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This can be tor, "checked easily by multiplication. or, F000002922050axy+axultiplication. or, F000002922050\ab\x+altiplication. or, F000002922050ax+\ab\wxiplication. or, $44 2 2b\x+\ac\y). l its terms #Factoring should always be checked rms by multiplying out the answer. ked rms F000002829000\ab\x+axy answer. ked rms F001004929050axy+\ab\y answer. ked rms F000002829000\ac\xy+\ab\yzwer. ked rms $43 2 23456 :61c\xy+\ab\yzwer. $42 2 23456 :61HʻN:QԶǗڟ `Uf7'A sum can be factored if all its terms contain a common factor. ll its terms Remember, px+py = p(x+y). l its terms F001102929050ax+ay p(x+y). l its terms F000002629050\ab\x+\ac\y). l its terms $33 2 23456 :61 nasaubnylyAAAAAAAAAAAAAAAAA.............................DE1α.TEXTGԱ[ڱ:mg!No negative numbers here, please.here.se.s.ı.CODE1α.TEXTGԱ[ڱ:mg$We multiply here (no mixed numbers).e.se.s.ı.CODE1α.TEXTGԱ[ڱ:mg&Press [RETURN] to end your expression.se.s.ı.CODE1α.TEXTGԱ[ڱ:mgA right parenthesis is needed.ression.se.s.ı.CODE1α.TEXTGԱ[ڱ:mg'Use [CTRL] D to start your denominator.e.s.ı.CODE1α.TEXTGԱ[ڱ:mg Use [CTRL] # to complete your $.inator.e.s.ı.CODE1α.TEXTGԱ[es the negative of the expression.ariables.gKWrite each term with coefficient first and variables in alphabetical order.es.g?Combine signs if possible, and move signs to standard position.tical order.es.g Multiply.igns if possible, and move signs to by 1 gives the original expression.of the variables.gEMultiplying an expression by -1 gives the negative of the expression.ariables.gOmit zero term(s).ression by -1 gives the negative of the expression.ariables.gCompute power(s)..ression by -1 givto the power 0 is equal to 1.y.g these values of the variables.g;The first power of any expression is the expression itself.s of the variables.g'Any expression multiplied by 0 gives 0.e expression itself.s of the variables.g=Multiplying an expressionrm standard polynomial simplifications.y.g these values of the variables.g$Rewrite expression in standard form.cations.y.g these values of the variables.gSimplify term(s).n in standard form.cations.y.g these values of the variables.g,Any expression .g,Type only letters from the given expression.y.g these values of the variables.g Start with the given expression. expression.y.g these values of the variables.gThis problem is finished.ession. expression.y.g these values of the variables.g,Perfo variables.g%These expressions are not equivalent.parately.g these values of the variables.gThat seems correct so far.equivalent.parately.g these values of the variables.g#This expression is too complicated.t.parately.g these values of the variablesues of the variables.g$Your simplification seems incorrect.eparately.g these values of the variables.g!This equation is too complicated.ct.eparately.g these values of the variables.g$ is not used in this problem.ed.ct.eparately.g these values of the these values of the variables.gAn equation needs an "=" sign.. and #.TURN].ing these values of the variables.g%Replace @ by your numerical solution..TURN].ing these values of the variables.g.Simplify each side of the equation separately.g these valETURN].ing these values of the variables.g$, then the value of this expression RETURN].ing these values of the variables.g&Please type a number between -# and #.TURN].ing these values of the variables.gAll right, that's close enough. and #.TURN].ing its points.st.using these values of the variables.gHere is how xy is plotted.n its points.st.using these values of the variables.g We cannot plot xy on the screen.points.st.using these values of the variables.g,Find xy using arrows^v. Then press [Ris the same as the first.using these values of the variables.g"These expressions seem equivalent.e first.using these values of the variables.g'These expressions are not always equal.st.using these values of the variables.g'To draw the xygraph we join a value for each variable. above using these values of the variables.g)Now you choose a value for each variable. using these values of the variables.gNHere is the value of the above expression using these values of the variables.g*The second graph g*When the cursor returns, please try again.ey..CODE1α.TEXTGԱ[ڱ:mgNEvaluate the expression in the box above using these values of the variables.gHere is the correct value. the box above using these values of the variables.g"Here isڱ:mgPress [#-arrow] to $.ete your $.inator.e.s.ı.CODE1α.TEXTGԱ[ڱ:mgPress the "#" key. $.ete your $.inator.e.s.