Honors Solutions. Honors Lesson 1. Honors Lesson = 2. substitute 3 for ( r = 90

Transcription

1 Honors Lesson. A. Muliplying by : x x x x. subsiue for ( r s): since i is a square, we know all sides are equal, herefore: A ( + 9) square unis using from # A ( + 9)( ) A square unis. ( + 9) ( )( + ) 0 same as # his soluion does no make sense. We say ha i is invalid.. : C C 0 C 0 slope rise run 80 º Y + Y Y Y+ Honors Soluions 0. Plug in values for and Y: () ( ) + ( )( ) + + one side oher side Area x square unis Honors Lesson hours or hours and 8 minues ( muliplied boh sides by 0) minues (muliplied boh sides by 0) 0 days 7. subrac his ime, since he fauce and he drain are working agains each oher: 0 0 (muliplied boh sides by 0) 0 minues or hour ALGEBRA Honors Lesson - HONORS LESSON 9

2 Honors Lesson - HONORS LESSON Honors Lesson. rae of work x ime worked porion of job done / hours / /0 / hours / he raes have already been filled in. We are given he amoun of ime ha he gardener worked, so we fill ha in, and hen figure ou how much of he job he compleed. if / of he job is done, hen / of he job is lef. Fill in ha amoun, and hen figure he ime worked by he helper by using he values and solving for ime. R J J R J J ( ) or hours 0 minues x 0 f; significan digis. 9 x 0 m; significan digi.. 0 x 0 ons; significan digis x 0 g ; significan digis 0 soluions ALGEBRA

3 Honors Lesson - HONORS LESSON Honors Lesson. rae of work x ime worked porion of job done 0 hours hours he mason works a he rae of / of he job per hour, and he worked for hours. We also know his helper worked for a oal of hours. using he formula, we find ha he mason did / of he job. His helper, herefore, did / of he job. use he formula again o find ou he helper's rae: R J R R or 0 0 Working alone, he helper would have aken 0 hours o do he job f ; round o 0 f....9 in ; round o. in. ( 8. x 0 ) + (. x 0 ) 8, , m round o 8,000 m or.8 x 0 m. 0, 000, 00, 00 g ; round o 0,000 or. x 0 g. x 90 f ; round o 900 f in ; wo significan digis 8. (.8 x 0 ) x (.0 x 0 ) (. 9 x 0 ) m ; round o (.9 x 0 ) m 9. (. x 0 8 ) (. x 0 ) 0. x 0 km; wo significan digis 0. Area 9. x. ; round o 00 m ( one significan digi) Perimeer m; round o 0 m ALGEBRA soluions

4 Honors Lesson - HONORS LESSON 7 Honors Lesson. d r d ( 0) d 0 miles. d ( )( 0) 0 miles 0 is wice 0, so increased by a facor of. d ( 0) 00 miles d ( 0)( 0) 00 miles 00 is wice 00, so increased by a facor of. i will double, or increase by a facor of is imes, so a facor of 7. 8 is imes, so a facor of 8. he value of should increase by a facor of. 9. L L 0. L L he lengh decreases as he widh increases. Doubling he lengh decreases he widh by a facor of.. he value of should decrease by a facor of. Honors Lesson.. use he pyhagorean heorem: A + B C subsiue for A, and for B: + C C C C answers will vary is close (.), bu you may have come 8 up wih somehing closer. Honors Lesson A Y ( Y A ) Q imes iself R imes a b b a a ( Y b) c d ac bd Y Y F Y G H F G ( ) ( H Y ) +. F Y F G FG Y FG x y z z x+ y M z M z y y 7. ( M z ) [ ] M x+ y y soluions ALGEBRA

5 8. 9. [( a ) b b c c ( ab + b ) a P a + P a b ] b P a a Honors Lesson 7 - HONORS LESSON 9 E F H 0. E F H Honors Lesson a negaive number ha is no a fracion or decimal, for example:. any fracion, for. π,,, ec.. see char below example:. Each number in he series is he sum of he previous wo numbers 7. 8,, # of monhs drawing of pairs # of pairs new Honors Lesson 9. Row 0: Row : Row : Row : 8 Row : Row : Row : he sum of each row is wice he previous row. ALGEBRA soluions

