# ГДЗ - алгебра - 7 класс - Мордкович

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• .. , ..

7

. 7 .: . . 2 : . /

.. , .. , .. . 6- ., . .: , 2003 .

• 2

1. ,

1.

1 ) 3,5 +4,5=8; ) 3,5+(4,5)= 1; ) 3,5 +4,5=1; ) 3,5+(4,5)=8.

2 ) 3,54,5=1; ) 3,5(4,5)=8; ) 3,54,5=8; ) 3,5(4,5)=1.

3 ) 15+7,5=22,5;

) 36,65 13

=3653 5 1

3= 183 16 549 80 469 431 ;

5 3 15 15 15 = = =

) 13,73,5= 7 5 137 7 959 1913 3 47 ;10 10 10 2 20 20

= = =

) 2 1 23 7 23 27 : 2 : 3 .3 3 3 3 7 7

= = = 4

) 1,5 3 = 4,5; ) 1,5 3 = 4,5; ) 1,5 (3)=4,5; ) 1,5 (3)=4,5. 5

) 1,5 : 3 = 0,5; ) 1,5 : 3 = 0,5; ) 1,5 : (3)=0,5; ) 1,5 : (3)=0,5. 6

) 1 12 3 6 35;2 3

+ = ;

1) 1 1 5 10 15 202 3 35;2 3 2 3 6

++ = + = = 2) 35 35 66 35;6 6 1 = =

) 1 1 12 3 6 222 3 2+ = ;

1) 1 10 63 6 203 3 1 = = ; 2) 1 5 20 5 40 45 12 20 22

2 2 1 2 2 2++ = + = = = ;

) 1 1 12 6 3 182 3 3 + =

1) 1 5 62 6 5 3 152 2 1 = = = ; 2) 1 15 10 45 10 55 115 3 18

3 1 3 3 3 3++ = + = = = ;

) 1 12 2 3 3 152 3 + = .

1) 1 5 2 102 2 52 2 1 2 = = = ; 2) 1 10 3 303 3 10

3 3 1 3 = = = ; 3) 5 + 10 = 15.

• 3

7

) 1 1 1(4 3 ) :113 ;3 5 15+ =

1) 4 1 1 13 16 65 48 113 83 73 5 3 5 15 15 15

++ = + = = = ; 2) 8 113 1 17 :11315 15 113 15

= = ;

) 1 117 : (4 3 ) 153 5 = ;

1) 1 1 13 16 65 48 17 24 3 13 5 3 5 15 15 15

= = = = ;

2) 2 17 15 17 1517 :1 17 : 17 1515 15 17 1 17

= = = = ;

) 1 2 26 7 18 9 3

+ = ;

1) 1 6 57 48 57 9 16 7 18 1 8 8 8 8

= = = = ; 2) 2 2 2 6 89 3 9 9

++ = = ;

3) 1 8 9 81 18 9 8 9

= = ;

) 1 14 3 115 4 3 2 78 15 5 4

= ;

1) 1 15 33 120 33 87 715 4 108 1 8 8 8 8

= = = = ;

2) 4 3 59 13 59 49 10 23 215 5 15 5 15 15 3

= = = = ; 3) 7 2 87 2 29 110 78 3 8 3 4 4 = = = .

8

) 1 17 : 2 4 :1 6;3 3+ = ;

1) 1 7 7 7 37 : 2 : 33 1 3 1 7= = = ; 2) 1 4 4 4 34 :1 : 3

3 1 3 1 4= = = ; 3) 3 + 3 = 6 ;

) 2 1 4 412 6 : 75 5 3 5

= ;

1) 2 1 62 31 31 112 6 65 5 5 5 5 5 = = = ; 2) 6 1 3 31 31 31 4 4: 7 : ;

5 4 5 4 5 31 5= = =

) 1 1 58 4 : 3 77 7 8 = ;

1) 1 5 29 29 29 8 8 14 : 3 : 17 8 7 8 7 29 7 7

= = = = ; 2) 1 18 1 77 7 = ;

• 4

) 1 6 1 3 142 2 : 5 13 7 4 4 23 = ;

1) 1 6 7 62 23 7 3 7 = = ; 2) 1 3 9 23 9 4 92 : 5 :

4 4 4 4 4 23 23= = = ;

3) 9 46 9 37 142 123 23 23 23

= = = .

