a c d d b a b b 9.2 10. 1 1. 12.0 13。 Solution: The original formula = 1+5 = 1 5 = 5 65438. Alternative assessment. 15. Solution:
16. Solution:
17. Proof that a pair of congruent triangles is △ pad △ PBC when PA=PB: ∵ PA = Pb ∴∠ A = ∠ B.
∵AD=BC ∴△PAD≌△PBC, as long as it can prove that the triangle is congruent, it will be scored according to the above scoring standard.
18. Solution: Suppose the price of a box of Fuwa toys and a badge is X yuan and Y yuan respectively.
To solve this equation set, the prices of a box of Fuwa toys and a badge are 125 yuan and 10 yuan respectively.
19. Solution: (1)P (draw card number 4)= (2) The rules of the game are unfair to both parties.
The reason for this is the following：
Xiao Li
Xiao Wang 3 4 5
3 (3,3) (3,4) (3,5)
4 (4,3) (4,4) (4,5)
5 (5,3) (5,4) (5,5)
or
As can be seen from the table or tree diagram above, there are 9 possible outcomes. P (the numbers drawn on the card face are the same) =,
P (the number of cards drawn is different) = This game is unfair, and Xiao Li is likely to win.
This highway doesn't pass through this area.
2 1. Proof:
22. Solution: (2) We transferred M from Group C to Group A and N to Group B.
The solution is m = 5+2n, and then ∵, ∴n= 1 or n=2. ∴ There are two methods: transfer 7 people to group A, and transfer 1 person to group B; Or 9 people in group A, 2 people in group B, 5 points.
23.( 1)20, 12; 2 does not exist. If it exists, it is decided by A? b？ :AB = B？ c？ BC, available: a? b？ :B？ c？ = AB: BC = 2: 1 again by 2(A? b？ + B？ c？ )= k？ 2 (AB+BC)。 Available: b? c？ = k，A？ B = 2 K. And then: K? 2 k = k？ 2, ∴ k2 = k, ∴k = 0 or 1. ∵ k ≥ 2, ∴ does not exist.
24. Solution: (1) Substitute A (1, 0) and B (4 4,6) according to the image.
The analytical formula of parabola is. (2) The original analytical formula of parabola can be expressed as: after the parabola is shifted to the left by one unit, the analytical formula is, let it be shifted up or down by h units, and the analytical formula of straight line AB can be obtained from the coordinates of two points A and B, y=2x-2, simultaneous, and simplified as x2-3x+h+2 = 0, ∫ parabola. ∴b2-4ac=0, that is, 9-4× (h+2) = 0 ∴ h =, that is, the parabola can only have one intersection with the straight line AB if it moves up by one unit. At this time, the analytical formula of parabola is (3) The parabola moves one unit to the right and then moves down by t units. The analytical formula is, as can be seen from (2).
Let the center of the circle be C and the midpoint of Mn be E, connecting CE and CM in triangles Ce, CM, ∵, ∴.
When appropriate, the area of the circle passing through m, n and p is the smallest, and the minimum area is.
25.( 1) EG = CG Proof: ∵∠DEF=∠DCF=900,DG=GF,∴ (2)EG=CG.
It is proved that the parallel line with BC passing through point F intersects the extension line of DC at point M and connects MG. ∴EF=CM, which proves that EFCM is rectangular.
∴∠EFG=∠GDM is in the right triangle FMD, ∴DG=GF,∴FG=GM=GD∴∠GMD=∠GDM.
∴∠EFG=∠GMD ∴△EFG≌△GCM.EG=CG。 (3) Take the midpoint H of BF to connect EH and GH, and take the midpoint O of BD to connect OG, OC: CB = CD, ∠ DCB.
∫△bef is an isosceles right triangle, ∴ ∴EH=OG.∵ Quadrilateral OBHG is a parallelogram,
∴∠BOG=∠BHG.∵∠BOC=∠BHE=900,∴∠GOC=∠EHG.∴△GOC≌△EHG.∴EG=GC.
Some can't be typed.