6 Honors Lesson 9 - HONORS LESSON ; + 0 ; 0 + ; 0 + hey are all perfec squares.. he Fibonacci sequence. x x x 7. x x x x ! 9 x 8 x 7 x x 7! x x x x 7 x x x x x x 9 x 8 7!!! x x x x 0 0 x x x x x x x x x x x 0 0 0! 00! 0 x 00! 00 0! 8 Honors Lesson 0. A, B, C A, C, B B, A, C B, C, A C, A, B C, B, A ways.!.! 70. 9! 9 P 9! ( 9 )!!.. 9 x 8 x 7 x x x x x x x x x x 9 x 8 x 7 x, 0 0 P 0! 0! ( 0 )!! 0 x 9 x 8 x 7 x, 80, 80 P!! ( )!! x 0 x 9 x 8 x 7 x 9, 070, 080 Honors Lesson. like ilke klie elik.. liek ilek klei elki leik ikle kiel eilk leki ikel kile eikl lkie ielk keli ekli lkei iekl keil ekil ways; yes look olko oklo loko ookl kloo lkoo oolk kool olok okol kolo ways; no P x! x x x! x x x 0 soluions ALGEBRA

7 Honors Lesson - HONORS LESSON. P!! x x 0 x x x x x x x. P!! x x x x x x x x x 0. P!!! x x x x x 7. m, 8. x x x x a, and each appear wice P!!!! x x 0 x 0 x 9 x 8 x 7 x x x x x x x x x x x x 0 x 9 x 8 x 7 x x x, 989, 00 0! 0 x 9 x 8 x 7 x P!!! x x x x 0 x 9 Honors Lesson. x x 7 x 8, 00 ( + ) ( ) Y Y! Y x x! Y!! x!. ( + ) A A 8A. + P Q. P Q 8! x x! PQ!! x x 0P Q! ( 7 ) 7 + ( ) 7 7!!! 0 7 x x x!! x x x Honors Lesson. Area ( ) ( ) 0, if fee, hen he long side would be: f if fee, hen he long side would be: f Area 0 0, , ( 0) ( 00) 0 0, if 0, hen he oher side would be: ( 0 ( 0) ) ( 0 0) 00 0 f 0 x 0,000 f if, he oher side would be 0 ( ( )) ( 0 00) 0 0 f 0 x 000 f ALGEBRA soluions

8 Honors Lesson - HONORS LESSON. Area ( + 8) ( ) 0 8, 8makes no sense if, hen he heigh is: in ( ) ( + ) ( ) 0, makes no sense if, hen he lengh is: + 9 in Honors Lesson. Done.,000 x. $ 7, 700 increase, , 700 $ 8, 700 now.. x 0 $7.0 amoun of decrease $. 0 new price. 8. x.9 8. more bushels per acre. x 8. $. 0 more per acre in sales $ 9. 0 benefi per acre x 0 $ 9,. 00 more han wihou ferilizer. x0 x 8. $ 7, 7. 9, WP x 7,7. WP. 079 or 7.9% (rounded) WP.079 or 7.9% (rounded). 9, 0, 78 8, 77 8,77 WP x 0,78 increase WP. or.% increase (rounded). x 9, $, 0. 9 increase nex year 9, +,0.9 $, 8. 9 in sales nex year if here is he same percenage increase gallons saved. WP x.7 WP. 8 or.8% (rounded) 8.. gallons saved per hundred miles driven, so. x. gallons saved. x.98 $7. saved (rounded) 9. 0,7 x.00 8,8 0. 8,8,70 WP x 0,7 WP or 00% Honors Lesson E f h PA F A F P P L+ W P L W P L W k PV P k V n a + b n a+ b n b a M a + b c+ d Mc ( + d) a + b c + d a+ b M c a+ b d M 0, 7,70 increase soluions ALGEBRA