9 ) (0,018 + 0,982) : (8 0,5 0,8) = 0,3125; 1) 0,018 + 0,982 = 1; 2) 8 0,5 0,8 = 4 0,8 = 3,2; 3) 1 : 3,2 = 0,3125;

) ( ) ( ) ( )273 51 22 1000027,3 5,1 2,2 : 0,00181000 18 = =

273 51 220 273 51 220 97 17 110 17017018 3 3 2 = = = = ;

) (0,008 + 0,992) : (5 0,6 1,4) = 1 : (3 1,4) = 1: 1,6 = 0,625;

) ( ) ( ) ( )135 91 33 10000013,5 9,1 3,3 : 0,0001310 10 10 13 = =

= 135 3300 91 : 13 = 135 3300 7 = 3118500. 10

) 1 13 2,5 16 433 3+ = ; ) 1 42 2 2,4 3,6

7 5 = ;

1) 2,5 16 = 40; 1) 1 4 15 142 2 3 2 67 5 7 5 = = = ;

2) 1 13 40 433 3+ = ; 2) 6 2,4 = 3,6;

) (24 +5,6) (24 5,6) = 544,64; ) 6 25 6 11 :119 38 19 2

= ;

1) 24 + 5,6 = 29,6; 1) 6 25 50 25 25119 38 38 38

= = ;

2) 24 5,6 = 18,4; 3) 29,6 18,4 = 544,64; 2) 25 6 25 19 1:138 19 38 25 2

= = .

11

) 1 1 12 2,4 15 2 36 383 3 3+ = + = ;

) 2 92 1 1,25 225 16

= ;

1) 2 9 52 25 52 132 1 3,2525 16 25 16 16 4

= = = = ; 2) 3,25 1,25 = 2;

• 5

) (25 + 5,2) (25 5,2) = 30,2 19,8 = 597,96;

) 8 1 1 24 1 :1 215 3 3 5

= ;

1) 8 1 68 4 68 20 48 14 1 315 3 15 3 15 15 5

= = = = ;

2) 1 1 16 4 16 3 12 23 :1 : 25 3 5 3 5 4 5 5

= = = = .

12

) 1 4 28 39 : 73 3 3 4

= = ; ) 1 2 7 14 212 7 73 3 3 3 3+ = + = = ;

) 2 1 16 1 16 16 354 1 : 3 : 75 5 35 5 35 5 16

= = = ;

) 1 2 13 41 17 103 123 85 103 1058 5 6 75 3 15 5 3 15 15 15

+ + = + = = = ;

13 ) 2 4,5 = 2,5; ) (2,3 + (14,8)) : 5 = 12,5 : 5 = 2,5;

) 1 2 1 19 22 75 95 132 75 37 753 4 2 2,56 5 37 6 5 37 30 37 30 37

= = = = ; ) 6 + 2,4 10,9 = 8,4 10,9 = 2,5.

14 ) . ) . ) . ) .

15

) 1 2 1 12 1 1 6;2 3 2 3+ + + = 1) 1 11 2

2 2+ = ; 2) 2 12 1 4

3 3+ = ; 3) 4 + 2 = 6;

) 2 33 2 5 7 2895 7 = ;

1) 2 173 5 5 175 5 = = ; 2) 3 112 7 7 17

7 7 = = ; 3)17 1 7 = 289.

