As shown in the figure, it is known that A.B.C is three points on the number axis, and the number represented by point C is 6, BC = 4, ab = 12 The moving point P.Q starts from A.C. at the same time, the point P-2 unit length per second has a uniform speed of work along the number axis, and the point Q-1 unit length per second has a uniform speed of work along the number axis to the left. Suppose the movement time is t (T > 0), and what is the value of T, one of the three points o and P.Q is exactly the midpoint of the line segment connected by the other two points

------A -------- o (0) --- B ------- C ------ - (1) write out the numbers represented by a and B on the number axis: (2) the moving points P and Q start from a and C at the same time. Point P moves uniformly to the right along the number axis at the speed of 2 unit lengths per second, and point Q moves uniformly to the left along the number axis at the speed of 1 unit length per second
------A--------------O（0）---B-------C-----→
(1) a means - 10, B means 2,
⑵AP=2t，CQ=t，
① O is the midpoint of PQ
Before meeting, Op = 10-2t, OQ = 6-T,
10-2t=6-t，t=4；
After meeting: OP = 2t-10, OQ = T-6,
2t-10 = T-6, t = 4. 4)。
② P is the midpoint of OQ
OP=2t-10，PQ=16-3t，2t-10=16-3t，t=5.2；
③ Q is the midpoint of OP: OQ = 6-T, PQ = 3T-16,
6-t=3t-16，t=5.5；
To sum up: when the movement time is 4 seconds, 5.5 seconds, 5.2 seconds, put away
From 6t-10 = 3t-6, we can find that when t = 1 1 / 3 second,
P and Q are two places on the left and right of O respectively.
As shown in the figure, a, B and C are three points on the number axis. The number represented by point C is 6, BC = 4, ab = 12
------A--------------O（0）---B-------C-----→
(1) Write the numbers represented by a and B on the number axis
(2) The moving points P and Q start from points a and C at the same time. Point P moves uniformly to the right along the number axis at the speed of 2 unit lengths per second, and point Q moves uniformly to the left along the number axis at the speed of 1 unit length per second. Suppose the moving time is t (T > 0) seconds, and what is the value of T, one point between the origin O and points P and Q is exactly the midpoint of the line segment connected by the other two points
(1) a stands for - 10, B stands for 2, and (2) AP = 2T, CQ = t. ① o is the midpoint of PQ: before meeting, Op = 10-2t, OQ = 6-T, 10-2t = 6-T, t = 4; after meeting, Op = 2t-10, OQ = T-6, 2t-10 = T-6, t = 4. (it's not right to omit the meeting need 16 / 3 > 4). ② P is the midpoint of OQ: OP = 2t-10, PQ = 16-3t, 2t-10 = 16-3t, t = 26
The corresponding points of the known number ABC on the number axis are shown in the figure, simplifying | A-B | - | B + C | + | c-a|
Figure: - c-b-0-a - →
The corresponding point of ABC on the number axis
a-b>0,b+c
2A & nbsp; this kind of topic is to test your definition and mastery of absolute value knowledge. From the graph, we can see that a ＞ 0, B ＜ 0, C ＜ 0. From the addition and subtraction of inequality, we can get A-B ＞ 0, B + C ＜ 0, C-A ＜ 0. In this way, we can easily get the absolute value | A-B | - | B + C | + | C-A | = a-b - [- (B + C)] + [- (C-A)] = A-B + B + C + a = 2A
As shown in the figure below, the numbers represented by a, B and C on the number axis are respectively ABC. Try to simplify | A-B | and | B + C|
∵ C and B are less than 0, a is greater than 0
A-B is greater than 0, B + C is less than 0
∴|a-b|=a-b
|b+c|=-(b+c)= - b - c
C and B are less than 0, a is greater than 0
When using the complete square formula, how to determine the sign of each item?
After solving the two numbers in the complete formula, each takes its square, that is, they are all positive numbers. Then, if the product of two terms is twice, it depends on the multiplication result of the original three symbols in the complete formula [respectively the positive and negative of the first number, connecting the symbols between two numbers, and the positive and negative of the second number, such as (2-3), then the first number is positive, the connection sign is negative, and the third number is positive. The result is negative]
The first volume of the first grade of junior high school
In a word, it's algebra off test calculation problem (35)
1.125*3+125*5+25*3+25 2.9999*3+101*11*(101-92) 3.(23/4-3/4)*(3*6+2) 4. 3/7 × 49/9 - 4/3 5. 8/9 × 15/36 + 1/27 6. 12× 5/6 – 2/9 ×3 7. 8× 5/4 + 1/4 8. 6÷ 3/8 – 3/8 ÷6 9. 4/7 × 5/9 + 3/7 × 5/9...