ı.CODE1α.TEXTGԱ[ڱ:mg-Hold down [CTRL] while you press the "#" key..CODE1α.TEXTGԱ[ڱ:mstandard position.tical order.es.gIAn expression times itself is written as a "square" using the exponent 2.r.es.g?Powers of the same base are multiplied by adding the exponents.xponent 2.r.es.gAdd or subtract.me base are multiplied by adding the exponents.xponent 2.r.es.g@Combine similar terms (terms having exactly the same variables).ponent 2.r.es.gFRearrange terms so that those with the higher powers of ^ occur first. 2.r.es.gRemove common factors.t those with the higher powers of ^ occur for @:for @ in the original equation.. -1).@.on.g:Here is the approximate value of @ where the graphs cross.equation.. -1).@.on.g6The graphs are identical, so there are many solutions.oss.equation.. -1).@.on.g3The graphs are parallel, so there are no ys true, so @ can be any number.as no solution. -1).@.on.gC check by substituting the solution for @ in the original equation.. -1).@.on.g$ solve the following equation for @:for @ in the original equation.. -1).@.on.gWe graph each side of quation fsign of each side of the equation (multiply both sides by -1).@.on.g5Multiply both sides by the denominator(s) and cancel.y both sides by -1).@.on.gDThis equation is not true, so the original equation has no solution. -1).@.on.g5This equation is alwaranspose a term to separate terms containing @ from terms without @.tself.on.gKSubtract a term on each side to separate terms with @ from terms without @.on.gFAdd a term on each side to separate terms with @ from terms without @.ut @.on.gIChange the .ion.g>Divide fractions by inverting the denominator and multiplying.ancellation.ion.gEDivide both sides by the multiplier of @ to prepare for cancellation.tion.ion.gKDivide both sides by the multiplier of @, and cancel to obtain @ by itself.on.gETmultiplication.g)Rearrange terms to prepare for factoring.r parentheses to show multiplication.gJFactor and simplify numerator and denominator to prepare for cancellation.ion.g>Multiply fractions by multiplying numerators and denominators.ancellationor and denominator.tor...gPerform the division.tor by changing signs of numerator and denominator.tor...gReplace variables by numbers.hanging signs of numerator and denominator.tor...gNReplace variables by numbers, with dots or parentheses to show h the terms of another polynomial..gICancel monomial factors common to both the numerator and the denominator.ial..gLCancel a polynomial factor common to both the numerator and the denominator...gHSimplify the denominator by changing signs of numerataising each factor to that power.).st terms..g8Compute a power of a power by multiplying the exponents.hat power.).st terms..gMRewrite a polynomial so that its terms match the terms of another polynomial..g#Remove parenthesized common factor.rms matces be factored in the form (a+b)(c+d). and last terms..g/Remove common factors from two terms at a time.rm (a+b)(c+d). and last terms..gDFour terms can sometimes be factored using ac+bc+ad+bd = (a+b)(c+d).st terms..gBCompute a power of a product by rtors so that monomials precede polynomials.her parentheses..r.es.gCThe difference of the squares of a and b is factored as (a-b)(a+b).eses..r.es.gMRewrite the middle term by factoring the product of the first and last terms..g=Three terms can sometimtiply monomials by multiplying coefficients and combining variables.2.r.es.g:Multiply each term in the parentheses by the term outside.ng variables.2.r.es.gHMultiply each term in parentheses by each term in the other parentheses..r.es.g8Rearrange faces.gSubtract by changing signs.n by removing parentheses.on factor. first. 2.r.es.g&Add a negative quantity by subracting.ng parentheses.on factor. first. 2.r.es.gRemove unneeded parentheses.ubracting.ng parentheses.on factor. first. 2.r.es.gGMulirst. 2.r.es.g?Make the first term positive by removing -1 as a common factor. first. 2.r.es.g(Rewrite the power as a repeated product. -1 as a common factor. first. 2.r.es.g5Add parenthesized expression by removing parentheses.on factor. first. 2.r.solutions.ns.oss.equation.. -1).@.on.g%So the solution is approximately @ = no solutions.ns.oss.equation.. -1).@.on.g'These lines meet somewhere off screen, o solutions.ns.oss.equation.. -1).@.on.g3so the solution of this equation is off the screen.ns.oss.equation.. -1).@.on.g3 to have the same solution as the earlier equation.ns.oss.equation.. -1).@.on.g&Now let's resume solving our equation.ier equation.ns.oss.equation.. -1).