) 3 2 1 3 2 1 3 414 14 14 714 7 2 14 7 2 14

+ = + = + = 1 14 7 6

14 + = ;

) 2 2 2 2 6 2 8 112 24 16 : 2 12 24 : 2 16 : 2 36 : 2 89 3 15 9 9 5 9 5

+ = + = =

= 4 1 166 41 830 369 461 1118 8 10 .9 5 9 5 45 45 15

= = = =

• 6

16 ) 4,16 + 2,5 + 6,04 + 3,5 = 4,16 + 6,04 + 2,5 + 3,5 = 10,2 + 6 = 16,2; ) 7,3 + 1,6 0,3 0,6 = 7,3 0,3 + 1,6 0,6 = 7 + 1 = 8; ) 1,06 + 0,04 7,04 + 2,16 = 1,06 + 2,16 7 = 1,1 7 = 5,9; ) 18,9 6,8 5,2 4,1 = 12,1 4,1 5,2 = 8 5,2 = 2,8.

17 ) 7,8 6,3 + 7,8 13,7 = 7,8 ( 6,3 + 13,7 ) = 7,8 20 =15,6 ) 6,95 3,42 5,05 = 6,95 3,42 ( 5 + 0,05 ) = 6,95 ( 17,1 + 0,171 ) = = ( 7 0,05 ) 17,271 = 120,897 0,86355 = 120,03345; ) 17,96 0,1 0,1 81,96 = 0,1 ( 17,96 81,96 ) = 0,1 ( 64 ) = 6,4; ) 4,03 27,9 17,9 4,03 = 4,03 ( 27,9 17,9 ) = 4,03 10 = 40,3.

18

) ( )1 1 1 157 6,8 7 3,2 7 6,8 3,2 10 752 2 2 2 + = + = = ;

) ( )3 3 3 342,4 2,4 42,4 2,4 40 304 4 4 4

= = = ;

) ( )1 1 1 132,5 16,5 32,5 16,5 16 44 4 4 4

= = = ;

) 1 16 4,8 6 5,2 6,2 (4,8 5,2) 6,2 10 62.5 5

+ = + = =

19 ) 60 60 = 3600 ; ) X 24 60 = X 1440 X ;

) X 1000 : 60 = X 32166

.. ;

) u : 1000 3600 = u 36 : 10 = u 18 : 5 = 3,6 u /. 20

) x = 3,5; 3x = 3 (3,5) = 10,5; ) x = 1; 3x = 3 (1) = 3;

) 47

x = ; 4 12 53 3 17 7 7

x = = = ; ) 133

x = ; 1 3 103 3 3 103 1 3

x = = = .

21 ) y = 1; 5y = 5 (1) = 5; ) y = 0; 5y = 5 0 = 0; ) y = 1; 5y = 5 1 = 5; ) y = 3,4; 5y = 5 3,4 = 17.

22 ) a = 3, d = 2; 48a + 12d = 48 3 + 12 2 = 144 + 24 = 168; ) u = 6, v = 1; u 3uv = 6 3 6 1 = 6 18 = 12; ) z = 8, t = 2; 8z 11t = 8 (8) 11 (2) = 64 + 22 = 42; ) p = 3, q = 6; 5p 4q = 5 (3) 4 6 = 15 24 = 39.

• 7

23

A 1 2 3 14

14

3 2 1

B 1 3 2 13

13

2 3 1

2A2B 0 2 2 16

16

2 2 0 1) 2 1 2 1 = 2 2 = 0; 2) 2 2 2 3 = 4 6 = 2;

3) 2 3 2 2 = 6 4 = 2; 4) 1 1 1 2 3 4 12 24 3 2 3 6 6

= = = ;

5) 1 1 1 2 4 3 12 24 3 2 3 6 6

= = = ; 6) 2 (3) 2 (2) = 6 + 4 = 2; 7) 2 (2) 2 (3) = 6 4 = 2; 8) 2 (1) 2 (1) = 2 + 2 = 0.

24

A 1 2 3 14

14

3 2 1

B 1 3 2 13

13

2 3 1

2AB1 1 11 11 56

56

11 11 1 1) 2 1 1 1 = 2 1 = 1; 2) 2 2 3 1 = 12 1 = 11;

3) 2 3 2 1 = 12 1 = 11; 4) 1 1 1 1 1 52 1 1 14 3 2 3 6 6

= = = ;

5) 1 1 1 1 1 52 1 1 14 3 2 3 6 6

= = = ; 6) 2 (3) (2) 1 = 12 1 =11; 7) 2 (2) (3) 1 = 12 1 =11; 8) 2 (1) (1) 1 = 2 1 =1.

