ГДЗ - алгебра - 7 класс - Алимов

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  • ..

    7

    : . 7 . . / ..

    . 10- . .: , 2002 .

  • 2

    I.

    1.

    1. 1) 75 3,75 = 71,25 2) 124

    10048,02548,0 ==

    3) 3112

    32 = 4)

    141

    81

    748:

    74 ==

    5) 1112211

    112

    215 =

    = 6) 1617

    148141:

    711 =

    =

    7) ( ) 429:185,4:18 == 8) ( 10.5) 0,4 = 4,2

    2. 1) (13 17) (13 + 17) 2) 7,2312

    3. 1) 158

    1535

    51

    31 =+=+ ;

    158

    15210

    152

    32 ==

    158

    158 =

    2) 40 0,03 = 1,2; 6 : 5 = 1,2 1,2 = 1,2 3) (10 ( 2)) 2 = 24; 3 (10 2) = 3 8 = 24 24 = 24 4) 3 (2 + 6) = 24; 2 (2 6) = 2 12 = 24 24 = 24

    4. 154 2 . 50 .; 76 3 .; 2,5 154 + 3 76 = 385 + 228= 613 . : 613 . ( ).

    5. 1) 3,815123237,1 2 =+ ;

    3,81583,1515123237,1 2 =+=+

  • 3

    2) 7,108,0:4,6100)21(7,27 2 =+

    7,1087,28:64257,278,0:4,6100)21(7,27 2 =+=+=+

    3) 48 0,05 2)31( 54 + 1,7 = 1,9

    9,17,164,27,1543105,048

    2

    =+=+

    4) ( ) 85,146,0:24,053155,2 2 =+

    ( ) ==+=+ 4,025,156:24925,66,0:24,053155,2 2 14,85

    6. 1) 241

    201

    65

    41

    51

    31

    21 =

    =

    +

    2) 569

    269

    2813

    21

    132

    43

    72 =

    =

    3) 531

    324

    311

    41

    324

    94

    971

    41

    324 =+=+=

    +

    4) 764

    72

    7152

    71

    715

    41

    431

    71

    715 ===

    +

    5) ( ) 07,0107,013:173007,013:)173313( 2 == 93,0=

    6) ( ) == 967,2251)367,23175(1 2

    ( ) 03,097,0103,24251 === 7. 1) 1

    5,7155,7

    45,315253,0

    25,31553,0

    2

    2==+

    =+

    2) 02,015

    3,05:75

    103

    3107,0

    5,0:5,7

    3,03136:2,4

    ==

    =

    3) ( )( ) ( ) 4033401,151,18

    3401,631,18

    3113 2 ===+

  • 4

    4) ( )( ) ( )( ) =+=+ 7,0:1,327267,0:1,333,0:8,7 3 ( ) 37,0:1,27,0:1,31 ==+=

    8. 1) 482402,0 = ; 6248 , 2) 60003,018 = ; 1818 = , 3) 775

    5215 = ; 7770011,0 =

    77 = 77,

    4) 5,41841 = ; 5,49005,0 = ; 4,5 = 4,5; .

    5) 111 : 3 = 37; 0,1 370 = 37; 37 = 37; . 6) 6,5 12 = 78; 78 77, .

    9. 1) 93,7852,2307,18 = , .. 011007,18;11052,23 >

    10. 1) 1,5 . + 41 . =

    47 .

    .

  • 5

    2) 541 (.) :

    47 (.) = 3

    74

    421 = ()

    541 .

    3) 6,5 . 541 . = 1

    41 . -

    3 /. 4) 3 (4 (/)) 1,5 (.) = 18 , 5

    41 .

    5) 141 (.) 3 (/) = 3

    43 ,

    141 .

    6) 18 () + 343 () = 21

    43 ,

    6,5 .

    .. 2143

  • 6

    13. 1) 5,4206030607 =+ .

    2) m = 60 m .

    3) p . = 160

    p .

    4) m l p =

    ++ plm60160

    14. 1) 44:21

    21

    415

    120

    4141

    5145

    414

    212

    516

    325

    ==+=+

    +=

    +

    +

    2) ( ) 213102,602,631

    201,2229,231,83 ===+

    15. 1) ( )02,466,0 + ; 2) ( )27,0:33,0 x

    16. 1) =+=+

    +=+

    +2,05,34,47,0

    2,885,3

    4,42,021

    2,82415,3

    4,42:4,0121

    17,37,3 =

    2120

    4240

    2,44,44,0

    2,81405,3

    4,41:4,0021

    ===++

    2) ( ) ( )( )

    ( ) 1,0101

    3161

    3116

    114111

    ==++=+

    ++

    ( )( ) =

    =+

    =+

    ++10

    412

    3112412

    3126

    124112

    409

    1049 =

    17. 1) a + 999999 = 0, a = 999999

    2) 05

    3 a , a

    3) ,047

    1 =+

    aa a = 1 4) 1a 2 + > 0 a

    18. (400 + 10b + c) : 30 b = 2, c = 0; b = 5, c = 0; b = 8, c = 0

  • 7

    3. . 19. p = 6x + 3y

    20. m = 15a + 20b

    21. m = al + cn

    22. (mn + k) , m = 30, n = 25, k = 60 81060750602530 =+=+ ()

    : 810 .