9 Honors Lesson - HONORS LESSON 7 M 7. i will increase., r 0 : d 0 80, r 0 : d i will decrease., r 0 d, r 0 : d () 0 9. R will increase as E increases. 0. R will decrease as i increases. Honors Lesson. he smaller gear will move faser.. Rn rn. 0() r( ), 0 r r 0 rpm Rn rn Rn n Divide boh sides by r. r R n Divide boh sides by n. r n. n rn R rn R n n Rn r Rn r n. r Rn n r 00( 0) 0, 000 r 0 r 00 rpm. n rn R n 0 0 8, 0 n 0 n eeh 7. R rn n R 00( 0) 90, 000 R 90 R 00 rpm 8., 000( 0) r(, 000) 0, 000, 000r r in Honors Lesson W + W 0 ( ) W + W ( + ) 8 + W 8 W + ( W ) ( W ) ( )( ) + + W + W + ( + ) W + W ( + ) + + ( ) + or ( ) ( ) ( + ) ( ) + ( ) ( ) ( ) + + ALGEBRA soluions 7

10 Honors Lesson 8 - HONORS LESSON 0 Honors Lesson 8. cener recangle: ( + ) [ + ] + ( + ) smaller recangles: [ ] ( + ) + ogeher : unis f. lower secion: ( + ) ( + ) ( + ) op secion: ( + ) (( + ) ) ogeher : unis. π( + ) π( ) or π + 8π + π+ π. Answers may vary choose a value for n. and raise o he sixh power. For example, 79. oher possibiliies are: ; 79; 0 n n xn n n 0 n x,09;, n x n x n x n n Honors Lesson 9... n P n s E P E s E s 00E s, 000 E s 0 vols n P n s E P E s 80 7, 00 n 0 s 7, 00n s , 00n s, 00 n s urns n P n s E P E s 00 E P E P E P 7, 000 E P, 0 vols Honors Lesson 0.. ρ m V m Vρ m ( 0)(. 009). 09 f f. 77 (rounded). 8 soluions ALGEBRA

11 Honors Lesson 0 - HONORS LESSON. PE mgh h h PE mg kq. F q r. kq r q F r 90. x x 0 0. x 0.8 x 0 r 7 x 0.8 x 0 0 x 0 r PV nr V nr P V (. )(. 08)( 9). 9. (rounded) Honors Lesson. hours b (baceria in housands) b (baceria in housands) (hours) ALGEBRA soluions 9

12 Honors Lesson - HONORS LESSON.. 0 Y Y Y M A(. ) d M 00(. ) M 00(. ) sudens Y increases faser and faser. Honors Lesson. Y M (sudens) since he number increases by a facor of. every years, see how many imes you have o muliply he original number (years) by. o reach, and hen muliply by : ( 00)(. ) 0 ( 0)(. ) (. ). so years 0 soluions ALGEBRA

13 Honors Lesson - HONORS LESSON Honors Lesson. Y Y YZ Z Z+. Q ( + B) R( + C) Q + QB R + RC Q R RC QB Q ( R) RC QB RC QB Q R. A B C C+ + E A B C E+ C A ( B C ) E+ C E+ C A B C. A ( + B+ C) + Y Z A A ( + B+ C) A Y+ Z A Y+ Z A + B+ C. C ( Y) + F CAB CY+ F C ( Y) CAB CY Y AB Y AB Your work for he following problems may look differen, depending on which equaion was subsiued ino he oher. You should have he same final answers.. Y R+ Y s+ subsiue s + for Y in he firs equaion: s+ R + s R s R Y E Y+ E Q subsiue E for Y in he second equaion: E + E Q E ( + E) Q Q E Y+ A BY B solve firs equaion for Y: A Y subsiue A for Y in he second equaion: B( A) B B AB B B AB B ( B) AB B AB B B Y Q Y+ R solve he firs equaion for Y: Y + Q subsiue + Q for Y in he second equaion: ( + Q) + R + R Q ( + R) Q Q + R Y C C Y+ D D solve he firs equaion for Y: Y C+ C subsiue C+ C for Y in he second equaion: C + C + D D C + D D C C ( + D) D C D C C+ D ALGEBRA soluions