@.on.g/ The solution checks in the original equation.ion.ns.oss.equ$ 6n "SIMPMAINTHELP TINPS TOUPS TSIMP INITPROBENDSIMP SEGPROC multiplication by right of the "base" g subtracted, umbers..g&However, it does not mean the same as ght of the "base" g subtracted, umbers..g ynsluybaanAAAAAAAAAAAAAAAAA..............................rall result is that we moved by each number being subtracted, umbers..g8(However, you may see a shorter way to do this problem.)g subtracted, umbers..g8, which is written above and to the right of the "base" g subtracted, umbers..g#, means repeated gIn this problem, we change bers.sign of each number being subtracted, umbers..gLet's start from 0. change bers.sign of each number being subtracted, umbers..gSince we started at 0, nge bers.sign of each number being subtracted, umbers..g'the ovenumbers..g*so the answer is 0, and no sign is needed. longer" number.hs" of the numbers..gFWe can subtract by changing the sign of each number being subtracted, umbers..g and then adding the new numbers.sign of each number being subtracted, umbers..s" of the numbers..g:The sign of the answer is the sign of the "longer" number.hs" of the numbers..g&In this problem, the longer number is the "longer" number.hs" of the numbers..g+In this problem, both are the same length, longer" number.hs" of the n expression is undefined.)n.g:Adding or subtracting 0 leaves the other number unchanged.ion is undefined.)n.gHTo add numbers with the same signs, we add the "lengths" of the numbers.ed.)n.gMTo add numbers with opposite signs, we subtract the "length signs are elect one correct answer.on.g+(0 divided by any number except 0 gives 0.)ns are elect one correct answer.on.gL(Remember to hold down [CTRL] and type "U" when an expression is undefined.)n.g)We add zero by moving a distance of zero." when always 0.tion.is 1.d.)ength zero.ult is zero.@.on.gKSince 0 times any number is 0, we have no way to select one correct answer.on.g$(Division by 0 is always undefined.)ve no way to select one correct answer.on.g2(In general, dividing two numbers whoseis 1, only 1 factor is needed.)ength zero.ult is zero.@.on.g/Any non-zero number raised to the 0 power is 1.d.)ength zero.ult is zero.@.on.g*Division is the reverse of multiplication.is 1.d.)ength zero.ult is zero.@.on.g%since 0 times any number is a for the number zero.o draw an arrow of length zero.ult is zero.@.on.gTherefore, its length is about draw an arrow of length zero.ult is zero.@.on.g*An exponent means repeated multiplication.row of length zero.ult is zero.@.on.g2(When the exponent &have no operation symbol between them. (*).cause the two numbers .). -1).@.on.gIHowever, this addition is repeated zero times, and so the result is zero.@.on.g=A dot or a small "x" is used to draw an arrow of length zero.ult is zero.@.on.gIt stands).@.on.gC(In general, any multiplication using 0 always gives the answer 0.). -1).@.on.gAThis expression requires multiplication, because the two numbers .). -1).@.on.g+are separated by a multiplication sign (*).cause the two numbers .). -1).@.on.gation.. -1).@.on.g3Replace @ by the numerical solution obtained above.ns.oss.equation.. -1).@.on.g)These equations have different solutions.ned above.ns.oss.equation.. -1).@.on.g%Sorry, not enough room on the screen.ons.ned above.ns.oss.equation.. -1 ۍ ڟˡڨٚ,ō zݤaڤaܤaۤaߓaɍ? 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You have completedall the lessons iצStart DENOMINATOR9צ[CTRL] BEnd denom. (go to BASELINE)׮9v; á Review Beginn ing lesson  .š TYPING REMINDERS[ESC] צSEE TYPING REMINDERS9? צ ASK FOR HELP9ǕɡCצ[o multiply)9[CTRL] FצFinished (no more steps)9 [up-arrow]תPb צ[CTRL] PPBegin Power (exponent)׮9צ [down-arrow]Pb [CTRL] BתPצEnd power (go to Baseline)9R:צ[CTRL] NStart NUMERATOR׮9[CTRL] D[ESC] for typing instructions,' and again to return to your problem. 7צ$For example, please press [ESC] now.& 6,٪PتP,צ . . . . . .U ,U:9צ[CTRL] XErase your answer׮9* צType a dot (t%You can skip many steps in the longer problems with a little practice.5,Ï7 צ IMPORTANT REMINDERSצ When solving a problem, you may:7!1. type a question mark for help,7'2. press !ʃ5ʃ52aƁ5a5" á,Ab j+2;ؕ !There are many correct ways to docomplicated problems.I'll accept any correct steps.צAlways look for shortcuts.!aƁ5a5adkl̃5ʃ5̃6ʃ6P̃7ʃ5bܓ ʃ6cš3ʃ6bʃ6bޡ1- ʃ7Ś4ʃ6eʃ7ʃ6dʃ6bX ʃ5!ɄY ʃ5ʃ5!ons.צYou will begin with lesson."During a lesson, when the flashingצ!cursor is visible, you can changeצ%to a different lesson by holding downצ%the [CTRL] key and typing "Z" and "/"צin rapid succession.$4쥁b ȄÍ P2lۢPȍFڣ2ˡ2ٚܢá%ܢܢ ܢܢܢ f1lȡ٢Uؤ٢U٣c٢c-B3ˡSצ'You are scheduled to skip some lessselect a different lesson.lesson titles.