ࡱ> dfeq` ;bjbjqPqP p::&       "!"!"!8Z!<!Lx(!!""""$$$'''''''$.)h+h'] $$"$$$'  ""2(C'C'C'$p " "'C'$'C'C'  C'"! ]D "!9%C''H(0x(C'+%+C'+ C'X$$C'$$$$$''&X$$$x($$$$"!"!       Overhead Sheets  A. 1C Writing equations & inequalities When we write equations or inequalities, we take the written description of a situation, and we represent that situation using mathematical symbols. Example: A boat is 40 times larger than its scale model. Write an equation to represent this relationship. Step 1: Identify your variables b = the size of the boat s = the size of the scale model Step 2: Write the equation boat is can be represented by b = b = 40s Practice writing equations for the following situations: (a) Pencils cost $.35 each. Write an equation to calculate the total cost of any number of pencils. (b) A motel charges $50 per night for a room. Write an equation to represent the charge for a stay at the hotel. (c) Bananas cost $.39 per pound. Write an equation to calculate the cost of buying bananas. In some math problems, we have one value which is a constant. That value does not change and does not depend on any other variable. We have other values which are dependent upon some other unit in the problem. Example: You hire an electrician to install a light in your kitchen. The electrician charges $68 for the house call, plus $50 an hour for service. Write an equation to represent the cost of hiring this electrician. c = cost h = # of hours Write the equation Name the constant Practice: (a) To rent a hotel room for one night, a company charges $85 plus $10 per person. Write an equation to calculate the total cost of staying at this hotel. (b) The admission to a state park is $5.00 per vehicle plus $.50 per passenger. Write an equation to represent the total admission to the state park for your family. Function Rule An equation represents a functional relationship. Sometimes we are asked to write a function rule instead of an equation. A function rule is a special type of equation that uses f(x) to represent y. In other words, instead of writing y = you would write f(x) = f(x) means the value of the function at x Your independent variable would go inside the parenthesis. Sometimes that variable is x, sometimes is it some other letter. Each month Jeans phone bill includes a $25 basic fee plus a charge of $.07 per minute for the number of minutes of long-distance calls she makes. Write a function rule to describe the total amount of Jeans monthly phone bill in terms of m, the number of minutes of long-distance calls she