14 Honors Lesson - HONORS LESSON Honors Lesson. AY + B C AY D E ( B D) C+ E C+ E B D. Y R A + Y A + R+ A ( + ) R+ R+ A + R + Y R A + R+ R Y A +. Y Q R QY + Q Q ( + QY ) R+ Q Y R + Q + Q Y + ( ) + Y 0 Honors Lesson. minimum.... maximum minimum A LW L 00 W A W( 00 W) W + 00W A W 00 W b ( 00) 00 a if W 00 hen: L 00 ( 00) x 00 encloses he larges area b a (. ). housand or,00 blouses. find maximum of 0, 000 : b ( 0) a unis of 0,000 00, 000 gallons 7. $ $. 8., 000, , 000, 700, 000 gallons sold $. x,700,000 $,, 000 Honors Lesson. H minimum (. ). (. ) H. (. ). (. ) + 0 H H 9. 7 f (rounded). P maximum 0 (. ) P. + 0 $,. H f (. 00) he ball will be a is highes poin a fee from where i was hrown, so afer ha, i will be descending. Find he value of H when is 00: H 0. 00( 00) +. ( 00) + H 0. 00( 0, 000) H f yes soluions ALGEBRA

15 Honors Lesson - HONORS LESSON 7. C 0. + ons (. ). C 0. + C. + C 7. + $ 0.. ry (0,0): (0) (0) < 9 0 < rue Honors Lesson 7.. ry (0,0): (0)(0) > rue ry (0,0): (0) + (0) 0 rue.. ry (0,0): (0) + (0) 0 false ry (0,): () > (0) + > rue. ry (0,): ((0) ) + ((0) + ) 9 9 rue ALGEBRA soluions

16 Honors Lesson 8 - HONORS LESSON 8 Honors Lesson 8 For clariy, only he final soluions are shaded.... parabola: (0) > (0) 0 > rue line: (0) > false. ellipse: 0 + ( 0) < 0 < rue circle: (0) + ( 0) 0 false hyperbola: (0) ( 0) < rue line: (0) < false For#,, and, i is a good idea o check addiional poins o accuraely deermine he shaded areas.. he inersecion is in he poins (,0) and (,0) soluions ALGEBRA

17 Honors Lesson 9 - HONORS LESSON 0 Honors Lesson 9. amoun cos per uni value. low grade lb.00 ground round 0 lb mixure + 0 lb.0.0 ( + 0) ( + 0) lb amoun cos per uni value meal lb meal lb mixure $ 00. per lb.. 7 $ 0. 9 whea corn mixure per lb amoun $. 7 per lb for whea $. per lb for corn cos per uni value Honors Lesson 0 ( ). R R R b 0 0 a ( ) people R 0 0( 0) R $ 800 ALGEBRA soluions

18 Honors Lesson 0 - HONORS LESSON + +. R W W R. W + W + 0 b a.. weeks. R. (. ) + (. ) + 0 R R $. 7 ( + ) R 00, 000, 000. R, 00 +, , 000 b a, 000, 00 $.00 + $ 0. $. 0 7 unis of.0 R + +, 00 7, , 000 R, 00 +, , 000 R $, 00. Y 0+ ( 0 Y b 0 more rees a ( ) 0 + rees per acre ) 8 Honors Lesson. + Y ; + Y 8 0 ( ) 0 Y ( ) 8 ( ) soluions ALGEBRA

19 Honors Lesson - HONORS LESSON. Y ; + Y 9 9 ( 9) ( ) Y ( ). + Y ; + Y 9 9 ( ) ( ) Y 9 9 ( ) ( ). Y+ Z ; Y Z ; Y+ Z ( ) + ( )( )( ) + ( ) ( )( ) ( )( ) ( ) ( ) + ( )( ) + ( ) ( ) ( )( ) ( ) ( 8) + ( ) + ( 0) ( 0) ( ) 9 ( 0) + ( ) + ( 0) ( ) ( 00) ( ) + Y ()( ) + ( ) ( )( ) ( ) + ( )( ) + ( ) ( ) ( )( ) ( ) Z ( 0) + ( ) + ( 8) ( 8) ( 0) ( ) 8 ( 0) + ( ) + ( 0) ( ) ( 00) ( ) ( )( ) + ( ) + ( ) ( ) ( )() ( )( ) ( ) + ( )( ) + ( ) ( ) ( )( ) ( ) ( 90) + ( 8) + ( 0) ( ) ( 0) ( 8) 8 ( 0) + ( ) + ( 0) ( ) ( 00) ( ) ALGEBRA soluions 7

20 8 soluions ALGEBRA