    23. , .. , - 45 ., : (45a + 15b + 10c)

    24. 1) ,2

    baba 2) 0,2 bb

    a

    3) 2,02,2

    aaab 4) baba

    ba ,0,

    2

    25. 1) ; 2)

    26. S c a b= + + 3 16

    1 23

    2 12

    ;

    = 3,3 /, b = 5,7 /, c = 10,5 /.:

    =+

    +=++=

    102575

    103335

    262119

    1075

    212

    1033

    321

    2110

    613S

    534

    2124

    57221334

    572

    114

    133 ==++=++= : 53 .

    27. ;. tS= .

    1. = tS

    28. 1) a b : a = 2n: b = 2k ,4:4,22 nknkknba == ..

    2) a = 2k; b = 2k + 2 ) k , k = 2n; a = 4n; b = 4n + 2 4n : 4; 4n + 2 : 4 ; ) k , k = 2n + 1

    ( ) n n= + = +2 2 1 4 2 4: ; ( ) ( )b n n= + + = +2 2 1 2 4 4 4: -

  • 8

    : .

    29. 1) C R R C= =22

    2) mV = ) = m

    V; ) m V=

    3) lts += ) l s t= ; ) = s l

    t; ) t s l=

    30. a + 0,8a + (0,8a + 5) = (2,6a+5) .

    31. 1) 1 34

    14

    2+ = 2. 7 . 15 . 2) .. 2 < a < 5, 10,5 : 3 = 3,5 (/) - . 3) , a , 2 < a < 5 S = 3,5 (a 2) 4) (7 + 3,5(a 2)) .

    4.

    32. 1) ( ) 184045,0112945,01145,045,029 ==+=+ 2) ( ) ( ) ( )( ) =++=++

    313,243,442,488,51

    313,242,483,448,51

    ( ) 4031120

    3120100 ==+=

    3) ( ) ( ) 671393,807,451,149,551,193,849,507,4 ==++=+ 4) 11,401 23,17 + 4,401 10,83 = 11,401 + 4,401 (23,17 + 10,83) = 7 34 = 41

    33. 1) 4a + 2b + a b = 5a + b 2) x 2y 3x + 5y = 2x + 3y 3) 0,1c 0,3 + d c 2,1d = 0,9c 1,1d 0,3

    4) 8 7 2 13

    23

    8 7 2 13

    1 23

    , , + + = +m n m n m n

    34. 1) 2,3a 0,7a + 3,6a 1 = 5,2a 1 2) 0,48b + 3 + 0,52b 3,7b = 2,7b + 3

  • 9

    3) 13

    12

    16

    56

    2 56

    2x x a a x a+ + = +

    4) 56

    13

    16

    23

    3 23

    13

    3y b y b y b + = + 5) 2,1m + n 3,2m + 2n + 1,1m n = 2n 6) 5,7p 2,7q + 0,3p + 0,8q + 1,9q p = 5p

    35. 1) 3(2x + 1) + 5(1 + 3x) = 6x + 3 + 5 + 15x = 21x + 8 2) 4(2 + x) 3(1 + x) = 8 + 4x 3 3x = 5 + x 3) 10(n + m) 4(2m + 7n) = 10n + 10m 8m 28n = 2m 18n 4) 11(5c+d)+3(d+c)=55c+11d+3d+3c=58c+14d

    36. 1) 5(3x 7) + 2(1 x) = 15x 35 + 2 2x = 13x 33

    2132

    266133

    2133

    26113,

    261 ====x

    2) 7(10 x) + 3(2x 1) = 70 7x + 6x 3 = 67 x x = 0,048, 67 ( 0,048) = 67,048

    3) ( ) ( ) 7462121555236

    31 =+=+ xxxxx

    04,5704,12701,34,01,3 ===x 4) 0,01(2,2x 0,1) + 0,1(x 100) = 0,022x 0,001 + 0,1x 10 = = 0,122x 10,001 ( ) 221,11001,1022,1001,1010122,0,10 ===x

    37. 1) ( ) ( ) 18,026,1715,31,214,0

    71 ==+

    2) ( ) ( ) 28,036,31212,124,08,4

    121 ==

    3) 281513

    417

    7263:

