!5"# " $%&'%('),-. -/0%12. -.2/ 3-,'2/ O*'P-&/',%,,-.% Q-0RS.'(% O&TUT%V

HTML
DOWNLOAD

Méret: px

Mutatás kezdődik a ... oldaltól:

Download "!5"# " $%&'%(')*,-. -/0%12. -*.2/ 3-,'2/ O*'P-&/',%,,-.% Q-0RS.'(% O&TUT%V"

Erika Bodnár
6 évvel ezelőtt
Látták:

1 MJˆ Š N g6;" C8 e\x36 7 EŒ >??A CBE9 1X ;bx1 >??A 9E 3WI1G!5"# " $%&'%(')*,-. -/0%12. -*.2/ 3-,'2/ ":"8!; <6;1= " 9 " >?@A BCDEFCEFEEB 01G1H56 6I7 JKLM NMK O*'P-&/',%,,-.% Q-0RS.'(% O&TUT%V =1IWX2X;1YZ6W3;"26W [ G3\23]X 51; 1GH6; ^ G\ 53_\G3]X I`6G 51 ;6G W1536G 51 26W\X3223]X WG3` I1G\;X 51 1G123; 3X1I6G I ; ;3XE =abg32 Z3GcX32 2\;" \Xd\1 ; `3; ; ;1X=\ 1GH6; G I G\\1G68 ; 26Xe\=23]X 51 `I36G _26I1G8 I1G\; 3XX1=4;1 d\1 ;6G W1536G 51 26W\X3223]X 2\W;1X \X I6; 3W6IX1 1X G\ 17XG3]X"!G\53I 1; 1GH6; 1X ;6G W1536G 51 26W\X3223]X 3W;32 231IW1X1 \X 51G_b6 556 d\1 ; 1WI1X53W31X6 I1d\31I1 I1GI 1X23]X 2\1G36X1G 1GI32W1X1 ;3X=abG32G8 1I6 W436X 6IG d\1 H1X ; 16Ib 51 ; 26W\X3223]X8 ; G6236;6=b ^ ; XI66;6=b" [ 64I fgi323]x 51; 1GH6; 1X ;6G W1536Gh E26W3;5 6I 0" i`3;e I1I1G1X \X 6I1 ; 1G\ ; G3\23]X 51; 1GH6; 1X ;6G W1536G 51G51 ; ]32 51 ; ;3X=abG328 G3X 51G26X621I ; X\I;1j W\;353G23;3XI3 51; _1X]W1X6 d\1 46I5" <6W6 3X532 G\ I];6=68 1; ;34I6 G1 =1G] 1X 1; WI26 51; ki6^126 93_\G3]X 51;!GH6; 6I ;6G 51536G 9>!?E 58 [:[#8 d\1 G1 `31X1 51GI6;X56 51G51 BB9 ^ d\1 I1lX1 `I36G 3X`1G3=56I1G 51 53_1I1X1G bg1g" [6G I4e6G \4;3256G _\1I6X 6I3=3X;W1X1 26X214356G 26W6 26W\X32236X1G 6I;1G8 6I ;6 d\1 1; ;126I X G1II \X IW31X6 X121GI3E W1X \1G3]X X;3j5"?\ 1G3;6 ^ _23; ;12\I Z21X d\1 =IX I1 51; ;34I6 E\Xd\1 X6 656E I1G\;1 221E G34;1 I \X l4;326 =1X1I; G3X `G6G 26X623W31X6G 51 ;3X=abG32" [6G 53123G63G I4e6G 26W3;56G G1 53`351X 1X 2\I6 1e1G 1Wc3E 26G7 f!; 1GH6; 3X1IX236X;h8 f!; 1GH6; 1X bg1g X6 Z3GcX326Gh8 mnopqrst v wqsxypqzp m{s }~ pxp }r} q v ƒ}qpt q przs oprp s v 6I 2\1G36X1G 64`3G 51 1G236E 1;46II6 \X G6W1I6 Xc;3G3G 51 ;6G Ib2\;6G d\1 26W6X1X 25 \X 51 ;G G12236X1G"