Finding the range of y = cos2x + 2sinx-3
y=cos2x +2sinx -3
= 1-2(sinx)^2+2sinx -3
= -2(sinx-1/2)^2 - 3/2
max y = -3/2
min y = -2( -3/2)^2 - 5/2 = -9/2 -3/2 = -6
Range = [- 6, - 3 / 2]
The sign of complete square formula
Usually, if the formula like x ^ 2 ± 1 / 2x + 1 can be written as a complete square formula
But if so, how can x ^ 2 + 1 / 2x-1 be written as a complete square formula?
The above is just an example, not necessarily a complete square
A kind of
Can't this formula be written as a complete square?
Not every formula can be written as a complete square formula
I'm a freshman in junior high school. I'm looking for 70 mixed operations of addition, subtraction, multiplication, division and power of rational numbers
1) (-9)-(-13)+(-20)+(-2)
(2) 3+13-(-7)/6
(3) (-2)-8-14-13
(4) (-7)*(-1)/7+8
(5) (-11)*4-(-18)/18
(6) 4+(-11)-1/(-3)
(7) (-17)-6-16/(-18)
(8) 5/7+(-1)-(-8)
(9) (-1)*(-1)+15+1
(10) 3-(-5)*3/(-15)
(11) 6*(-14)-(-14)+(-13)
(12) (-15)*(-13)-(-17)-(-4)
(13) (-20)/13/(-7)+11
(14) 8+(-1)/7+(-4)
(15) (-13)-(-9)*16*(-12)
(16) (-1)+4*19+(-2)
(17) (-17)*(-9)-20+(-6)
(18) (-5)/12-(-16)*(-15)
(19) (-3)-13*(-5)*13
(20) 5+(-7)+17-10
(21) (-10)-(-16)-13*(-16)
(22) (-14)+4-19-12
(23) 5*13/14/(-10)
(24) 3*1*17/(-10)
(25) 6+(-12)+15-(-15)
(26) 15/9/13+(-7)
(27) 2/(-10)*1-(-8)
(28) 11/(-19)+(-14)-5
(29) 19-16+18/(-11)
(30) (-1)/19+(-5)+1
(31) (-5)+19/10*(-5)
(32) 11/(-17)*(-13)*12
(33) (-8)+(-10)/8*17
(34) 7-(-12)/(-1)+(-12)
(35) 12+12-19+20
(36) (-13)*(-11)*20+(-4)
(37) 17/(-2)-2*(-19)
(38) 1-12*(-16)+(-9)
(39) 13*(-14)-15/20
(40) (-15)*(-13)-6/(-9)
(41) 15*(-1)/12+7
(42) (-13)+(-16)+(-14)-(-6)
(43) 14*12*(-20)*(-13)
(44) 17-9-20+(-10)
(45) 12/(-14)+(-14)+(-2)
(46) (-15)-12/(-17)-(-3)
(47) 6-3/9/(-8)
(48) (-20)*(-15)*10*(-4)
(49) 7/(-2)*(-3)/(-14)
(50) 13/2*18*(-7)
(51) 13*5+6+3
(52) (-15)/5/3+(-20)
(53) 19*4+17-4
(54) (-11)-(-6)*(-4)*(-9)
(55) (-16)+16-(-8)*(-13)
(56) 16/(-1)/(-10)/(-20)
(57) (-1)-(-9)-9/(-19)
(58) 13*20*(-13)*4
(59) 11*(-6)-3+18
(60) (-20)+(-12)+(-1)+(-12)
(61) (-19)-3*(-13)*4
(62) (-13)/3-5*8
(63) (-15)/1+17*(-18)
(64) (-13)/3/19/8
(65) (-3)/(-13)/20*5
(66) 3/12/(-18)-18
(67) 5*(-19)/13+(-6)