(צ For lesson, just press [RETURN].LESSON ( toצ) ? "  10ġɡ ݂0š  áښݓa fƁƁ"šʁʁōʁʁP܍ʁÍʁʁ ŴʁʁȄʁʁƁ!.ܓf - צYou'll now do lesson number,צ%unless you ous record of thisstudent (Y or N) ?"ڳ@@NnÍ- 0ۡ l/ܶ ލ0ݍݡ,ۡ lצX, ad kݓlcz..ĺʁṔ)adɩl"ák!* 2,lڢP ZY٢٢٢š٢ ٢Ŷō< v/lۢׯThis disk belonged toۢ'May I erase the previice problems on this material.ǰ b'SYSTEM.STARTUP.תPa'צPlease return your disksצto your instructor or tutor.  To run another program,insert the appropriate disk.pV Fn this portionof the course.áY&However, this demonstration version isצ'much shorter than the complete version.adYour next lesson will be*Then you'll return to*!˥bDinstruction and(#practRETURN]End your answer9[SHIFT] צType an upper symbol9 [left-arrow]צErase a character9,ġ [CTRL] UצType "Undefined"9;ġ:Ǖġ;&צOne moment, please. $|8š;SOLVEׯ;SIMPMׯ넡5ń68a ;'쥁b ;;;bتPRتPR צ .۪P٪P. ء&m K"form or bUSYSTART  @ ""F#ڨ&_# #" 0!  ,٪PتP&,Press [] to continue.>$تPRETURN$+! T* Pۡo! ?צPZ"ٹPlease Then  #צ!hold down the [CONTROL] or [CTRL]צ$key while you press the [RESET] key.ء لء  /ˡ8ء &<   r d ۡo s  sp..//P0.áDisk is write-protected.צ System error. o!X O:%%,}  t 쥁f!ڢ!ؓ!ޢ Äޢɷޢ÷s%.......ת ۢ" INTROׯÄ0ܣ'á'_ K ^שr r rr  X  šړۓrؤrؤ؏؂rš-8 errXr,-.ݤݤݤáݤše g4[uld prophesy, but that the weary and cold hand of death lies on my tongue.USYSTART m!J,VfrpP z , n Z`$<F.&T,z$p6Xl0 X8v;adsworth, Inc.ת(צBelmont, California 94002.(צa division of Wadsworth, Inc.(%Pascal Runtime System (C) 1979, 1980,ת(צ%1983 and 1985 by Apple Computer, Inc.("Portions of this software (C) 1979ת(yצby University of California.(dTelephone: 4O8-373-O728ת(  ;+ b)y any means -- electronicת(6#mechanical, photocopying, recordingת(!צ!or otherwise -- without the prior( $written permission of the publisher,ת((C) 1986 by Wadsworth, Inc.ת(צBelmont, California 94002.(צa division of Wadsworth, uld prophesy, but that the weary and cold hand of death lies on my tongue.?h"%&p| 5r7\r:\)CF~rc;8[- e/Gro4XrX;rE,2E- t\ݰ}#bk4ݤ_ á&ݤ4_q˦eiGlXguT4#thisstudent (Y or N) ?!ڳ@@NnÍ- 0ۡ p/ܶ ލ0ݍݡ*ۡ pצX, eh oݓpax..ṕʁṔݓehɩp" šo!.,pڢPZY٢٢٢š٢ ٢Ŷō< v/pۢׯThis disk belonged toۢ'May I erase the previous record of ms on this material.ǰ f'SYSTEM.STARTUP.תPe'צPlease return your disksצto your instructor or tutor.  To run another program,insert the appropriate disk.pV F)etionof the course.áY&However, this demonstration version isצ'much shorter than the complete version.ehYour next lesson will be*Then you'll return to*!˥fDinstruction and(#practice probleer to the Algebra Mentor١Instructor Manual orצStudent Workbook for Rl(-٨تP.//P00ġ lesson/e0ڕ.ZD* #CONGRATULATIONS. You have completedall the lessons in this porration צ student diskġ ئf .(צin driveצ and close the door.&تPR צ'צThis disk is assigned to  8צ#04:P 0 0&'تP Ref&$ء צESC$!á  "%Versiond.d  * צ & š"STUDENT DISK #ئ NEEDED.Please insert ɡ any צAlgebra Mentorá!š non-צ demonst @ ""F#ڨ&_# #" 0!  ,٪PتP&,Press [] to continue.>$تPRETURN$+! T* Pۡo! ?צPZ"ٹPlease Then  #צ!hold down the [CONTROL] or [CTRL]צ$key while you press the [RESET] key.ء لء  /ˡ8ء &<   r d ۡo s  sp..//P0.áDisk is write-protected.צ System error. o!X O:%%,}  t 쥁f!ڢ!ؓ_ޢV }ޢ9퀬_?4(|X......ת ۢ" INTROׯÄ0ܣ%'&`'l_ 6yK ݣשrr Drr$X: -š2 jƁƁ" šʁʁōʁʁP܍ʁÍʁʁ ŴʁʁȄʁʁƁ!.ܓf - צYou'll now do lesson number,צ%unless you select a different lesson.lesson titles.(צ For lesson, just press [RETURN].LESSON ( toצ) ? !  10ġɡ ݂0š  áښȄÍ       J,VfrpB l  b| HN*>nZ6\RVV r0 X2v;adsworth, Inc.ת(צBelmont, California 94002.(צa division of Wadsworth, Inc.(%Pascal Runtime System (C) 1979, 1980,ת(צ%1983 and 1985 by Apple Computer, Inc.("Portions of this software (C) 1979ת(}צby University of California.(hTelephone: 4O8-373-O728ת(  ?+ f)q!:#mechanical, photocopying, recordingת(%צ!or otherwise -- without the prior($written permission of the publisher,ת((C) 1986 by Wadsworth, Inc.ת(צBelmont, California 94002.(צa division of Wadsworth, Inc.(%Pascal Runtime Sy?bتPRتPR צ .۪P٪P. ء&q O"form or by any means -- electronicת([SHIFT] צType an upper symbol9 [left-arrow]צErase a character9,ġ [CTRL] UצType "Undefined"9;ġ:Ǖġ;%צOne moment, please. $|8š?SOLVEׯ?SIMPMׯ넡5ń68e ?'쥁f ??RL] BEnd denom. (go to BASELINE)׮9v; á Review Beginn ing lesson  .š TYPING REMINDERS[ESC] צSEE TYPING REMINDERS9? צ ASK FOR HELP9ǕɡCצ[RETURN]End your answer9inished (no more steps)9 [up-arrow]תPf צ[CTRL] PPBegin Power (exponent)׮9צ [down-arrow]Pf [CTRL] BתPצEnd power (go to Baseline)9R:צ[CTRL] NStart NUMERATOR׮9[CTRL] DצStart DENOMINATOR9צ[CTs,' and again to return to your problem. 7צ$For example, please press [ESC] now.% 6,٪PتP,צ . . . . . .U ,U:9צ[CTRL] XErase your answer׮9* צType a dot (to multiply)9[CTRL] FצF in the longer problems with a little practice.