2 !!" #$%& ()*+,-&./0(1/+2.-/+& : 6;<9 : => 8! ;9:< :? :9 : :@8" 6!9A 68:9!9B!9 8 ;>!!" ::!: 9 : 6 6:B!" C 99!" : D8 8E8 69 : 6;<9 > 9; 9 :9 :!98F!!" 9 C5 6!85 9;!869 6> :@8F " :?9 6>"A G 986 : ;6B!" : 9!9!69 :?9 6!9 C?9 8! 9! : D89 D9 #!99 9 <9H 95 C >995 6!4A G :!!" : 9 D9 :?9 869 #E8!9!:!9 8 : 6 >:F : E8 D?9 6!94!6 86:!9 8 <9 : :9;< C 8;668:9 8 7!8 :A IE F9 :9 :!"F!!9 DJ76! E8 69!8:9 :9; 9 8;668 :@6 >9 #/(K01-L +1M(/0./-L 2+)0(&+/-L N(O.2+/-4A 69 :69!8666> !96:9!9 969!866>9 # 99 : 8 9; : 9:8!!"5 8 :F!69 :!9?7 : 669 C 8!" 99 : 889 : D84A 6;<9!5 :P5 D8!9 E8 9 9 :9: 9 E8 6;Q 8: 86 : 6Q!69 FC E8!66 96!!6B!" : 976! : 99!" :?9 9 :9F!99 DF!" DJ76! 6> 6:8!!" C :9;< :@6 RSTUVU XYURSZ[XS\]SZ^VU_ `Sa\YbZ SRScVdVe fv aszvcs ascgyzs]e hzs!" 96>!9!9"! E8 D87 976! : fyihuyjz_ ksdys V] lzs] fv] ^cs\sm[e ]S RcV[dhRSdYjZ fv] Sh^[c gycs VZ 699!9>>! 6 8:: C :>:: DJ76!H $n-) /K(o-) N(p.-) q r s+/ *(1N.0.p- tk( &+ M(/0( 0-N( 2-/2.(/2.+ p( tk( &+) p.n(/).-/() p( &+ &(/MK+ ()*+,-&+ 1(u+)+/ &-) &vn.0() p( )K +&p(+w %)0- )(MK1+N(/0( s+1x tk( )( o+&-1( Nx) yk)0+n(/0( &+.N*-10+/2.+ p( &+ K/.p+p &./Mzv)0.2+ { tk( )( 2-N*1(/p+ &+ /(2().p+p p( tk( 2-/o.o+ 2-/ &+ p.o(1).p+pl tk( &+ (/1.tK(2(3 #A }4A 6 8D 9@!:9 F!9!6!86F :>:: 9 :!66 : aszylvu^[ ~hv hz S\[cfSmV U[dY[]YZgTU^Yd[ fv V]S cv~hyvcv d[zuyfvcsc 96!869 #:9"D!5!868 C Q6!4A <:9 : :9 6!86" FE8!66! 9;<6>9!6 6:9 R[c Y]Sƒ VU^V ^cs\sm[ fvuryvc^s VZ V] ]Vd^[c hzs \hvzs cv V YjZ U[\cV

3 ! 9 "9# $9 % &' (% 9 9 9) *+,-./01 3/ +* * 78 9/5,7+ 6*:8;6/ < 90-+;:9-6/ +;8/ => /4- -0,;* *0-74/5 *A,0;9; ;:9704-6*+ B7* *8C5*84D -0 =/E 9 9# F % &' ( G ! /5*94- /,5*+95;,4;H-1 I-=J;K8 L-9* /4-9;D8 B7*,7*6*,-5*9*5 G G G 9 M )# $9 9 ) 9! 9 9 9%!9 9 9 N *C*94;H-=*84* +/8 0/+ 6;99;/8-5;/+O P5-=>4;9-+ < /54/P5-CQ-+R1 I-=J;K8 99% # S 9 T9% 9!' U9E '9V U9V 9 % 9 9 # $ 9% G G W # S9% G G9 N9 9 9 N N 9 9 G9 N G 9 9' ! 9 "9# X YZ[ ]^_àb[ ]c _`d^]^ cb ef^_gcfhb^i N 9 9 "9 j#? 9% ' % G 9 9 # $ 9 Fk 9 G G 9M UG [b lm] _`^n hbc ][ ]^_àb[ ]c om]hf`v #pq# $ 9% 9 9 N 9 9