25 a+b = 10, c = 7. ) a + b +2 c = 10 + 2 7 = 10 + 14 = 24; ) (a + b) : 2 c = 10 : 2 7 = 5 7 = 2;

) 10 7 17 18 8,52 2 2 2

a b c+ + += = = = ;

) ( )7 2 7 10 2 7 70 14 84 14 4,23 1 3 7 1 21 1 20 5

a b cc+ + + += = = = = .

26 ) a b = 12, b a = 1 (a b) = 1 12 = 12; ) c d = 0, d c = 0.

• 8

27

baba

22 ?

) a = 1, b = 2; 2 2 2 21 2 1 4 3 3 ; 1 2 3 ;

1 2 1 1a b a b

a b = = = = + = + =

) a = 3, b = 1; 2 23 1 9 1 8 4 ; 3 1 4 ;3 1 2 2

a b = = = + = + = ;

) a = 1,4, b = 1; 2 2 2 21,4 1 0,96 2,4

1,4 1 0,4a b

a b = = = , a + b =1,4 + 1 = 2,4;

) a = 3, b = 1; 2 2 9 1 8 2

3 1 4a b

a b = = = ; a + b = 3 + 1 = 2.

28

) x=2, y=3; ( )( ) ( )( )2 2 2 22 2 2 2 2 3 2 4 2 9 10 2

2 3 2 3 1 5 5x y

x y x y = = = = + + ;

) x=1,5, y= ( )( )2 2

2 2 2 23 1 9 22 21 2 2 77 362 3 2 9; 211 73 1 3 13 18 77

6 62 3 2 3

x yx y x y

= = = = + + ;

) x = 2, y = 0; ( )( ) ( )( )2 2 2 22 2 2 2 2 0 8 2

2 0 2 0 4x y

x y x y = = = + +

) x = 1,3, y = 0,5;

( )( )( )

( )( )222 2 2 1,3 2 0,52 2 2 1,69 2 0,25 2,88 2

1,3 0,5 1,3 0,5 0,8 1,8 1,44x y

x y x y = = = = + + .

29 ) x = 7, y = 4; 5x 3y = 5 7 3 4 = 35 12 = 23; ) x = 6,5, y = 2,1; 5x 3y = 5 6,5 3 2,1 = 32,5 6,3 = 26,2;

) x = 2125

, y = 293

; 5x 3y = 5 2125

3 293

= 62 29 = 33; ) x = 18, y = 7,4; 5x 3y = 5 18 3 7,4 = 90 22,2 = 67,8.

30

) a = 20, b = 12; 6 7 6 20 7 12 120 84 204 173 4 3 20 4 12 60 48 12

a ba b+ + += = = = ;

) a = 2,4, b = 0,8; 6 7 6 2,4 7 0,8 14,4 5,6 20 53 4 3 2,4 4 0,8 7,2 3,2 4

a ba b+ + += = = = ;

) a = 10,8, b=6; 6 7 6 10,8 7 6 64,8 42 106,8 5123 4 3 10,8 4 6 32,4 24 8,4 7

a ba b+ + += = = = ;

• 9

) a = 12, b=5,6; 6 7 6 12 7 5,6 72 39,2 111,2 383 4 3 12 4 5,6 36 22,4 13,6 17

a ba b+ + += = = = .

31 ) x = 8, y = 3; 2 22x xy y+ + = 64 + 2 8 3 + 9 = 64 + 48 + 9 = 121;

2 2( ) 11 121x y+ = = ; ) x = 7,6, y = 1,4; 2 22x xy y+ + = 57,76 + 2 7,6 1,4 + 1,96 = = 57,76 + 21,28 +1,96 = 81; 2 2( ) 9 81x y+ = = ; ) x = 10, y = 2,6; 2 22x