makes. f(m) = 25 + 0.07m How would you write this as an EQUATION? Functional Notation To write an equation in functional notation, we give the function a name, typically a letter such as f, g, or h. Then use an algebraic expression to describe the y-coordinate of an ordered pair. Equation: y = 2x + 16 Functional notation: f(x) = 2x + 16 Equation: m = h 2 Functional notation: f(h) = h 2 On the TAKS, you will be asked to solve problems in which you must write an equation or inequality for a given situation. Example: Grade 9 TAKS The Alejo family budgeted $2000 for their vacation. Their budget consisted of $800 for travel costs and $75 per day for other expenses. Which inequality represents the number of days, x, the family could have stayed on vacation? A 800 + 75x d" 2000 B 800x + 75 e" 2000 C 800x  75 e" 2000 D 800  75x d" 2000 Grade 9 TAKS The temperature in degrees Celsius, C, is 5/9 of the difference between the temperature in degrees Fahrenheit, F, and the constant 32. Which equation best represents this relationship? A C = 5/9 (F + 32) B C = 5/9 (F + 32) C C = 5/9 (F 32) D C = 5/9 F + 32 Grade 10 TAKS Vicki works as a salesclerk in a clothing store. She earns $10 per hour plus a commission of 6% of her total sales. Which equation represents e, her total earnings, when she works h hours and sells a total of d dollars in merchandise? A e = 10h + 0.06d B e = 10h + 0.6d C e = 6h + 10d D e = 0.06h + 10d Grade 10 TAKS A candy company sells chocolate-covered cherries in a box. The empty box weighs 4.2 ounces. Each piece of candy weighs at least 1.8 ounces. Which inequality best describes the total weight in ounces, w, of a box of chocolate  covered cherries in terms of c, the number of candies in the box? A w e" 1.?@Cm n \ ] ^ f   ) * 3 4 C g l ȿѿxxmbh{+56CJ0aJ0h{Z56CJ0aJ0h{+h{+56CJ0aJ0h{+h{+5>*CJ0aJ0h{Z5CJ0aJ0h{+5CJ0aJ0h)56CJ0aJ0h)h)56CJ0aJ0h)5CJ0aJ0hx5CJ0aJ0hA5CJ0aJ0h,g5CJ`aJ`%jhA5CJ`UaJ`mHnHuhA5CJ`aJ`&?@ABCH I j k gdA$a$gdA;; 7 8       w x y M N W X ( ) 3 B C V i gdAi j k l v w XY$a$gd['gdAl 1>VWYklŷłhuX56CJ0aJ0h['h['56CJ0aJ0huXh['56CJ0aJ0h['h['5>*CJ0aJ0huXh['5>*CJ0aJ0h['56CJ0aJ0h{+56CJ0aJ0huX5CJ0aJ0h['5CJ0aJ0h{Z5CJ0aJ0h{+5CJ0aJ0/'(gdA &'9:=>Z[\]ghmvx Ķ󖭍vvh h 56CJ0aJ0h{Z5CJ0aJ0h 5CJ0aJ0h{+5CJ0aJ0huXhuX56CJ0aJ0huX5CJ0aJ0huXh{+5>*CJ0aJ0huXhuX5>*CJ0aJ0hHh56CJ0aJ0h{+56CJ0aJ0h['56CJ0aJ0huXhuX5CJ0aJ0.+,-.CDghijkl(*TVgd $a$gd gdA 8:np)*23?