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àb c]v]yt[ RSTUTSTV_ Tdcef [T ]XTVdaS]V **)! * **% '! * - 8) '$ % %$'-g hijk mnopmkqrsjk tumvmumn wr qmwmxykyzn kpmor { I@E BEA>=E>A }@=@ I ~GD EB~@~BE ~GE >? D EHG BI} EB~G ƒ> E?GI ~GD>EA@=BGI H>?GI >EA=>CBIA@HGI I> } >H> H>H ~B= IBE =B>I G > EG AB>E>E }=Gˆ?>D@I H> BH>EABH@H = ~AB~@D>EA> AGHGI >IA E ~GEI~B>EA>I H> > AB>E>E HGI ~?A =@IŠ K+ Œ3 %* ^ Z[fe ŽZ ]R]STcTV TV TY ds] ] Z TUV c ZVT[ ZRTS]d X][ T czvctrdz[ */ $ 4$ % %! /$*!03 *!%!3 *)%)$ " '!*)%)$!+ 9 %! '!*)%)$! $* 8)$!# *! 5*)!/ % ) $6*%!* *!*)%)$ %!!#$% K* *) $)*%! * )!**!0N+ % 3 *$! " *)! $ 5!*!0 %$'- /!*! 8)!' % ) /$!0 6 5% )!#$ $ 6 *' '$!!0!%!%$!.*)%)$ %!!#$%3 % '!; %$ $6*%!* *%!!+, %$*$ **!0 %6 * )% $ *)%$ %$'- 8)!. 7 *)%! ;5!* "!%6*%!*!4$% ~G=}G=@ $ *$!%+ 9 %;$! #'3 %* $!#)$! %0#!*

5 !"#$% 9 & '( # 99)* & 9 99) & + 9 9, )9( # & ) & + 9 9, ) 9( # / & )9 0!& :;84<5= >;=?39=;@5= A38 >8=8:B8C5 34 9DE B9;@;E8F;5>D 84 8E B9D?8=D?D:34;?5<;@D B89;D>G=<;?DH ( IJ'( # /, 9 K+9 L9* /99* /9' )9 M N9( $ 9 ' 9 9( O 9 P* 9 K+9 / * * / (!9Q 9 R & 9 )9* STUS STUWXYZ U[\]Y^_ `WSXS TSa Y_USaST[_US [ b_st cz\`[a[uydzt cz_ ( e &!+ f/ g N+ + 9!"#$% 9 L9 )9 - h3@84<3> 98i8E>8 j954:5* 9'( $ 9 ) ( #,) L `[a[ kzt STUWXYZTZT XSk k^lyczm XS_TYX[Xn bky[cyo_n WTZ XS cwkuyt\ztn 9 99* 9(* /99 9 9),99 9) 9+ ( e 99 9 STUWXYZT àsdyzt XS às_t[ STcaYU[ p XYbSaS_ XS \[_Sa[ ST`Sa[]kS cz_ ( N& % R & 99) 9 )9 )9( e / 9,99 L9 9 9

