéricos dados para las variables en la expresión y se realiza la operación indicada. En otras palabras, es el resultado obtenido al evaluar la expresión con valores concretos para sus variables.</div> <div> P r o c e d i m i e n t o :</div> <div> Para encontrar el valor numérico de una expresión algebraica, se deben seguir los siguientes pasos:</div> <div> 1.<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Sustituir los valores numéricos dados para las variables en la expresión.</FONT></div> <div> 2.<FONT SIZE="4" COLOR="#000000" FACE="Bell MT" > Realizar las operaciones indicadas, respetando las reglas matemáticas.</FONT></div> <div> 3. <FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >Simplificar la expresión todo lo posible.</FONT></div> <div> Por ejemplo, si tenemos la expresión algebraica 2x + 3y y se nos dan los valores numéricos x = 4 e y = 5, podemos encontrar su valor numérico de la siguiente manera:</div> <DIV ALIGN="LEFT"></DIV> <div> 2(4) + 3(5) = 8 + 15 = 23</div> <div> Por lo tanto, el valor numérico de la expresión 2x + 3y cuando x = 4 e y = 5 es 23. </div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Enunciados de los problemas del Ejercicio 11</B></div> <bR> <div> <B>          S</B><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" >olución en imagen <IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> y o video <IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"> de los dieciocho problemas del Ejercicio 11:</FONT></div> <bR> <div> <FONT SIZE="4" COLOR="#0099FF" FACE="Bell MT" ><B>H</B></FONT>allar el valor numérico de las expresiones siguientes para <I>a</I> =1, <I>b</I> =2, c = 3, <I>m </I>=1/2, <I>n </I>=1/3, <I>p </I>=1/4:</div> <div> <FONT SIZE="4" COLOR="#111111" FACE="Bell MT" ><IMG SRC="739f3b150.gif" border=0 width="59" height="21" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#1" TITLE="11"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/Z0YWD6Eg9Ss" TARGET="_top" TITLE="https://youtu.be/Z0YWD6Eg9Ss"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a051170.gif" border=0 width="81" height="23" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#2" TITLE="11"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/Z0YWD6Eg9Ss?t=1m29s" TARGET="_top" TITLE="https://youtu.be/Z0YWD6Eg9Ss?t=1m29s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a148170.gif" border=0 width="72" height="23" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#3" TITLE="11"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/Z0YWD6Eg9Ss?t=3m44s" TARGET="_top" TITLE="https://youtu.be/Z0YWD6Eg9Ss?t=3m44s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a2651b0.gif" border=0 width="101" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#4" TITLE="11"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/Z0YWD6Eg9Ss?t=6m7s" TARGET="_top" TITLE="https://youtu.be/Z0YWD6Eg9Ss?t=6m7s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a364300.gif" border=0 width="100" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#5" TITLE="11"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/0t4kGqya3hM" TARGET="_top" TITLE="https://youtu.be/0t4kGqya3hM"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a467300.gif" border=0 width="103" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#6" TITLE="11"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/0t4kGqya3hM?t=3m47s" TARGET="_top" TITLE="https://youtu.be/0t4kGqya3hM?t=3m47s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <FONT SIZE="4" COLOR="#111111" FACE="Bell MT" ><IMG SRC="73a5591b0.gif" border=0 width="89" height="27" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="#7" TITLE="11"><U><IMG SRC="598018180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://youtu.be/0t4kGqya3hM?t=7m40s" TARGET="_top" TITLE="https://youtu.be/0t4kGqya3hM?t=7m40s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a677300.gif" border=0 width="119" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/0t4kGqya3hM?t=10m30s" TARGET="_top" TITLE="https://youtu.be/0t4kGqya3hM?t=10m30s"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a7511c0.gif" border=0 width="81" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/Orz9ihy7_rg" TARGET="_top" TITLE="https://youtu.be/Orz9ihy7_rg"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a87c1c0.gif" border=0 width="124" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/83YV8YGj7tQ" TARGET="_top" TITLE="https://youtu.be/83YV8YGj7tQ"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >       <IMG SRC="73a97b1c0.gif" border=0 width="123" height="28" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/Rou9u-buwck" TARGET="_top" TITLE="https://youtu.be/Rou9u-buwck"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><FONT