初中程度Maths....急需解決(15分!!!)

1)(a)
18x2 - 2y2 + 6x - 2y
= 2(9x2 - y) + 2(3x - y)
= 2(3x - y)(3x + y) + 2(3x - y)
= 2(3x - y)[(3x + y) + 1)]
= 2(3x - y)(3x + y + 1)

1)(b)
1 - y3
= (1 - y)(1 + y + y2)

1)(c)
27x3 - 64
= (3x)3 - (4)3
= (3x - 4)[(3x)2 + (3x)(4) + (4)2]
= (3x - 4)(9x2 + 12x + 16)

1)(d)
125x3 + 27y3
= (5x)3 + (3y)3
= (5x + 3y)[(5x)2 - (5x)(3y) + (3y)2]
= (5x + 3y)(25x2 - 15xy + 9y2)

1)(e)
(x2 + 16x + 64) - (y + 2)2
= (x + 8)2 - (y + 2)2
= [(x + 8) - (y + 2)][(x + 8) + (y + 2)]
= (x + 8 - y - 2)(x + 8 + y + 2)
= (x - y + 6)(x + y + 10)

1)(f)
x2 - 2xy + y2 - 4z2
= (x2 - 2xy + y2) - 4z2
= (x - y)2 - (2z)2
= (x - y - 2z)(x - y + 2z)

=====
2)
Let L and W be the length and width of the rectangle respectively.

Original area
= LW

New area
= (1+25%)L x (1-15%)W
= 1.0625LW

Percentage change in area
= [(1.0625LW - LW)/LW] x 100%
= +6.25%

=====
3)
A rhombus is a //gram with the four sides equal in length.

DA = DC (sides of rhombus)
CAD = ACD (base s of isos. Δ)
CAD = 24o

BTS = 90o (given)

In ΔATS:
BSA = CAD + BTS (ext. of Δ)
BSA = 24o + 90o
BSA = 114o

=====
4.
Through A, draw a line //DC to cut EF at H and BC at K.

ADCB is a //gram.
CK = AD (opp. sides of //gram)
CK = 5.5 cm
BK = BC - CK (BKC is a st. line)
BK = (8.5 - 5.5) cm = 3 cm

FAH = BAK (common)
AFH = ABK (corr. , FH//BK)
AHF = AKB (corr. , FH//BK)
ΔAFH ~ ΔABK (AAA)
AF/AB = FH/BK (corr. sides of similar Δ)
(3 cm)/(9 cm) = FH/(3 cm)
FH = 1 cm

ADEH is a //gram.
EH = DA = 5.5 cm (opp. sides of // gram)
EF = EH + FH (EHF is a st. line)
EF = (5.5 cm) + (1 cm)
EF = 6.5 cm

=====
5)
Let a be the number of adults.
Then the number of children = 300 - a

200a + 130(300 - a) = 51600
200a + 39000 - 130a = 51600
70a = 12600
a = 180
300 - a = 120

Ans: There are 180 adults and 120 children.

=====
6)
Let t be the tens digit.
Then the units digit = 12 - t

[10(12 - t) + t] - [10t + (12 - t)] = 54
[120 - 10t + t] - [10t + 12 - t] = 54
120 - 10t + t - 10t - 12 + t = 54
108 - 18t = 54
-18t = -54
t = 3
12 - t = 9

Ans: The number is 39.
=

1a) 18x² - 2y² + 6x - 2y
=2(9x²-y²-y+3x)
=2[(3x+y)(3x-y)+(3x-y)]
=2(3x-y)(3x+y+1)

1b) 1-y³
=(1-y)(1+y+y²)

1c) 27x³-64
=(3x-4)(9x²+12x+16)

1d) 125x³ + 27 y³
=(5x+3y)(15x²+15xy+9y²)

1e) (x² + 16x + 64) - (y + 2)²
=(x+8)²-(y+2)²
=(x+y+10)(x-y+6)

1f) x² - 2xy + y² - 4z²
=(x-y)²-(2z)²
=(x-y+2z)(x-y-2z)

2)let the length be x width be y
new area=1.25x(0.85y)
=1.625xy
percentage change=(1.625xy-xy)/xy
=62.5%

3)∠BCA=∠ACD (prop. of rhombus)
=24度
∠CDA=[360度-(24度x4)]*0.5 (∠sum of poly.)
=132度
∠CST=360度-132度-90度-24度(∠sum of poly.)
=114度
∠BSA=∠CST (vert opp ∠s)
=114度

4)唔識 sor orz

5)Let the no. of adult be x, children be y
x+y=300----(1)
200x+130y=51600----(2)
(1)*130:
130x+130y=39000----(3)

(2)-(3):
200x+130y-130x-130y=51600-39000
70x=12600
x=180----(4)
Sub(4)into(1)
y=120

The no. of adults is 180,children is 120.

6)Let the ten-digit be x,unit-digit be y.
x+y=12----(1)
10y+x=10x+y+54----(2)

By (1),
x=12-y----(3)

Sub (3) into (2)

10y+12-y=10(12-y)+y+54
9y+12=174-9y
18y=162
y=9----(4)

Sub (4) into (3)
x=4

The original no. is 49.

2008-12-23 00:01:38 補充：
第2題錯左

應該系

2)let the length be x width be y
new area=1.25x(0.85y)
=1.0625xy
percentage change=(1.0625xy-xy)/xy
=6.25%

2008-12-23 00:03:33 補充：
6)Let the ten-digit be x,unit-digit be y.
x+y=12----(1)
10y+x=10x+y+54----(2)

By (1),
x=12-y----(3)

Sub (3) into (2)

10y+12-y=10(12-y)+y+54
9y+12=174-9y
18y=162
y=9----(4)

Sub (4) into (3)
x=3

The original no. is 39.