&5,Ï7 צ IMPORTANT REMINDERSצ When solving a problem, you may:7!1. type a question mark for help,7'2. press [ESC] for typing instruction42eƁ4e4,` \+2;ؕ !There are many correct ways to docomplicated problems.I'll accept any correct steps.צAlways look for shortcuts.%You can skip many stepse4ehop̃4ʃ4̃5ʃ5P̃6ʃ4fܓ ʃ5cš3ʃ5bʃ5bޡ1- ʃ6Ś4ʃ5eʃ6ʃ5dʃ5bX ʃ4!ɄM ʃ4ʃ4!!ʃ4ʃill begin with lesson."During a lesson, when the flashingצ!cursor is visible, you can changeצ%to a different lesson by holding downצ%the [CTRL] key and typing "Z" and "/"צin rapid succession.&$4쥁f !eƁ4 P2pۢPȍFڣ2ˡ2ٚܢá%ܢܢ ܢܢܢ f1pȡ٢Uؤ٢U٣c٢c-B3ˡSצ'You are scheduled to skip some lessons.צYou w                  $PROCEDURE WSTRING(S: STRING); $PROCEDURE CHARTYPE(MODE: INTEGER); "IMPLEMENTATION X E )4#i JL` T$Q%P)Q I L`#JI`'  I` I0ݩ(0/,",i8i#Hiihifi`i,i,3iPII4ifH8H hIiH CREENBIT(X,Y: INTEGER): BOOLEAN; $PROCEDURE DRAWBLOCK(VAR SOURCE; ROWSIZE,XSKIP,YSKIP,WIDTH,HEIGHT, 8XSCREEN,YSCREEN,MODE: INTEGER); $PROCEDURE WCHAR(CH: CHAR); ` 8`*UH)JJh & & fDURE PENCOLOR(PENMODE: SCREENCOLOR); $PROCEDURE TEXTMODE; $PROCEDURE GRAFMODE; $PROCEDURE FILLSCREEN(FILLCOLOR: SCREENCOLOR); $PROCEDURE VIEWPORT(LEFT,RIGHT,BOTTOM,TOP: INTEGER); $FUNCTION TURTLEX: INTEGER; $FUNCTION TURTLEY: INTEGER; $FUNCTION S $TYPE $ SCREENCOLOR=(none,white,black,reverse,radar, 3black1,green,violet,white1,black2,orange,blue,white2); & &FONT=PACKED ARRAY[0..127,0..7] OF 0..255; & $VAR &FONTPTR:^FONT; $ $PROCEDURE INITTURTLE; $PROCEDURE MOVETO(X,Y: INTEGER); $PROCEتPDŽE  RDŽE ٪P E   (   >6Vz.@~CODE.CODEACKE.CODE1.TEXTG[:mƳgEʷ  تP,,PT  @ \ ܡ@ ܡڡ݂P تPǜE  RCL<<ʷZ\\ʷxR` [E :E BODY3 WRITELINUNITPARTCOMPOPTINUMSTRIN\\ER.CODE1\.TEXTGb[h:mng>ʷB `^ph.CODE.CODEACKE.CODE1.TEXTG[:mƳgEʷ "PROCEDURE SETCHAIN(TYTLE:STRING); "PROCEDURE SETCVAL(VAL:STRING); "PROCEDURE GETCVAL(VAR VAL:STRING); "PROCEDURE SWAPON; "PROCEDURE SWAPOFF; "PROCEDURE SWAPGPON;  IMPLEMENTATION E 2L 8<=>F?A:CGJJLʷ"L(E(c)1987 by John C. Miller; 1983,1985 by Apple Computer; 1979 by UCSD.D < #',1=R DJJN CHAINSTUSHORTGRASHORTGRAGRAFA GRAFA GRAFC CONIO SHOBL STRAP EXMAK ALGIO EVALU AXDRW LINXT TABGR  "%+0;CIMd, stored in a retrieval"system except as an essential step'in its execution, or transcribed in anyBrooks/Cole Publishing Co. 555 AbregoMonterey, CA, 93940, Student diskLicensed for use only at%Please respect the license agreement. Published by BrnP6 V >DPژZ   O ?"¨n6 r P  ^  All rights reserved.No part of this program may be!reproduce               Q%P)Q I L`#JI`'  I` I0ݩ(0/,",i8i#Hiihifi`i,i,3iPII4ifH8H hIiH ǯ?Ǭ?ǰ?Ǯ?ǩ? áǫ?Ǭ?0 ٢ؚ ڢؚڢٚ ۚܢښܢٚܢؚɡšܢɡܢǿšܢǿɡܢɡܢ  USES {$U A.LIB}SHORTGRA; CONST "XC=6;YC=10;YCHMAT=8;CHSPACE=2;YRV=184;YMAX=191;XMAX=279; "INFINITY=1E36;ASCMAX=127;BKMAX=15;PLACEMAX=79;LEVELMAX=8;ECON0=64;ECONMAX=95; "VARMAX=7;ALPHAMN=97;ALPHAMX=122;ROWMAX=24;STEPMAX=4;COLMAX=2; "CTRLB=2;CTRLD=4;FTURTLEY 8 SCREENBI5 X 0505Y DRAWBLOCT96l5  SOURCE 555 LROWSIZE 55XSKIP 555YSKIP 65QH?\H ` h  (j` , ~  ( FILLCOLOp:t1VIEWPORT4P4LEFT f4|4f4RIGHT 4|4BOTTOM 4TOP TURTLEX 4 *)fjfjfj+*fjfjfj8 8)eeL )` (J(F ((Lee L  )L6I1L6)QL6        zjZ )# " `' & 8 ! 0%ee8` !  e e8"#088$ % 0%ee8`$ %  e e8&'08e*e+) [B  ""##8&$iT8&UU ! U"# UT`+%$Y)!p JhhhhhhhhhhH8 )%HHH`5>hhh)hh h h h hhhhhhhhhhhhHH J "  ` ` `SN-(' . hhhhhhHH `  [HH8H8 hhhL.+ rhh heheheheHHLh< L)ˢ   â LE % %  )  `8`&e epɀj f f&e e pɀjff %) % )`% L=`0(%$ $ @' &    0&!"   #eNEDh0h1hhhhh.h/h,h-h*h+h(h)(ȱ(*ȱ*,ȱ,.ȱ. HH1H0H(ȹ(*ȹ*,ȹ,.ȹ.`   ""##  )`%)8`)     e e  `(J 8 e  ` Z Z< $ %$PQ $  ߩ $ Li`t^cY}z I L`#JI`'  I` I0ݩ(0/,",i8i#Hiihifi`i,i,3iPII4ifH8H hIiH h hL8Iif E J j 8TEM.CHARSETx @4` - G`` 8`*UH)JJh & & f)4#i JL` T$Q%P)QتP+,+,ȡ+ ++V 0  آآآǿآآǿآآ@ ǻٚ SYSTEM.CHARSETáSYSl    ڪP."ˡ[̄$ʄ$N.ʄ$M ń.ʄ$M  ʄ$̄$.ʄ$M .ʄ$M Y@'    4 INI=6;BEEP=7;BKSP=8;CRET=13;CTRLN=14;CTRLP=16;CTRLR=18; "UNDEF=21;LABS=22;RABS=23;CTRLX=24;LPAR=40;RPAR=41;ASTK=42;PLUS=43;MINUS=45; "DECPT=46;SLASH=47;ASC0=48;LTHAN=60;EQUAL=61;GTHAN=62;QMARK=63; "DRAW=10;ERASE=0;AXORS=6;LEAVE=12; "SHFSIZE=12;MAXTERM=33; "UNDEFST='Undef.';FINISHED='Finished';  TYPE "intPtr=^integer; "cvalBlks=RECORD -codBlk,qusBlk,msgBlk,proBlk,nesBlk,lesBlk,dusBlk,ustBlk:integer +END; "cvaldata=PACKED RECORD -dummyLength:integer; -curVol,tstVol,dusVol,startVol:0..15; -bit12, & ب     (ܪP/0/0ȡ Ǹؕ/ //*V H؏ ١ ڢ؏ڢٍDުP_MAX:INTEGER):INTEGER; PROCEDURE GETMSG(VAR ST:STRING;M:MSGTYPE;MSGNUM:BYTE); PROCEDURE INFRAME(LEFT,RIGHT,TOP,BOT:INTEGER); PROCEDURE OUTFRAME; PROCEDURE CLEAR(X,Y:INTEGER;L:BYTE); PROCEDURE BOTTOM(VAR X,Y:INTEGER;L:BYTE); PROCEDURE CLRBOT(L:BYTE); PROCEDURE