6 ! "#$#"#% &#"%'!%(!# ( &")%%(!# *+,-./ 123,/ :;3; 6+7<=23 6.-,/>, <3.<?/2>.@ 6.72,-A; &" "#(%"!( ( "#"B(%( C#'"%( D &"E%(F!# GHIJKL M# %N D #O&# "%!! # &!# &"%!!# "PQR ST V WX YZ [IZ\Z ]^LGKIL^_Z` WY Yab^GH ckxg^hxz GH\H YZ ZI[WI^Z JI^XG^JZY defghfi f kf lfemhghlfghno pq rsetfi qilqghfktqomq ihdohugfmhvfi w HI^x^XZYWL` ykw IWJIWLWX[ZX YZ zzlw LHzIW YZ ykw LW GHXL[IK{WX YHL ]^L[^X[HL [Wb[HL ykw JIWG^LZ WY H\zIW WX LK GH\KX^GZG^}X GH[^]^ZXZ~ C& F ƒ# %N # "%( %%)( $"##%!# &"%%'!# )P( M%#( #!%$#"##( %%( (%!#" >;7 2ˆ- Š, 7;-,3; 7;3 2-;= 4 /2-6+;->2Œ6;62.-,/,= +/. Š, Š2,Ž "##( #O"Q#"%(( C(P"#! %%((F #" &#!# Š;3 6.- ;= +-;/ ;=.3;62.-,/ +, /, 3,;=2A;- ;62;,= Œ-;= Š,= "PQ CSWL YZ\WX[ZzYW YZ _KYxZI^ ZG^}X Yab^GZ ykw Z_ZX Z XH L}YH ]W YZ \ZXH ]W ZzYZX[WL ]W X^_WY LHG^HGKY[KIZY zz H` L^XH [Z\z^aX ]W ^X[WYWG[KZYWL ]W Z_ZX Z]Z ykw LW _ZYWX \KG ZL _WGWL ]W WbJIWL^HXWL LHWGWL Z \H]H ]W JIH[WL[Z JHY [^GH LHG^H GKY[KIZY~` & F (% #Ž P" # #(!% "## &"!( )%(( D P(#")%#( &#"%##( (P"# # #(& # ( #!%( D # #(# ( &"%" # &"#( ƒ " D š% (#%'!# %P" CS Z]^H` [WYW_^L^}X { G^XW~F #( M# %## # š#" D"!# "PQ( "#( '&%( # %#"#(#(!%$#"##( œ"%(!# ( "PQ( %N #(%#( $Ž %(!# #(& # ( #!%( (( ##"## &"#!# %( %)%' &" ( %)#(% %' #"%"## $"! &" )%R SžyKa ]^cwiwxg^z Wb^L[W WX[IW WY ZzYZ JIWL[^x^HLZ ]W KXZ IWx^}X H ]W KX JZ L { WY YWXxKZ W ]W LKL \W]^HLŸ~ " # ( #(Ž!%( "#% ( (( $ %( # ( #!%(!# %%' 6.- =./ +/./ <3.<2./ Š, =;/ Š;Š,/ Š, 3,,3,-62;@ 6.-,= Œ- Š,!#%%" # "!!#!%)#" #% )#" #% #"# P( "( 1= ;,/>+Š2;,= 6.7<.3>;72,->..-ˆ>26. Š, / Œ-;= Š, / =; ;,- %%#"(!# #&šp% %% &D! # #(!%(!%##( #"%"#( ŽD! # # (%%'!# "( "# %#(!# P %(&Ž # " %%N # #& P)%!# %&#""#%' &" #O&%" # &"%# % B(%!# ( %!"#( M# #)%!#% $"##%!# #%%#!# ( D" ( "# # # P "!# %!!!# "#$#"#% ( #(!% (P"# "( #Žª"#( P% &"!(!#

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`#)72a' &'-3&'5"#' E b9 = c S d = 9 I9 b d = 98 9c ei< fe; < 8 I9 9d g9 Q9 9 b J9

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`! % )" %()&! (% %(%a %!," %"% +&%! +I%"!" &% M%( &!&!')(!,"* b% &% )" _ H)%F $ () ")%TF $%( %($%! %"!," "%$ &% %!,"!&!U! %" %"I) c%.&!% %!"&!%%"%. -!( )%(!"%( &% $d!!"ied(!* f ) "!T )" "_)" &% %"%I( &% +&%! (% ( )(( %(g!"%( %I!(& %" % &!()( &% ( )%( I%"!"( %" &W& &% )%" &% h! (!I* f "U!(!( %() &% I"!"%W( && H)% ( "(!&%!"%( H)% (% "(!I"" $ &!'%%"%( "!-%%( &% %"I)_% E'"W!F 'IdF (!"G!( -)!# (" %-!&%"! &% ( )((!"Ied(!( $$!( &% ( I%"!"( &% W$ F &%U(F &% (!%!( &% %!," $%(!$!," &% %" %()&!&* f - &% _ &% `! &! %" & % %$"!"%W(. $(!!," $d!.!"%-%"!. "!(. &% +&%! +I%"!" &% M%( %" &% %(%a -d")( " ( %&!( &% )"!!," (!-* V T"%( -!( &% %($! " %!TW )" "U!(!( &%&( &% ( )((!"Ied(!( "!T&(F $% ( " &-%!. a% % ). H)%!%"( I)"( &% %( a" $%&!& -!I%"! a" %-%!& ()!"'!," (!!"Ied(! (!&F ( (% "!%"%" %" +I%"!" )* i"%%(& $ ( $!)!&&%(!"Ied(!( H)% $%(%" % 37=@90[7 :7/2>8;j25 k048>2 C:;2 82Z0 9=0 Z9748>0 :7 9= =28;<;7>2 &%$!- )" $ %!T )" "U!(!( WG!.(%U"!* f(% _ (% %" %" % &!(%c %,!.%&,I! &% $% lifb.mf $ H)%. % % &-%!U. (%!) &% "%

