Algebra II. Student Name. Teacher

Transcription

1 Algebra Student Name Teacher

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3 3ol Solvng Systems of Equatons by Graphng 1 Mara wants to send her package by the least expensve overnght courer servce, Ar Express charges $4,00 plus $0.50 per pound, Quck Mal charges $2,00 per pound. a, Wrte both equatons and graph: Ar Express Quck Mal lo t g 10 bÿ f Mara has a 2 pound package, how much does t cost to shp t wth each company? c, f she has a 3.5 pound package, whch company has the better deal?

4 Systems of equatons can be classfed by the number of solutons. Graphcal Solutons of Lnear Syÿtÿmg u Two Varables ntersectng,mÿ,s Concdng,hw,,s Y ÿ ;+.'! 7ÿ',*)l t >ÿ,r"ÿ 0,v! f ollo sohÿlcm lo tlllqtle, soltlllon ÿu.soltlton n depend en l Dependcnt [no oll s,stcll ; 1. ndependent: 11 soluton --ntersectng lnes-othe answer s a pon/l! 2, Dependent: nfnte soluflonsoÿthey are the same lne--tlÿe a l+swe+' +s the equato1+ of t:he lheo 3. nconsstent: No so]utlon: Parallel lnes-=-'l'he answer s n(+ soluton., 2x+y = 5 - +y=2! J

5 'x + 2y = (2x-3y =0 J!! 4x-6y= -26-2x + 3y = 13 3x + 2y = x+4y=15 r m r J 1

6 Wthout graphng, classfy each system as dependent, ndependent, or nconsstent and state the number of solutons. (2x + 3y = 12 o 7. 3yx= +y=6 4-x -2x + 4y = 6 8, -3x+6y=8

7 Chapter 3 Warm-Up, You have 2 optons to pay for your lunch, Opton 1: pay $6 month plus $20 a meal, Opton 2: pay $3 plus $,40 a meal, A) Wrte and graph a system of lnear equatons to model the cost (c) of each servce for (b) blls that you need to pay each month. System: B) Fnd the pont of ntersecton, What does ths pont represent -- C) f you buy 18 meals a month, whch opton provdes the best value?, Graph the followng 2, y-4=21x , 2y+6=lx-21+8 ll -- ll ll -l- - ] ' - ll... ll ll '-- ' "- lll " - \3

8 3.2A SoMng Systems of Equatons by Substtuton Solve the followng, Check your answers, 4x + 3y = 4. 1, (2x-y=7 y-7= -2x 2, lox + 5y = y=3 x+5y= 1 4, 2x = 2 - loy

9 5, The length of a rectangle s three feet less than twce Fnd ts wdth. the dmensons of the rectangle f the permeter s 42 feet, 6. Kate has 85 cons n dmes and quarters, The total value of the cons s $13,90, How many of each con does she have?. Mary bought a total of 12 tckets for a move, She pad $8,00 each for the adult tckets and $6,00 for the chldren's tckets, She pad a total of $88,00 for the tckets, How many adult tckets dd she buy?

10 Chapter 3 Warm Up 2 1. You have 2 optons to pay for your lunch. Opton 1; pay $2 month plus $,80 a meal, plus $,50 a meal, Opton 2: pay $8 A) Wrte and graph a system of lnear equatons to model ths, System: B) Fnd the pont of ntersecton, What does ths pont represent C) f you buy 8 meals a month, whch opton provdes the best value?, Graph the followng 2 2, y- =ÿ(x+l) 3, 2x-3y=12 -ÿ-ÿ 1 ÿj... ÿ ÿ. -J l n ll l J r ul 1 JJ_L

11 (4x - 2y = 7 1. (x+ 2y=3 2x+4,y= -4 2, 3x+Sy= -3 2x + Sy = x= loy+2-3x + Sy = 7 4, (6x- loy = -14

12 5. The owner of men's clothng store bought 6 tes and 8 hats for $140, A week later, at the same prce, he bought 9 tes and 6 hats for $132. Fnd the prce of each, 6. Thomas has a total of 38 cons n nckels and dmes. The total value of the cons s $3,20, How many of each con does he have? 7, Stephane s bakng muffns, A tray of corn muffns takes 4 cups of mlk and 3 cups of flour, A tray of bran muffns takes 2 cups of mlk and 3 cups of flour. She has 16 cups of mlk and 15 cups of flour. How many trays of each type of muffn can she bake? 8, Roast beef has 25 grams of proten and 11 grams of calcum per servng, A servng of mashed potatoes has 2 grams of proten and 25 grams of calcum. How many servngs of each are needed to supply exactly 29 grams of proten and 61 grams of calcum?