@HIUV_`  +ghmnst{|ɭɭɭɭɭɭɭɭɭɭɭɭh)h 5CJ0aJ0h{Zh{Z56CJ0aJ0h{ZhAh56CJ0aJ0h{Z5CJ0aJ0hAhhAh56CJ0aJ0hAh5CJ0aJ0h 5CJ0aJ0h h 56CJ0aJ0>   $%:;PQfghijklz{hi}~gdAh$a$gdAhgd 88:8<8b8d888888<:gdo-gd{Z$a$gdAgd gdAh028888888*8,8D8F8R8T8l8n8z8|8888888L9:޹ްްvmvdhdT~5CJ8aJ8hA5CJ8aJ8ho-5CJ8aJ8h,ghA5CJ4aJ4hA5CJ`aJ`h{Zh,g5CJ4aJ4h,gh,g56CJ4aJ4Uh,g5CJ4aJ4h,gh{Z56CJ4aJ4h{Zh{Z56CJ4aJ4hA5CJ4aJ4h{Z5CJ4aJ4hAhA5CJ,aJ,h]hA5CJ`aJ`%8c + 4.2 B w e" 1.8c  4.2 C w e" 4.2c + 1.8 D w e" 4.2c  1.8 Grade 11 TAKS Eddie s Towing company charges 440 to hook a vehicle to the tow truck and $1.70 for each mile the vehicle is towed. Which equation best represents the relationships between the number of miles towed, m, and the total charges, c? A c = 40 + 1.70 B c = 40 + 1.70m C c = 40m + 1.70m D c = 40m + 1.70 Grade 11 TAKS An artist studies human proportions in order to make realistic drawings. He observes that a persons kneeling height, y, is of the persons standing height, x. Which equation best represents this relationship? A y = x B y = - x C y = x - D y = x +     PAGE  PAGE 14 : :9:::;:<:A:B:T:U:a:b:g:i:n:o:v:w:}:~:::::;;>;?;y;z;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;ǽhHh0JmHnHuhHh hHh0JjhHh0JUhkojhkoUhAhA5CJ8aJ8ho-5CJ8aJ8hdT~5CJ8aJ8hdT~hdT~56CJ8aJ8B<:=:O:P:c:d:x:y:::::::t;u;;;;;;;;;;;;;gddT~$a$gddT~gdo-;;;;;;;;;;;;;h]hgd{Z &`#$gd~ ;;hA,1h/ =!"#$% `!,˳[c$Nq,xڭ|Usp'@4   >[p AC©o}VBV{9}zU= |1}y|)>$Vl|N_b`ϟ>c$0#f੪gEڵk>c&=ru'ߗi 5iC cxfJYWB8[90:S1sw+F=$|qgr6|vKMftNsIh`dw{;hYV47{ӡ>9xu֟zˬ"(7yO3~/YN-ﹰ0GHl) !AFRT&I%" d2BZBp_rmI$Frju7֥GT!Ւ\3p<_L{fj+E[wFvzMom~+̩bڊ䶼ϘҾ)d f||e t&5}(}A|?Q|A1|(WXi2=սHDw?t]QKΩC7^rorv{u2J{}5GiN}S'tF)N?H %2Rl5G;EϠ4A5BztPPyӛ6'Xԝ;w|Lf ɡZx/2/$󒕶Ia+i4ґjJ?* c("+]aT~ ռjB50Az&YjP-ԝ;Pw&tf<߂z^C=14P{r< k*k_AA J *P9n×Px. D3J.!ӹ Nҝp Q2Q(A>&@>&1rq*";v*gCU?qWD@6!߶Zȵ|DW\CKN!7LuDl[[ve(a^q "lRmUŵ-%mi-lPi+iz[ESjWM9nJ,SDѢsd?)FQ*FяC/E(DQGT"9cȡ}yH*RHsj/2<d2U7 Ӵs?z߆!zrrv>+E A큓ȫu[{N_!ڥ<}vctxat.\^r %vvL?hHHDgFIuDJZOr&Ԍ6ARdĦx6ƴUMZoR]aPS-dX>5=!7CYD. T~]N|$Rj@KZ)r4S&MJel8"o[N1i9#9ND&iϹQIlh>zNT+D'r)r vB@ke?߱'W{ۻ|þ'md3"_L[RGo)vT ]/^IoHb{[;} rJݎMhD,=? 0Fm`LlrOhr0:53Ri~\>3_}s-lc|4J[tu[n3bzM[w21&9bZ9;l;ܴ۝㼵z6klvR \Q}s=hI3爆8'}ȴD 46oxv^*ejJMSN04厍[e=OIbvPYB&r =/h>b_z ^pnAct3=jghUhfe&kiVkP;mJ*.IGS|Hz#\Bx@/-vD.W2dF*hJT汴5%*#6?e6_zd,08eKf*c4i5M-iZh8w.ޣp=GՏ/h~1~,le4TpSX07`3N`C_L-O?*v뚇`HD-K>0YG;QIC|R{ddyrK7`5okb^IaJwif;پ`v XƓ ~+&?&^7, &˂ :T^~chmP˘57L6Ϳ>P 6fr`D4L^X\ F`b>\(Oc5i;ګCS4Y8gxOk4"=98`ﯲD=0Hc$y'ER60;Zf*ce@;MB=s&;v_Qr)G)nHSIM5mG]SWˁ|`3=Lʼn7yl䈱0y ]C}:BKCt j`h4t6V[V>˂B`4'>{~I}Vzځ᝼tZGqa/XȤ(WS:lHQhXm, _pQ4uvͧ̆sv^0YL&K2: YYTVf&l͗^Pg'Ee'+t[j0@N@>NvCƷcϚb4>"&k{?èBC8R"MQ7π;`5uL M͎W V~9X C`կǕ&6IPzd&.@KMQ0YL>`!ج6 |l&1Zze2i0y".e72TRt['#cG#"{Bfg]2Y }D% 0LVBg*RvI).