(68) 4+4*(-19)-11
(69) (-2)+17-5+(-1)
(70) 9+(-3)*19*(-19)
(71) (-12)-(-6)+17/2
(72) 15*(-5)-(-3)/5
(73) (-10)*2/(-1)/4
(74) (-8)*16/(-6)+4
(75) 2-11+12+10
(76) (-3)+(-20)*(-7)*(-9)
(77) (-15)+8-17/7
(78) (-14)*10+18*2
(79) (-7)+2-(-17)*19
(80) (-7)/18/1+1
(81) 11/(-9)-(-16)/17
(82) 15+5*6-(-8)
(83) (-13)*(-18)+18/(-6)
(84) 11-(-1)/11*(-6)
(85) (-4)+(-12)+19/6
(86) (-18)/(-1)/(-19)+2
(87) 9*(-8)*(-6)/11
(88) 20*(-3)*(-5)+1
(89) (-18)-2+(-11)/20
(90) 15*1+4*17
(91) 1-10+(-14)/(-1)
(92) 10+(-4)*(-19)+(-12)
(93) 15/14/5*7
(94) 8+(-13)/3+1
(95) (-14)+6+(-2)*(-14)
(96) (-5)/(-13)/4+7
(97) (-15)/(-2)/(-12)+(-2)
(98) (-17)-(-20)-20*(-10)
(99) (-7)-10-13/3
(100) (-20)+(-18)+11+9
2/9 ×3
4. 8× 5/4 + 1/4
5. 6÷ 3/8 – 3/8 ÷6
6. 4/7 × 5/9 + 3/7 × 5/9
7. 5/2 -（ 3/2 + 4/5 ）
8. 7/8 + （ 1/8 + 1/9 ）
9. 9 × 5/6 + 5/6
10. 3/4 × 8/9 - 1/3
11.7 × 5 /... Deployment
2/9 ×3
4. 8× 5/4 + 1/4
5. 6÷ 3/8 – 3/8 ÷6
6. 4/7 × 5/9 + 3/7 × 5/9
7. 5/2 -（ 3/2 + 4/5 ）
8. 7/8 + （ 1/8 + 1/9 ）
9. 9 × 5/6 + 5/6
10. 3/4 × 8/9 - 1/3
11. 7 × 5/49 + 3/14
12. 6 ×（ 1/2 + 2/3 ）
13. 8 × 4/5 + 8 × 11/5
14. 31 × 5/6 – 5/6
15. 9/7 - （ 2/7 – 10/21 ）
16. 5/9 × 18 – 14 × 2/7
17. 4/5 × 25/16 + 2/3 × 3/4
18. 14 × 8/7 – 5/6 × 12/15
19. 17/32 – 3/4 × 9/24
20. 3 × 2/9 + 1/3
21. 5/7 × 3/25 + 3/7
22. 3/14 × 2/3 + 1/6
23. 1/5 × 2/3 + 5/6
24. 9/22 + 1/11 ÷ 1/2
25. 5/3 × 11/5 + 4/3
26. 45 × 2/3 + 1/3 × 15
27. 7/19 + 12/19 × 5/6
28. 1/4 + 3/4 ÷ 2/3
29. 8/7 × 21/16 + 1/2
30. 101 × 1/5 – 1/5 × 21
31.50＋160÷40 （58+370）÷（64-45）
32.120-144÷18+35
33.347+45×2-4160÷52
34（58+37）÷（64-9×5）
35.95÷（64-45）
36.178-145÷5×6+42 420+580-64×21÷28
37.812-700÷（9+31×11）（136+64）×（65-345÷23）
38.85+14×（14+208÷26）
39.（284+16）×（512-8208÷18）
40.120-36×4÷18+35
41.（58+37）÷（64-9×5）
42.(6.8-6.8×0.55)÷8.5
43.0.12× 4.8÷0.12×4.8
44.（3.2×1.5+2.5）÷1.6 （2）3.2×（1.5+2.5）÷1.6
45.6-1.6÷4= 5.38+7.85-5.37=
46.7.2÷0.8-1.2×5= 6-1.19×3-0.43=
47.6.5×（4.8-1.2×4）= 0.68×1.9+0.32×1.9
48.10.15-10.75×0.4-5.7
49.5.8×（3.87-0.13）+4.2×3.74
50.32.52-（6+9.728÷3.2）×2.5
51.[（7.1-5.6）×0.9-1.15] ÷2.5
52.5.4÷[2.6×（3.7-2.9）+0.62]
53.12×6÷（12-7.2）-6 （4）12×6÷7.2-6
102×(-4.5)-(-3)×(-5) ÷2
7.8×6.9＋2.2×6.9
(-2)+2-(-52)×(-1) ×5+87÷(-3)×(-1)
5.6×0.258×（20－1.25）