SIZE="4" COLOR="#111111" FACE="Bell MT" >      <IMG SRC="73aa49300.gif" border=0 width="73" height="48" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></FONT><A HREF="https://youtu.be/xa5FWWvfIDw" TARGET="_top" TITLE="https://youtu.be/xa5FWWvfIDw"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <IMG SRC="73ab5d340.gif" border=0 width="93" height="52" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/_7YMaFXEsVo" TARGET="_top" TITLE="https://youtu.be/_7YMaFXEsVo"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73ac4c5c0.gif" border=0 width="76" height="92" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/3ew0ap7g3-M" TARGET="_top" TITLE="https://youtu.be/3ew0ap7g3-M"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73ad4d330.gif" border=0 width="77" height="51" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/-zWOgBXC5p8" TARGET="_top" TITLE="https://youtu.be/-zWOgBXC5p8"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73ae6b370.gif" border=0 width="107" height="55" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/YjlP3Zn4doE" TARGET="_top" TITLE="https://youtu.be/YjlP3Zn4doE"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73af78350.gif" border=0 width="120" height="53" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/9nYVk2m0kWc" TARGET="_top" TITLE="https://youtu.be/9nYVk2m0kWc"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT>       <IMG SRC="73b07f5c0.gif" border=0 width="127" height="92" ALT="MathType 6.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"><FONT SIZE="4" COLOR="#000000" FACE="Bell MT" ><A HREF="https://youtu.be/HiPz485AnAA" TARGET="_top" TITLE="https://youtu.be/HiPz485AnAA"><U><IMG SRC="598118180.jpg" border=0 width="24" height="24" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></FONT></div> <bR> <div>        Hay que tener presente que el valor numérico de una expresión algebraica puede variar dependiendo de los valores numéricos dados para las variables.</div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <B>Lista de reproducción sobre las soluciones del Ejercicio 11</B></div> <bR> <div> <B> <iframe width="853" height="480" src="https://www.youtube.com/embed/videoseries?list=PLq_SQwoOZHo2YjvjSy_PTaKU_wn5LP8g8" frameborder="0" allowfullscreen></iframe>  </B></div> <bR> <div> <B>H</B><FONT SIZE="4" COLOR="#000000" FACE="Times New Roman" >allar el valor numérico de las expresiones siguientes para:</FONT></div> <DIV ALIGN="LEFT"></DIV> <div> <IMG SRC="739e08290.gif" border=0 width="264" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="1"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>1</div> <div> <IMG SRC="58c4606c0.gif" border=0 width="608" height="108" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="2"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>2</div> <div> <IMG SRC="58c5998b0.gif" border=0 width="665" height="139" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="3"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>3</div> <div> <IMG SRC="58c6eced0.gif" border=0 width="748" height="237" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="4"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>4</div> <div> <IMG SRC="58c728130.gif" border=0 width="808" height="275" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="5"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>5</div> <div> <IMG SRC="58c8071b0.gif" border=0 width="775" height="283" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="6"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>6</div> <div> <IMG SRC="58c9380c0.gif" border=0 width="824" height="268" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div>  <A NAME="7"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A>7</div> <div> <IMG SRC="58cae3d70.gif" border=0 width="739" height="215" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <bR> <DIV ALIGN="LEFT"></DIV> <div> <A HREF="http://twitter.com/Calculo21" TARGET="_top" TITLE="http://twitter.com/Calculo21"><U><IMG SRC="2fc828280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="http://www.facebook.com/juan.beltran.58511" TARGET="_top" TITLE="http://www.facebook.com/juan.beltran.585"><U><IMG SRC="76fa28280.gif" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A><A HREF="https://www.youtube.com/user/MatematicaAplicadas" TARGET="_top" TITLE="https://www.youtube.com/user/MatematicaA"><U><IMG SRC="2fca28280.jpg" border=0 width="40" height="40" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <bR> <div> Por: <FONT SIZE="4" COLOR="#FF9900" FACE="Times 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