9 !99 "#$ %9 &'()*+ -./+ *0(12)' 304)*'2 02 '452/(/(.0 2' 2+46/)1. 7*+80./ :; <9 :;$ = 9 9A BCD FGHIFJCH CKLMNHCFCOMH OCD PMFGNQDGHRM OCLMHJRPMS DG RTFMHLMU HGFRVT OC CWJHGTXCHRYKMY RTTCFCYGHRMY Z CD CKLDCM OC QT D[WRFM TM HCFMTMFROM LMH DG \CGD ]FGOCKRGS CTJHC MJHGY^?$ `#9 a 9 9?9 $ b999 c9 %?d9?<9 9e 9 9@ 9 9$ = 9 a 9 9 d 9e RfCf g >9 9e? ># 9 :9 9 < 9@ 9 9@9 $#$ %9 <99 9g?<9 < 9 9@ 9 a? $ h < 9 9 9??9 9 :9 )*'jk(.0 0()0*0+)/7+( 2/46lm()/3+( n10 /.04)/o3'4 3/0*)+( (1pq6*17+( A BrG JCDCTMPCDG GLDRFG QT KMOCDM YRKLDC OC CYJHGJRU stutvwx z{ {x}~u{ z{ z{ ~xu v vwx uxu z{ u {u vzuz ƒ vt {x}~u{ { v v uz ˆ Š { {x}~u{ ~ }u ƒ ~{ {Œ~{ u v u}vxu v YMFRMCFMTVKRFMY Z FQDJQHGDCY CYJIJRFMY CT DMY JCDCPROCTJCY^f Ž < e? :;9 ; $# >>9??9 9<99 9 9??99 $#$ Ž <9 9?9? :? g a?9? 9 a @ 9 ;@9 9 9 a 9 a g9 9?9 9a :9 9:? 9$ p(0*j'3/ 4 o4'2 3'p0 (0 '2'* n10 2+( )*'p' +( 3+8? 9 <9?d 9?99 9 g9?9 9 < <$

10 !"# #!" $#$ " %"#"!## "&% &!#' $ &% ( )%&*%# *+% ",%*-$ "&-,%*#." * $#* &!(*" ( * " "#/#0 & # : <=>2? 47>@1@9 >@4>@?@9=7> 59=@>@?@? 3A? @9=@?B #C D"%$E F%"#$ "G "# &%.*%#!!%# & "&# %)"%#*%, & # *##G *$ *# & HIJK-LE J & &"#*#G # )MG C # & "#/#0 # *0# & $##,!"%$# N( O$ &*%& &!P%#-.&#$ " %QD"%*G *%,%* ( #"!,%* / #0 $ &% & *$%*#*%, $#%)#E R# *$!%#*%, & S)%#!"# * T+%" "#& & # *- "%, & "&% /!#' $ &% & *$%*#*%, $#%)#G # # )M C %"&* *0" & "$# & %"T!## # %QD"%*# U%!P%*# #*"# (!## "# &%*%!%# #*%#&#E

Hasonló dokumentumok

VÁLASZLAP ..BF.. KockaKobak Országos Matematikaverseny MINTA 2012. Kezdő feladat: KockaKobak Országos Matematikaverseny MINTA 2012.

VÁLASZLAP ..BF.. KockaKobak Országos Matematikaverseny MINTA 2012. Kezdő feladat: KockaKobak Országos Matematikaverseny MINTA 2012. ..BF.. 1. AZ CP OJ VZ 2. DT ID WR ZX 3. AT ER NX RD 4. KF NF TF XJ 5. CV HF LD TL 6. MB SZ XD ZF 7. GB JH NL SB 8. FJ OD OP XP 9. FP PB RP WL 10. IP MH TX WX 11. BX JZ QL YB 12. HX KL MZ ST 13. FV JT VN