MSGBOT(M:STRING;L:BYTE);  IMPLEMENTATION E DURE BAR(X0,Y0,X1,Y1:INTEGER;C:SCREENCOLOR);  PROCEDURE ADDCHAR(VAR S:STRING;A:BYTE); PROCEDURE GETSTR(VAR S:STRING;A:BYTE); PROCEDURE DISPLAY(A:BYTE;M:MODE;VAR X:INTEGER;Y:INTEGER); FUNCTION RAND(MIN,MAX:INTEGER):INTEGER; PROCEDURE GETMSG(VAR ST:STRING;M:MSGTYPE;MSGNUM:BYTE); PROCEDURE INFRAME(LEFT,RIGHT,TOP,BOT:INTEGER); PROCEDURE OUTFRAME; PROCEDURE CLEAR(X,Y:INTEGER;L:BYTE); PROCEDURE BOTTOM(VAR X,Y:INTEGER;L:BYTE); PROCEDURE CLRBOT(L:BYTE); PROCEDU-Y,CS:INTEGER;CLRKBD:BOOLEAN;M1,M2,MLAST:MODE); PROCEDURE BAR(X0,Y0,X1,Y1:INTEGER;C:SCREENCOLOR);  PROCEDURE ADDCHAR(VAR S:STRING;A:BYTE); PROCEDURE GETSTR(VAR S:STRING;A:BYTE); PROCEDURE DISPLAY(A:BYTE;M:MODE;VAR X:INTEGER;Y:INTEGER); FUNCTION RAND(MIN,valdata);  PROCEDURE PAUSE(CS:INTEGER); PROCEDURE WSTR(S:STRING;M:MODE;VAR XP,X:INTEGER;Y:INTEGER); PROCEDURE FLSHRD(ST:STRING;M1,M2:MODE;VAR XP,X:INTEGER;Y,CS:INTEGER); PROCEDURE GETCH(VAR CH:CHAR;ST:STRING;VAR CT,XP,X:INTEGER; "ZMAT:^ZARRAY; "TERMS:^TERMARRAY; "NVAR:VARPOS0; "SEED,XSCR,YSCR:INTEGER; "K128:BOOLEAN; "cvaldatPtr:^cvaldata; "SCP:^SCRNPAR; "FRAMES:^FRAMESET; "NUMV:NUMVAR; "FR:FRAME;  FUNCTION KEYPRESS:BOOLEAN;  PROCEDURE CLEARKBD;  PROCEDURE MSGINIT(cv:cPWRARRAY; $TCOEFF:REAL "END; "TERMNUM=0..MAXTERM; "TERMARRAY=ARRAY[TERMNUM] OF TERMRECORD; "SOURCE=(PROGINV,PROGVIS,USERVIS,DICTATE); "VETO=(NOVARS,NOOPS,NODEC,NONEG); "VETOSET=SET OF VETO;  VAR VARS,DIGITS:^ASCIISET; "LEV:LEVEL; "EXPL:^EXPLIST; $XB,YB,XBEG:ARRAY[DVCOL] OF INTEGER; $YBEG:INTEGER; $GRFR:FRAME; $AXASC,PXBL:PACKED ARRAY[1..2] OF BYTE; $BLX:ARRAY[1..2] OF REAL; "END; "MSGTYPE=(MSGDUM,ERR,TAB,SIMP,SOLV,MISC); "PWRARRAY=PACKED ARRAY[ALPHAVAR] OF BYTE; "TERMRECORD=RECORD $TPWR:ESET=ARRAY[LEVEL] OF FRAME; "VARPOS=1..VARMAX; "VARPOS0=0..VARMAX; "ZROW=ARRAY[VARPOS] OF REAL; "ROW=0..ROWMAX; "ZARRAY=ARRAY[ROW] OF ZROW; "ALPHAVAR=ALPHAMN..ALPHAMX; "NUMVAR=PACKED ARRAY[ALPHAVAR] OF VARPOS0; "DVCOL=1..COLMAX; "SCRNPAR=RECORD OF PLACE; $BNM,BA:PACKED ARRAY[BLOC] OF BLOC; $BK:PACKED ARRAY[PLACE] OF BLOC; $RBLOCK:BLOC; $RPLACE:PLACE; $BTOT:INTEGER "END; "STEP=1..STEPMAX; "EXPLIST=ARRAY[STEP] OF EXPR; "FRAME=PACKED ARRAY[1..2,0..2] OF INTEGER; "LEVEL=0..LEVELMAX; "FRAMY[ECONPLACE] OF REAL; "EVALUATOR=RECORD $EOPS:STRING; $ECONPTR:ECONPLACE; $ECON:ECONARRAY "END; "EXPR=PACKED RECORD $EV:EVALUATOR; $EXPRST:STRING; $XMP:ARRAY[PLACE] OF INTEGER; $YMP:PACKED ARRAY[0..3,BLOC] OF INTEGER; $BB:PACKED ARRAY[BLOC,0..1].false:(cvalstr:string); .true :(cvaldat:cvaldata) ,END; "SHFARRAY=ARRAY[0..SHFSIZE] OF INTEGER; "MODE=0..15; "BYTE=0..255; "ASCII=0..ASCMAX; "ASCIISET=SET OF ASCII; "BLOC=0..BKMAX; "PLACE=0..PLACEMAX; "ECONPLACE=ECON0..ECONMAX; "ECONARRAY=ARRAbit11,disk35,twoPlus,normalExit,myDemo,ssDisk,init, /stayGraf,dumpOk,silent,fast,slow:boolean; -cvblks:cvalBlks +END; "cvalCheat=RECORD CASE boolean OF --)vPv RL Pۡ5 Ý ˄ǐ6666á 7á 7777á7á7á7á7/á 5á5 ˡ Ä 5Í ˡ SUWX>ǿەǿٕ " צ.Pؿ ٦תPġ á ٦Undef.תPáצFinishedP<    &     ( //#ڤ./j. //#ڤ/ڤ/./ڤ Vz 10a 5106d؏ :ڪP R áBPress [RETURN] to continue._S h ,؝37/Q7Q746š3š  03á04Ȅ6 3 /0121410/Ȅ71 á121110/š2š211132ō4/ɍ7a0ʀʀȡʀ̀ʀʀ ʀÍʀʀ Í݂ݎ̀[2Pʀá[ Pʀ[צʀÍʀ0<ުP (Y or N)?P 132_YN2ڡ 1XR70 á 00 ܪPƀʀʀƀƀƀƀPƀʀʀ ̀ʀ̀ʀ ̀̀ʀʀ ̀ʀƀʀʀ[צNʀ̀ʀ̀ʀʀʀ[ƀƀʀʀʀ ̀ƀƀƀʀƀצƀ ̀ʀʀ ˍʀƀʀá^ ƀ۪P[ڪP2٪P تPƀצ?ulrd Pƀ ƀ ƀ ̀̀ʀ̀̀̀ʀʀȡƀׯ ƀ.ƀ̀ʀ̀ƀƀʀƀ ƀƀʀ2ڪP ٪P[ [\ צw\2\ ]a؄  Ʉ] Í]]2ױ\Ǹܕ  2צ ׯ6^2\ ^]\ ]Í]Í[[ [[(S:STRING;VAR CT,X,Y:INTEGER;ERASE:BOOLEAN):BOOLEAN;  PROCEDURE WRTLNS(ST:STRING;VAR X,Y:INTEGER;LF,SECPAUSE:BYTE);  PROCEDURE MESSG(S:STRING;LF,SECPAUSE:BYTE);  PROCEDURE PCR;  PROCEDURE HOME;  PROCEDURE MARKSPOT(VAR Y0:INTEGER);  PROCEDURE GOTOSPOT(Y0:INTEGER);  PROCEDURE BOX(X0,Y0,X1,Y1:INTEGER);  PROCEDURE EXPRBOX(VAR EX:EXPR;B:BLOC;XB,YB:INTEGER); PROCEDURE SCROLL(XLEFT,XRIGHT,YTOP,YBOT,LINES,PAUS:INTEGER);  IMPLEMENTATION E :BYTE; /ITEMS,DO_MSG,CHGMSG,RETMSG:STRING);  FUNCTION MSGYN(S:STRING;VAR CT,X,Y:INTEGER;ERASE:BOOLEAN):BOOLEAN;  PROCEDURE WRTLNS(ST:STRING;VAR X,Y:INTEGER;LF,SECPAUSE:BYTE);  PROCEDURE MESSG(S:STRING;LF,SECPAUSE:BYTE);  PROCEDURE PCR;  PROCEDURE HOME;  PROCEDURE MARKSPOT(VAR Y0:INTEGER);  PROCEDURE GOTOSPOT  USES {$U :A.LIB}SHORTGRA,GRAFA; PROCEDURE GETOKCH(VAR CHP:BYTE;VAR CT,X:INTEGER;Y:INTEGER; 2VAR CH:CHAR;CUR,OKCH:STRING;LCASEOK:BOOLEAN); PROCEDURE MENU(M:MSGTYPE;REC,OPTIONS:BYTE;VAR CHOICE:BYTE; /ITEMS,DO_MSG,CHGMSG,RETMSG:STRING);  FUNCTION MSGYN,.-X(@ @  6 ^D@! ǿ8r8&HpN,ؤښ4  ۧč4ڧ٧ ؏*٪P.-.