`0xM,-Vk8F`p9Xџm`2e3&^B9 ]n9u)3壑}fGT*`L 6 ZL;7&PKĥ5tz}N;ϡ.VgY,}n:XUSjZUS h9Fg:!:it;N'SSKL&W㣿Z`,ܸ`#'y`ԯ-`_#g<\id[\N~ 6C%fnt`3z:Sc}Aԏ?X&,Y kT_6e{tN?FBP- }~ }E/{|&cWe~٬vf]LQ=>CO(5L &Sd`22gj[/X: _o#S4gtICrL}dx#֫?wCL=Kc)P}FB[+Sc #.tXY]5 sfXY ~Eѿsf޳1z@{Ԛ+Ao0:F#迺Lt:\Ƃo^WFfG);_FvǾ7X7oWTq6D}lTs[:q18 z=B]o`Wzl{ʨNATB^es\eiY}5%200ޞ]杁Goq ؛ CM{u^"}n*jjПP 7^vc7HQv#NϜkES^8ÎW1zǀtr#v )aKO|cZISQژԐѦ6QWLΚU=3 j:I\En -Um_gK t$A6BFΔvԶK M~'2w/kroKD$*KiW6X3AŴft3e0NM]ozDs`[ % Pv@h;ЮJ@ |= ׁ ^o ҋ3n@:lf 7CbTéBz4k9h˅H_c;K2 ͊8F+~NvT/yIoI"SES }?( _ MbPVFTGgdO(LD.&BSfBr!nYR'"dF ,@v\vBYgMtFPh@uy5Z?@21[r--v$% Tg ODك@8r#ȪeEO䨹tnw@&kjT(4P]B@57ר*Xuw(Pa8.sDr;P5G2͏ )@w.9 9$n9l`(\ 8G? Qy BX@/ʯ+|a4;NCX/2cf{tsVSc*;Lawn6Iܻstot=S}l/MKטn;Mi'9]ֱv;c]家Cv{Nwn޲{6~>'sؑ/v wN.{);u{7u<{Lvntc_fLug%}_kyʏɬ~vVSvp;S}e2bv0/67xpuNEin89 q 7svڌ%u]&HF-Y TPdIm;7p40d:$g~'t*ٵ@ 8\x~طN޴0JWaHYïHn vLqFBlmƵ]Ӊm8%')dw;U $[k|76{f(^7~"Z)Z$v[ӎqKΞnrca͂YCNBIe9)=T[ڝ@qØ a4 `-̃q,VF$cv[clK7& lIVOs'i/8%5!=$Q<aQwcwv*¯HK-n趎△}QYls7~$1!wBT5~)m9 {ϑK|xg3ݰ L~"P l[;ԭ]Bwšٯ)bsC9mԶ,wFz k0o+{~{`w/i7 ~ERHH`xlCb/ylcĥ+Hms`8nfh?}-.b9 דp./Ǽ ;agmݕ~HI! GlІUR5J#ĥV^9 # 'p?|Z>s*cQm aDܟ1o o{[{kaw)ρI7~E葄&įr"Vʹ1{bs>)c_n=sڇN[+9饑+^,gm;m帴\ԁP}rMMSnK ;nؑtNH;~hHnjgh{VctҞ%KTRI}4&^M?S!GҧJ FT_S')C$?MDRvIH'%n˟+s^r f\;wPC+G`acð׻,yd7Zy-t%#~cp"ͩi4g^Zq 8ס܌rFAtՎ#d|մ֮v[)"D!^DQ<8bBIeTLQ MKQ-G@$tY{(oGR%/W^-^O] יT-WGFDwyOam FX #^HL2[踞rIc~cRp:ʟSw.HM4UTS&n-v"c{;:lF;?Q ^NCxtgc@PPFL%UzT*S7)IC%M,TRB Kt|%^>z:ǛykwRejphj=RK|ˋ=td}U^&s/~…1J\ r-?0NOUd}ZLK>00J>.T@ZQEi@uF4QO6I:"1)J< XJ^%ZRoNf#c#wNej`DDL=K1`ˤj,#kۃV*9x{ǿzw|Z PRD97uFl2WPf0 -`w`j:JY h䠹 8tڎTzxīۼf g7AGCQ>{Go{Ú_+0F+?uאW,~2 OBp|vuo 0{5~Mة{ `)췁.~#A]g!j9K:+؇Ŋvae۰>d%Yρi@1q]=xo ;a=vp#?輬=ao/SL7&_~"F 63_]w& \==_-+lvQ_p|0rKSJc3q{50U2F=I/$&yge+ \K:t:RtA'縔Ũ 1KNAjh쾩bR;M o7^җv/CY˲@@@ ANormalCJ_HaJmH sH tH DA@D Default Paragraph FontRiR  Table Normal4 l4a (k(No List4 @4 {ZFooter  !.)@. {Z Page NumberD?@ABCHIjk78wxyMNWX()3BCVijklvwXY         ' (   + , - . C D g h i j k l    * + @ A B O P Q   $%:;PQfghijklz{hi}~  12EFGUV<=OPcdxytu0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000I000I00I000I00I000I00I000I00I001I00I00@0@0I00I00 %%%(l  :;;! i <:;; ; !(!!l,2$˳[c$,.D@(    c BA j0396942[1] $z(Y#R![Z V'}$ $D-n.n4$!99N>lPSY#S0*SN9N`TdI`T:?@ABCDEFGHIJKLMNPQRSTUVXYZ[\]^aRoot Entry F]D c1Table9+WordDocumentpSummaryInformation(ODocumentSummaryInformation8WCompObjq  FMicrosoft Office Word Document MSWordDocWord.Document.89qRoot Entry F h1Table9+WordDocumentpSummaryInformation(O  !"#$%&'()*+,-./012345678:;<=>?@ABCDEFGHIJKLMNPQRSTUVgDocumentSummaryInformation8|CompObjq  FMicrosoft Office Word Document MSWordDocWord.Document.89q՜.+,D՜.+,H hp  Texarkana ISD#  Overhead Sheets Title4 $,