1. 10 , 20 . ( ). ?
2. ABC A 40o, B 20o, AB - BC = 4. C.
3. a b,
² + = ² +
4. A, B C 100 . A , B 10 , , B , C 10 . A C?
5. , . (. ), . ?
1. , :
x + y = 0 x+ y = 2.
2. 2/3 3/5 . , 1900 ?
3. AB O C ,
CAB OC. 蠠
CO ACB?
4. , 3.
5. .
.
.
. ,
, .. ,
, .
?
1. n 1000. n.
2. a 2 + a² - 4=0 2² + (² -4) + =0 ? .
3. ABC CD. ABC, , DBC 3 ADC.
4. . , , , 20%. ?
5. 100. 800?
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1. , .
2.
:
3. 5 . 50 /, 40 /, 30 /, 20 /, 10 /. , . 21-?
4. ABC BD ( D AC). , , AB =2 CD CB =2 AD. ABC.
5. : . , 21 , 10 . ? ( ).
5
1. : : 879 + 426 = 1305.
2.
. .
, , .
, . ,
, , .
. 24 .
7 5 10 - 2 10 =30 , 21 3 30= 90 . 3 30 .
. 28 ,
: (120 : 30 ) 7 , , 120 (,
).
5. : 503
: , , . . 6 , 2000 500 . 3 , 503 .
6
1. .
1 + (2 + 3 + 4). (5 + 6) = 100. .
2. : , , .
, , . , .
. 160 .
,
, . , . 102222 = 160 .
4. : 19 11 .
12 , 11. 20 , 19. 30 , 11, 19.
5. :
) )
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7
1. :
, 2 × 2 2: 2 = 5 5: 5 5: 5 22: 22 = 55: 5 5 5.
2: 2 + 2 + 2 = 5 + 5 5 + 5 5.
2. : 1760 .
:
, , , , . , , . 720 , 7203 = 2160 . , , 400 . ,
2160 − 400 = 1760 .
3. : = 9
, .
4. : , , .
6 , 5 , , ; , , , . , , , .
5. : 320
. , (. .).
. 10 1010 = 100.
, 1003 = 300 . , , . 20, ,
300 + 20 = 320 .
. 10 100 . 5 , 100 500 , , , , .
, . 40 , , 100 , . , 500 140 = 360 "" . , 140 + 360: 2 = 320 .
. , . 9 , ( ), , : 110 . 110 . 100 ( , :
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1).
8 .
1. : 5 .
x , 10 . 10 x (.). 20 . 20 3 x (.). 10 x = 20 3 x, x = 5 (.)
2. : 4
AB BD, BC. BCD - 20o, 80o(. .). CE - ABC. , ACE = 60o, AEC = 180o- (40o+ 60o) = 80o. , DEC , . C 20o, ACD = 60o- 20o= 40o. , ACD , , CE = CD = AD = AB - BC = 4.
3. : 1
: a² b² - (a- b) = 0 (a - b)(a+ b - 1)= 0.
. . ,
a +b - 1 =0, a+ b = 1.
. 19 .
, B 0,9 A, C 0,9 B. , C 0,81 A. , A 100 , C 81 .
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5. . 1. , 5.
, . .
9
. 2.
x + y = 0
x + y = 2, . x + y = 2, 2 . , 2, √2.
. 1200 .
x , y . , 2/3 = 3/5 , , + = 1900.
, : x = 900, y = 1000. 2/3 ∙ 900= 600, , , 1200.
3. : 2: 1
CAO CAO,
CA = AO. OA = OC , , CAO . ACO = 60º. , OCB (OC = OB) COB = 120º, OCB = 30º ( , , ACB , 90º).
. 225.
3, , 3. , 9 , 9 99 = 81 . , , 3 0, , . 89 = 72 . , . : 81 + 72 + 72 = 225 .
. .
, , , 20. , . , 50. , .. , (, ..) , .. .
10 .
. 125 1000.
: 1000 : 10001, 5002, 2504, 2005, 1258, 10010, 5020, 4025 .
2. . = 0, x = 2.
x 2 + ² - 4 =0 , (2 x+ a ² - 4) = 0, 2 x ² + (a ² - 4) x = 0. , , x 2 x ² + (a ² - 4) x + a= 0. x (2 x ² + (a ² -4) x+ a) (2 x ²+ (a ² 4) x) = 0, a= 0 , a x = 2.
3. . CAB = 60 º, CBA = 30 º.
, CBD ACD ( ). . CB CA √3. , tg CAB= √ 3, CAB = 60º.
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