-  T a s ۝ GGە6 Rپ؂צP ˡ. ́-ʁ- Pʁ-RTNǿǿDġ ؤښ ǀ@(߂ ȡ,ާߕە 6  hhhhhhhh4i@Hihi$ Hi(hiɥHH`\t&p "USES {$U :A.LIB}SHORTGRA,GRAFA; "PROCEDURE CIO(VAR ZOUT:REAL;VAR OUTST:STRING;INSTR:STRING;SRCE:SOURCE; 0BASEVETO:VETOSET;XB,YB,CMAX:INTEGER);  IMPLEMENTATION E  #2L 8<=>F?A:CGJJLʷ"L(  USES {$U :A.LIB}SHORTGRA,GRAFA;  PROCEDURE ADDCH(A:ASCII;VAR ST:STRING);  PROCEDURE APPEND(AST:STRING;VAR TAR:STRING);  PROCEDURE PUTPARS(VAR S:STRING); FUNCTION ASCSGN(A:ASCII):BOOLEAN;  FUNCTION REALST(ST:STRING;VAR C:BYTE):REAL; PROCEDURE STREAL(ō梀ؤÏ á á梁#梁;梁#ݤ ń梀 梀梁#ݤ ɍ  á(梀ݤ梀ݤ  墁#ݤ ɡj  ȡ墁#ݤ ȡhj 墀 墀墁; @*墁;墁#墁;Ä ߕ  n  ˡ梀梁3 á梁#ݤō梀ؤÏ á á梁#梁;梁#ݤ ń梀 梀梁#ݤ ɍ  á(梀ݤ梀ݤ  墁#ݤ ɡjآ#آj  áآ7آ#N آآ   آjآ#  آ3   á3 l١ ˡ梀梁3 á梁#ݤ E CL<<ʷZ\\ʷxR` [E :E BODY3 WRITELINUNITPARTCOMPOPTINUMSTRIN\\ER.CODE1\.TEXTGb[h:mng>ʷB `^ph.CODE.CODEACKE.CODE1.TEXTG[:mƳgEʷ "USES {$U :A.LIB}SHORTGRA,GRAFA; "CONST YOF=5; "PROCEDURE DRAWBARS(VAR EX:EXPR;BH:BLOC;XB,YB:INTEGER;M:MODE; 5STARTONLY:BOOLEAN;BEGPTR:PLACE); "PROCEDURE SHOBLOCK(VAR EX:EXPR;B:BLOC;XB,YB:INTEGER;M:MODE; 5FLASHES,CSPAUSE:INTEGER);  IMPLEMENTATION   0.á@p ^P4-ٳ(`áJ 4 ؊0@{Η.á *`á@{Η @{Η^ ˡڡۡ   ݪP  ^ˡ ^ P2^`^ooצ05532`aצ,9225Q~p[~06/T~%<~hfem~u[v4̀4ʀȡǞa444 C $PBX=0.á@p ^P4-ٳ(`áJ 4 ؊0@{Η.á *`á@{Η @{Η^ ˡڡۡ `Ŷ!^ á  -Ä^`á#ö^`?á`á á ` ˶Ä  .á  .R^^B35ȸ^^5333_`Ä5^Fɡ 222+_4 ظ4  `á^ `0 ء  4 ɡצ^*Pس__Ʉš 5P$5^P`á5? `á5 ^3R ö^ 44  4 Ŷ4ĄCL<<ʷZ\\ʷxR` [E :E BODY3 WRITELINUNITPARTCOMPOPTINUMSTRIN\\ER.CODE1\.TEXTGb[h:mng>ʷB `^ph.CODE.CODEACKE.CODE1.TEXTG[:mƳgEʷVAR ST:STRING;Z:REAL;SF:INTEGER);  FUNCTION APPROX(Z:REAL;SF:BYTE):REAL; PROCEDURE SHUFFLE(VAR SHF:SHFARRAY;MX:INTEGER);  FUNCTION BINOPLOC(VAR ST:STRING;LOC:BYTE):BOOLEAN;  PROCEDURE NUMSUB(SUB:STRING;VAR TAR:STRING;C0,C1:BYTE; ,TP,MSG:BOOLEAN;VAR AST,PAR:BOOLEAN); PROCEDURE APPROXSTR(Z:REAL;SF,SFMAX:BYTE;VAR AP:STRING);  FUNCTION SMALLDIF(Z1,Z2,ERR:REAL):BOOLEAN; FUNCTION VERYCLOSE(TAR,TRY:REAL;SF:BYTE;SFONLY:BOOLEAN):BOOLEAN;  PROCEDURE GETXVALS(RND:BOOLEAN;N:VARPOS;RX:ROW;ZMIN,ZMAX:INTEGER);  PRO ݪP00 11\ˡ1b1)á30200&11iɄ1a2102307030270*1(á0 701ȡ 1 \13 h   t |١MڀÄɄ  ń )@ Ä ޮ Ä؄  ܹڂ(ڕ!ڏچ*/ %"  :7+3צ P öÄ öń'Xؕ  צ-Pxؓ *ؓ ءš CL<<ʷZ\\ʷxR` [E :E BODY3 WRITELINUNITPARTCOMPOPTINUMSTRIN\\ER.CODE1\.TEXTGb[h:mng>ʷB `^ph.CODE.CODEACKE.CODE1.TEXTG[:mƳgEʷ "USES {$U :A.LIB}SHORTGRA,GRAFA,STRAP; "PROCEDURE EXMAKE(VAR INST:STRING;MINCO,MAXCO,MINEX,MAXEX, 'PRPOSNEG,PRADDSUB:INTEGER;VARCHG,SHUFL,OMIT0:BOOLEAN;VAR XSUB:INTEGER);  IMPLEMENTATION E <=>F?A:CGJJLʷ"L(*Í22   ݕ PV Ʉ=/ @ 2 ڡ[[[2 [ 2 2ȡEܡݤ $ݤٕŕL Z צ System error.Hold [CTRL] and press [RESET]. ndPL$\2š 2Í22   ݕ PV Ʉ=/ @ 2 ڡ[[[2 [ 2 8 ōھ@0 *ײ P, ߪPń -ÄB333 3+Í +-3  -Ä@ 2š2,Pá 0Pߡ0. -P`{pT  ؂ š ȡݤޕȡ' ݤݤܤܤۚ šg:X  v ɡ%؀צP  $   ? ȡ9 =  0ނ  ȡ 0ؑ ȡ0Pɡ1݂ɡצ.10)51=133100.35/Lb  =̲,4پáٕ# 2@{ΗۦUndef.תP0Páצ Pٿ٪PPRצ(P),ȡ 000۪P5.3/00-á..053 3000.á<CEDURE ERRORQUIT;  IMPLEMENTATION E APPROX(Z:REAL;SF:BYTE):REAL; PROCEDURE SHUFFLE(VAR SHF:SHFARRAY;MX:INTEGER);  FUNCTION BINOPLOC(VAR ST:STRING;LOC:BYTE):BOOLEAN;  PROCEDURE NUMSUB(SUB:STRING;VAR TAR:STRING;C0,C1:BYTE; ,TP,MSG:BOOLEAN;VAR AST ɏ   ؿ ڶ ȡ ھ۹S     ɡ-   ؊ +}F]  "$&(*,.02468:<>@BDFHJLNPRTVXZ\^`hjlnprtvxz|~\˂ צ 0P +á #A02\P ء  a3ٳ`a&a cŏcš  @ٿaÝɄaz ˍ bŶ !`bá7 j^ áb áb ?áb á  á b ػ +ö -Í -á '@!ب  - <  \+,ö \ -Ä+ɡl^g  ˡNس@aa5٢٢j[٢٢;٢jZb ء   |ö ö` [ ؓ ,Yؓ  á  öÄ ءYY^``8 š- ,Y á  á YY á^   ˡfr ?š  \@ ٿצخ ,Y*á`؝ á leftצerase a character G áצupstart an exponent $ á  á  ġ@ á_[Z  ۚ   á ٸĄ á[[ ز[Z ö]TPɡ ɡخ آj   آ;آj:Xqȸ`` qXXXa_bÄ,.02468:<>@BDFHJLNš qP5q^Pbáq? báq báq `X TVX  ˡ ,,,j[ ˲Ą Ŷ[ ɡ jצ^*Pس__ɡ    Vabsolute value CB denominator T  Bexponent  5Bצradical %J N3X)Pw  "$&(šP&8  ڪ٪# $ v. צdownend your exponent & צخ  [[  ٶڢj$š ٶk&qa Ŷ`     cp@$k,  ,^ˡ ^ײ,PYa`bP ٪ت ODE);  IMPLEMENTATION E R` [E :E BODY3 WRITELINUNITPARTCOMPOPTINUMSTRIN\\ER.CODE1\.TEXTGb[h:mng>ʷB `^ph.CODE.CODEACKE.CODE1.TEXTG[:mƳgEʷ "USES {$U :A.LIB}SHORTGRA,GRAFA,SHOBL; "CONST MAXCODE=63; "TYPE CODEPOS=0..MAXCODE; 'CHARCODE=PACKED ARRAY[CODEPOS] OF CHAR; "PROCEDURE IO(VAR EX:EXPR;SRCE:SOURCE;BASEVETO,PWRVETO:VETOSET; .XB,YB,CMAX,FRACMAX,DEPTHMAX:INTEGER;INSTR:STRING;TASC:CHARC3zp & pz @@p@pōaAzkAkȡ{Aiɡ Aa [Apɡ Aa Cۡ5ڡ Aap3Ap Aa@@@@zšp@ AaAAA a@k@kȡ@ @@  @@ȡ`@AAaġ:Apɡ/B AaB@@ AaAi@@A AAAZȄA @@ׯ0P=á 0P=á0 |F6*$ az 3zp & pz @@p@pōaAzkAkȡ{Aiɡ Aa [Apɡ Aa Cۡ5ڡ Aap3Ap Aa@@@@zšp@ AaAAA a@k@kȡ@ @@  @@+:"^ %\% .á  .%= 0 .áH&%  0@{Η<' )_ bá0] ' .á&]!@{Ηbá ` ܢ*ܣ)@ܣ)i $   ˡ خ./˄ >( ݢ#ؤݢ#ؤݢݢ#٨QܢOÂܢOšەܢOá ܢOhؼ!ؼ^]k  س@{Η4 @{Η@{Η   ?