    4321

    7618 =+=

    +

    4) 112377

    1634

    713

    51

    161520

    7515 =+=

    +

    38. 1) 1,2a (0,2a + b) = 1,2a 0,2a b = a b 2) 0,7x (2y 0,7x) = 0,7 2y + 0,7x = 1,4x 2y 3) 0,1(x 2y)+0,2(x+ y)=0,1x 0,2y+0,2x+0,2y=0,3x

    4) nmnnmmnn321

    32

    312

    32)2(

    31)3(

    32 =+=+

    5) 8(a+3b) 9(a+ b)=8a+24b 9a 9b=15b a 6) 3(c+d) 7(d+2c)=3c+3d 7d 14c= 11c 4d

  • 10

    39. 1) ( ) ( );421831732 baba +=+

    6a + 14b = 6a + 14b .

    2) ( ) ( );231013,02,0 yxxy =+

    0,2y + 0,3x = 0,3x 0,2y .

    40. 1) 3; 2) 4; 3) 4; 4) 2

    41. II x . I 0,8 x , III ( ) 5,08,0 + xx . ( ) xxx 9,05,08,0 =+ . III -. x > 0,9x >0,8x, II , I III .

    5. 42. 1) 4,385 + (0,407 + 5,615) = 10 + 0,407 = 10,407

    2) 18134

    18134

    873

    1813

    877 =+=

    +

    3) 0,213 (5,8 + 3,413) = 3,2 5, 8 = 9

    4) 958

    94312

    17131

    943

    17410 ==

    43. 1) a + (2b 3c) = a + 2b 3c; 2) a (2b 3c) = a 2b + 3c 3) a (2b + 3c) = a 2b 3c; 4) (a 2b + 3c) = a + 2b 3c

    44. 1) a + (b (c d)) = a + (b c + d) = a + b c + d 2) a (b (c d)) = a (b c + d) = a b + c d 3) a ((b c) d) = a (b c d) = a b + c + d 4) a (b + (c (d k))) = a (b + (c d k)) =

    =a (b + c d + k) = a b c + d k

    45. 1) 3a (a + 2b) = 3a a 2b = 2a 2b 2) 5x (2y 3x) = 5x 2y + 3x = 8x 2y 3) 3m (5m (2m 1)) = 3m (5m 2m + 1) = 3m (3m +1) = 1 4) 4a + (2a (3a + 2)) = 4a + (2a 3a 2) = 4a a 2 = 3a 2

    46. 1) a + 2b + m c = a + 2b + (m c) 2) a 2b + m + c = a 2b + (m + c) 3) a m 3c +4d = a + ( m 3c + 4d)

  • 11

    4) ( )3232 2323 abmaabma ++=+ 47. 1) 2a + 3b + m c = 2a + 3b ( m + c)

    2) 2a + b + m 3c = 2a + b ( m + 3c) 3) ( )2222 3232 bamcbamc +=+ 4) ( )3232 2323 abmaabma +=+

    48. 1) (5a 2b) (3b 5a) = 5a 2b 3b + 5a = 10a 5b = 5(2a b) 2) (6a b) (2a + 3b) = 6a b 2a 3b = 4a 4b = 4(a b) 3) 7x + 3y ( 3x + 3y) = 7x + 3y + 3x 3y =10x 4) 8x (3x 2y) 5y = 8x 3x + 2y 5y = 5x 3y

    49. 1) (2c + 5d) (c + 4d) = 2c +5d c 4d = c + d c = 0,4; d = 0,6: 0,4 + 0,6 = 1 2) (2a 4b) (2a + 3d) = 3a 4b 2a + 3b = a d a = 0,12; b = 1,28: 0,12 1,28 = 1,16 3) (7x + 8y) (5x 2y) = 7x + 8y 5x + 2y = 2x +10y

    025,0;43 == yx

    25,125,05,1025,010432 =+=+

    4) (5c 6b) (3c 5b) = 5c 6b 3c + 5d = 2c b

    ( ) 3212

    21

    21225,02:

    212;25,0 ==== bc

    50. 1) ( ) ( ) nmnmnmnmnmnm +=++=+=+ 3:3;333458 ( ) ( )[ ] 3:458 nmnm

    2) ( ) ( ) nmnmnmnmmnnm +=++=+=+ 4:4;444735 ( ) ( )[ ] 4:735 mnnm +

    51. ( ) ( )( ) 012657106657532

  • 12

    ( ) ( )caca = 911:99 ( ) 9:99 ca 11 I

    53. 1) +=+

    +

    +

    4,0625,0

    665,104,1

    201356

    7

    4,025,083

    6434,2

    2504,2196,304,12025,099,004,1

    2077 =+=++=++

    2) ( ) =+=

    +

    432,1

    5:75,1

    54:25,1

    25,65,2

    43)8,02(

    5:4335,5

    54:75,0