(-7.1) ×〔(-3)×(-5)〕÷2
-2.5×(-4.8)×(0.09)÷(-0.27)
127+352+73+44×(-2)
89×276+(-135)-33
25×71+75÷29 -88÷(-2)
243+89+111+57
9405-2940÷28×21
920-1680÷40÷7
690+47×52-398
148+3328÷64-75
360×24÷32+730
2100-94+48×54
51+（2304-2042）×23
4215+（4361-716）÷81
（247+18）×27÷25
36-720÷（360÷18）
1080÷（63-54）×80
（528+912）×5-6178
8528÷41×38-904
264+318-8280÷69
（174+209）×26- (9000^0)
814-（278+322）÷15
1406+735×9÷45
3168-7828÷38+504
796-5040÷（630÷7）
285+（3000-372）÷36
1+5/6-19/12
3x(-9)+7x(-9)
(-54)x1/6x(-1/3)
1.18.1＋（3－0.299÷0.23）×1
2.(6.8-6.8×0.55)÷8.5
3.0.12× 4.8÷0.12×4.84
3.2×1.5+2.5÷(-1.6)
（-2）×3.2×（1.5+2.5）÷1.6
5.6-1.6÷4+(6.8-9)
5.38+7.85-5.37÷89
6.7.2÷0.8-1.2×5
6-1.19×3-0.43
7.6.5×（4.8-1.2×4）
0.68×1.9+0.32×1.9
8.10.15-10.75×0.4-5.7
9.5.8×（3.87-0.13）
(-8.01)+4.2×3.74
10.32.52-（6+9.728÷3.2）×2.5
11.[（7.1-5.6）×0.9-1.15] ÷2.5
12.5.4÷[2.6×（3.7-2.9）+0.62]
13.12×6÷（12-7.2）-6
14.12×6÷7.2-6
15.33.02－（148.4－90.85）÷2.5
(-5)-252×（-78）
(-6) ×(-2)+3÷（5+50）
7-7+3-6-（-90）
(-8)(-3)×(-8)×25
(7+13) ÷(-616)÷(-28)
（8+14-100-27）÷4
(-15) ÷(-1)-101÷10
16÷0.21×(-8) ×(4.1+5.9)
(-10) ×(-2) ×4÷{-9÷[6+(-5.67)]}
(-18)(-4)2×[8.01×(-3.14)
9-32{-890-[79+8.1] ×9}
(-20)-23+(-9) ×9.42
(-24)3.4×104÷(-5) ×200.96
[-|98|+76+(-87)]*23[56+(-75)-(7)]-(8+4+3)
5+21*8/2-6-59
68/21-8-11*8+61
-2/9-7/9-56
4.6-(-3/4+1.6-4-3/4)
1/2+3+5/6-7/12
[2/3-4-1/4*(-0.4)]/1/3+2
22+(-4)+(-2)+4*3
-2*8-8*1/2+8/1/8
(2/3+1/2)/(-1/12)*(-12)
(-28)/(-6+4)+(-1) +√9
2/(-2)+0/7-(-8)*(-2)
(1/4-5/6+1/3+2/3)/1/2
18-6/(-3)*(-2) ×2^7
(5+3/8*8/30/(-2)- √36
(-84)/2*(-3)/(-6)
1/2*(-4/15)/2/3
1+2+3+4+......+100000
1/1+1/2+1/3+......1/50
1+1/2+1/4+1/8+1/16+......1/512
3+9+27+81+243+......9999
1 + 1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56 + 1 / 72 + 1 / 90 respondents: 3656686zwb | grade I | 2010-10-30 16:44
1.345x0.345x2.96-1.345 (power 3) - 1.345x0.345 (power 2)
=-1.345(1.345^2-2*1.345*0.345+0.345^2)
=-1.345(1.345-0.345)^2
=-1.345
1 + (- 2) + 3 + (- 4) +... + (- 1) (n + 1 power of) * n
N is odd
1 + (- 2) + 3 + (- 4) +... + [(- 1) to the power of N + 1] n
=[1 + (- 2)] + [3 + (- 4)] +... + [(- 1) to the power of N + 1] n
=(-1+ -1+...+ )+n
=(1-n)/2+n

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