^-@U % LINEAR,IDENT:BOOLEAN; % XFACTOR,SOLVED:EQNTYPE %END;  FUNCTION EVAL(ES:EXDAT;RW:ROW;VAR RHS:REAL):REAL;  PROCEDURE VARSORT(VAR VNEW:BYTE;ES:EXDAT;INIT,NEWVAROK:BOOLEAN);  FUNCTION IDENTICAL(STEPL:STEPLIST;INIT:BOOLEAN; 0COUNT:INTEGER;VAR FINITE:BOOLEAN):BOOLEAN; PROCEDURE LINCHK(S:STEP;V:VARPOS;VAR EDAT:EQNDATA);   IMPLEMENTATION E %EXDAT=RECORD 'ESTEP:STEP; 'ESIDE:SIDE %END; %STEPLIST=PACKED ARRAY[DVCOL] OF EXDAT; %EQNTYPE=ARRAY[SIDE] OF BOOLEAN; %EQNDATA=RECORD % ROOT:REAL; % LINEAR,IDENT:BOOLEAN; % XFACTOR,SOLVED:EQNTYPE %END;  FUNCTION EVAL(ES:EXDAT;RW:ROW;VAR RHS:REAL):REAL;  PROCEDURE VARSORT(VAR VNEW:BYTE;ES:EXDAT;INIT,NEWVAROK:BOOLEAN);  FUNCTION IDENTICAL(STEPL:STEPLIST;INIT:BOOLEAN; 0COUNT:INTEGER;VAR FINITE  USES {$U :A.LIB}SHORTGRA,GRAFA,STRAP;  CONST LSIDE=0;LRSIDE=1;RSIDE=2;  TYPE SIDE=LSIDE..RSIDE; %EXDAT=RECORD 'ESTEP:STEP; 'ESIDE:SIDE %END; %STEPLIST=PACKED ARRAY[DVCOL] OF EXDAT; %EQNTYPE=ARRAY[SIDE] OF BOOLEAN; %EQNDATA=RECORD % ROOT:REAL; ` $$n!: P` * L  D h l2^.<Zrnd2٤Zá#jpák t  Ǣ UVWݢ)@]ܢj^P^P \[Z ޢ;ޢPޢ#^p  š0ܢOܣPܢO ܢ#ܢjܢ#ܢ# ,٪P ب @1ȡ#P٤P/ ō21PZ <ġ !#" ٤Zá#jpákەššxe / ڣPȡڢؤ٤ڢؕ٤&<1 1  á٣P*2 P P3ٻ^ˡ#já ظ[٤ݢۤؤقɶقō áݢ3ݢۤؤš ݢۤؤٚá4 0 ńk0ܢ3ܢܢ3öܢڤەōܢڤ c, á."- cڍ\١-ړ * *  c@  (z # ݣPȡ5ȡ#ݢܤڤݢܤڤܢjآjá M[[\U .(UUUVWá  \ á l.!bŶ @$ á)x   (` á@ (G (á (. á+"ܢ7ۻ[ ٮ /[šܢܢ#ۤ[[ɡظ[ܢܢj[**VVUU )U W  (WWUU2+ ., ݢݢ#ݢܤݢۤݢj۾ˏـš9 ˡȡݢڤݢڤق)  * U V ܢjܢj Ą%`Xqš`  ܣP[ ܣP /-) ܕ܊   Z ) @{Η)  @&s 0_p$܊      e ȡ*! @{ΗڑšV@{Η@{Η@{Η"ڡ   ܊               )޶Ʉ  &     S^ $ ٳ=ټ ؼ  @{Η@{Ηȡ  Q? ܕܕݢ ݢ 0    8 ȡޤ@{Η6š޶ɡ@{Η@{Η;LAB:INTEGER); "PROCEDURE DRAWAXES; "FUNCTION COREAL(RW:ROW;N:INTEGER;NV:VARPOS):INTEGER; "IMPLEMENTATION E R.CODE1\.TEXTGb[h:mng>ʷB `^ph.CODE.CODEACKE.CODE1.TEXTG[:mƳgEʷ "USES {$U :A.LIB}SHORTGRA,GRAFA,STRAP; "PROCEDURE LOCAXIS(N,PXBLMIN:BYTE;BEGPOS,ENDPOS:VARPOS; ,ENDROW:ROW;USENDPT:BOOLEAN); "FUNCTION REALCO(CO:INTEGER;N:BYTE):REAL; "PROCEDURE AXBAR(N:BYTE;STDCOLOR:BOOLEAN); "PROCEDURE DRAWAXIS(N:BYTE;LAB0:BOOLEAN$$$8 4$%$84$1$+$+$%$+$@{Η7$+$87$7$%$4$%$8$$7 7@{Η7+71*(0lBz  Zz$9$9ȡm%$$$%$+$$$+$$$$8$8ȡ1$$$$$8 4$%$84$1$+$+$%$+$@{Η7$+$87$7$%$4$%$8$$7 7@{Η7+ z$9$9ȡm%$$$%$+$$$+$$$$8$8ȡ1$$5 @{Η8  z 788ȡ" 99ښ97 7+ %+G ǦB 88   Q߾ޝaáޚء a áء?az ȡ0aŝɄa7 ݨńܡ3 ȡ%G ǦB   ڤɡ (ɡ:@ɡ 1aɡ*@a   ۤ@{Η ڤ    ܨ \ ,ڨ١ p_N=@{Η*/ dUH;  0? 4'@ 2nQe   @{Ηފ @{ΗG.ފ     q W z -- á'----Tt  ܢ( Äۢ ٕٕۢۢۢۢ٤ j   &  ۢڤۢ4 #   USES {$U *A.LIB}SHORTGRA,GRAFA,STRAP,SHOBL,GRAFC,CONIO,EVALU,AXDRW;  TYPE CSET=SET OF DVCOL;  FUNCTION ONSCREEN(RW,NV1,NV2:BYTE):BOOLEAN; PROCEDURE CONBAR(RW,NV1,NV2,N,CT:BYTE);  PROCEDURE PLOT(RW,NV1,NV2,FCT,ERX:BYTE;UP,HP,PX,PY,C2:BOOLEAN;VAR ERR:I  _  áB @ t<d ;⢁e;⢁d ⢁b   !   ˄?á  ˡߑ Bá.ˡ      dڨáReviewBeginn  ˍ  ! ب     U⣁c ⢁c⣁cP١⢁e;⢁e;⢁d ⢁b   !   ˄?á  ٦Shall we do another lesson J بܕ   ١V    ŴĄ;צ#04:USTRT.CODEP; 0; 0;  ddeePf ePd ,,# 6& ^__ȡٶ^ٶ čٶ   Äړٶ Äڡ ٝ ۡ5צIf x=#P߸a  ``ȡK aš5ŏ,"R!ءڶ צPlease evaluate: ء1ݓ.1 1# 1dݡء!ڤ ض   #تPƏݢK ڤ   ܸV6צ 2,"@{Η"L  Q٢٢ Q٢٢   (ݢݢاݢa۶ azȡ/ašٿ ȡ٢٢$  `1ȡȡ ٮ82'FI ضPZ ȡ\٢ȡ0٢Q٢ȡVQ٢٢ۢ٢٢٢Qɡ ܢO6٤؂*Qܢܢ#ڕڕ:  ٢٢٢ height~=~=)Pۓ =)Pړ =)P ݡ צ   צ ܡGڄ&צThe lines meet at the point צThus, this is where     e ݶܶō     `١(,)תP ̀̀ʀġ=) =)Pʀaġ*X~=~=)P=)ʀöڳ ڳ  ۶ˍ ڹەۂ~ۂwەp;h$ 7 "$&(*,.02468:<>@BDFHJLNdRTVXZ\^`bdfu    ?Í? "٪  š    Fڡ$ ߢߢ 2ت     ?ُ؏:     ݢلݢöڕnݢaġ צcorrespond to =)Pצhave =)P=)צPoints on this line ڡڂڡڕ$. ȡ *   áߢߢ ߢߢ  XتPP.P2R0ö   /٪PتPۡ/ái/theצeach /צanotherצmore /valueצvalues /צthisthese /variableצ variables /צxy ܝ  !/ (";"=up,~"/"=down)צ^v /צ^v YXYX/YX  ە5&5צ , and x=#P    & `aaQ`` is~#.&^צ dٝdړۂ؝ٶĶŶJf,(%  č ɕצLet's try more values: dȡ) ɡ 2%'7  ȡ4 ɡ %operation required is MULTIPLICATION.P   Correct, 8áצIn this case,  צNo, 6٪P ǸR(צ,what is the LAST operation to b))VVP))Vڲ)ڕVPthe LAST operation is toC MULTIPLY צby :צADD and ' SUBTRACT צfrom 4#Oٓdؓ^צ&An expression is factored if the last צ "$&(*,.024KW:V>P~-ڪP٪P-)ؕ)Dצ"Thus, this expression IS factored.PˡNOT PfR\áx-d)(ax-b)תP    )(ax+b)(cx+d)(ex+f)תP   )צ(ax[e]+bx[f])-(cx[g]+dx[h])P   )צ(ax[e]+by[f])(cv[g]+du[h])P0 Q\WRMH/@  )צax(bx+c)P)ax[e]+(\ab\x-\ac\)תP)צ(x+by)-(ax+\ab\y)P )צ(ax[e]+b)(cy+d)P)צ (ax+b)(cx+d)P)(ax-b)+(cULTIPLICATION by 2. צHowever,multiply 2 by y.צthe ADDITION of 6. (We are interested in the LAST operation.8 )צax+\abP)a(x+b)תP)צa+\ab\yP is to .P.צThe LAST operation is P =We have been simplifying expressions by removing parentheses.For example, we know thatצ~ צ 2(Y+3)=2Y+6 Notice thatצ add y and 3.צM١T XتPQ ;@**-*-***-****-+*+****-**-*******-*******+++,*,-*----------**+++-ڡ.١RWڪP.٪PتP when we evaluate WPWWthe first operation ٫ث ,    "Q ۢۢ#٤ۢۢ#٤؂ FتPQ0Qݝ 00#ݤ : FAINT ەצ  K  .&H4f6< B J <  dtP:jJfT P(  (second תá צٝá צfirst צ  (ٝɡ$צ ٝá ' ޢ  #   ##ݶȶۍ$'    $ ȡ}٤@{Η@{Ηضض,  (second תá צٝá e performed ? ?Addition.Subtraction.Multiplication.Division.Power.Help needed.צצáצfactored (Y or N)?   _צYN??Yïڡڮ nIs the expressionתPn~ RFzڤ)ڤ)ءB  خ ۢöÄۢö  ..// //.آ צUSTRTPצ#04:P 0 0Zx -ء-  Welcome to Algebra Mentor by John C. 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