13 3,3 Systems of nequaltes r!... ' - ÿ4- [ o y < -2x + 4 x > -3 l'tl rl llgl n 1 4V, ll!!r, ll 111 ; ]ll [l v f '! - Sl!J J: m, y<3x-6 y > -4x+2 gl H Jll ll H ll[ H[ fll!_... ll ll B ll +ÿ- g[ H

14 l y<4 4, y _ x y>>.x 5, y_<lx+sj-2 J.,, [ --ÿ!11 6, x+y<8 x>o y>o mz ÿmnmm ÿmÿm... ÿ

15 atrx ntroducton -rectangular array of numbers wrtten wthn brackets - Name t wth a CAPTAL letter - Classfed by ts dmensons rows X columns Ex. Wrte the dmensons of each matrx. 7-4 A= [12 9] C= [0 6 15] - Each number wthn the matrx - dentfed by ts poston n matrx - Use lowercase wth subscrpts Dmensons k12= K N /1::42 ÿ f9

16 *To multply matrces... the NUMBER the NUMBER OF COLUMNS n the OF ROWS n the 2Nÿ EQUAL Amxn Bnxp = Fnd the dmensons of each product matrx, EXAMPLES: (1) C2 3 D3x4 = (2) Elx2. F2xl = (3) G2x3 H2x3 = Set up a matrx equaton and solve the system., x-y=o 3x- 2y + 6z = 9 -x+y-2z= -2, 2x+y+z=8 x+y-z= -5 z=2x-y

17 Matrx APPJcatons 1. Fnd the number of nckels, dmes and' quarters n a collecton of 80 such cons f the nckels and the quarters are worth $4.50 and the value of the quarters and the dmes s worth $ A geometry teacher orders an assortment pack of shapes that contans trangles, squares, and pentagons. He receves a total of 29 shapes that have a total of 111 sdes. He gets 2 more trangles than squares. How many of each shape does he receve?

18 3. Mchael s plannng to vst a few places n the Houston area and he needs to fnd out how much t wl! cost to vst each place. When hs J aunt and uncle went to the Fne Arts Museum and the Natural Hstory Museum, they spent a total of $66. Hs grandmother took 2 of her grandchldren to the Fne Arts Museum, NASA, and an Astros game and spent $210. Hs best frend sent to the Fne Arts Museum, the Natural Hstory Museum, NASA, and an Astros game and spent $88. Hs sster went to 2 Astros games and the Fne Arts Museum for a total of $85. How much dd t cost to vst each place?

19 Secton 3.4: Lnear Programmng f 1, Fnd the values of x and y that maxmze or mnmze the objectve functon for the graph, Then fnd the maxmum or mnmum value A 11) k la mze for P = 3ÿ.\' -ÿ ÿ l' Graph each system of constrants, Name all the vertces, Then fnd the values of x & y that maxmze or mnmze the objectve functon, Also state the mnmum or maxmum value., 2 +y<lo +y _>,yÿo <6 Maxmze for P = 4x + y ll ll ll ll ll ll l ll ll ll lll ll... ' m Wl B lj

20 , yÿ_ÿx-3 y(_ -x+7 xÿ_o,yÿo Maxmze for P= 3x + 2y. f llll ll O l glr gl ll gl gl g gl -ÿ,f gl gl ll lal ll ! ll l,,, ]. x+y>5 4x+y > 8 x>_o,y>_o L [_ Mnmze for C = x + 3y :

21 5. You are gong to make and sell baked goods, A loaf of bread s made wth 2 cups of flour and ¼ cup of sugar, A cake s made wth 4 cups of flour and 1 cup of sugar, You wll make a proft of $1,50 on each loaf of bread and $4 on each cake. You have 16 cups of flour and 3 cups of sugar, Constrants: Objectve Functon: A, How many of each knd of baked good should you make to maxmze the proft? B, What s the maxmum proft?