Earlyface

1a.) 2xpower2-7x+3=0. 2xpower2*3=6xpower2. Factors of 6xpower are -6x and -x.
(2xpower2-6x)-(x+3)=0.
2x(x-3)-1(x-3)=0.(2x-1)(x-3)=0. Either 2x-1=0. 2x=1.
X =1/2. Or x-3=0. X=3.
Hence the value of x= 1/2 or 3.

(no2) X:2,3,4,5,6,7.
F:11,12,25,30,12,10.
FX=22,36,100,150,72,70
(x-xbar):2.5,1.5,0.5,0.5,1.5,2.5
F(x-xbar):27.5,18,12.5,15,18,25,116.
(a)?Xbar=Efx/ef=450/100=4.5
(b)?M.d=(EF(x-xbar))/Ef=116/100=1.16

NB: COMMA MEANS UNDER eg: F: 11,12,25 means u wil draw a table and F is on top under it is 11, then under 11 is 12, then 25.... 

No3) 2x=8+y.
2y=x+z.
2z=32+y.
from eq 1
y=2x-8
sub eq 4 into 2
2(y)=x+2.
2(2x-8)=x+z.
 4x-16=x+z.
4x-x=7+16.
3x=z+16
sub eq 4 into 3
2z=32+y 2z=32+(2x-8)
2z=2x+24.
Combining eq 5 and 6
3x=z+16.
3x-16=z
sub eq 7 into 6. 2z=2x+24.
2(3x-16)=2x+24.
 6x-32=2x+24.
6x-2x=24+32.
4x=56 . 
x=56/4=14 x=14
from eq 4 y=2x-8
.y=2(14)-8=28-8=20.
Y=20
and from eq 7; z=3x-16..
Z=42-16=26 
z=26..

(4a)x=1380-130=50(corresponding angle), y=180-125,=55 degree(corresponding angle)
(4b) 1/3(x+8)-1/7(2x-4)less or equal to 1, multiply both sides by 21(Lcm). 7x+56-6x+12 less or equal to 21, x less or equal to 21-56-12., x=-47.


6a) total amount earned=#24000.00/month .expenses. House keeping=6400.00.perol and eletricity=#1700.50. Water rate=#1000.90. Insurance=#900.30. Income.tax=#4100.10..

6ai) amount paid on water rate/year= amount paid/month*12months=#1000.90*12.=#12,010.80k.

6aii) percentage of income tax paid. X percentage of #24000.00=#4100.10. X/100. X 24000.1/240=17.084percent. Percentage paid as income tax 17.08=17.08percent..

6ciii) if petrol: electricity=16:5 total=16+5=21, but petrol and eletricity. Petrol amount only=16/21*1700.50=#1295.62. Eletricity amount only=5/21*1700.50=#404.88. Difference of amount on petrol and eletricity =#1295.62-404.88=#890.74..

(7a) R=kl, r=0.6, k=0.8, R=0.08L. R=0.08*35.5=2.85 ohms
(7bi) Tn= ar^n-1, a=10/3, r=1/2. T8= 10/3*1/128=10/384.
(7biii) sn=(a(1-r^n))/1-r= (10/3(1-(1/2)^10))/1-1/2=( (10/3)(1-1/1024))= 1705/256

7B) 10/3, 5/3, 5/6.
a=10/3.
R=5/3 divided 10/3=5/3*3/10=1/2.
 R=1/2.
Tnth=arn-power 1 T8th=10/3*(1/2)power8-1.
=10/3*(1/2)power7.
 =10/3*1/2*2power6.
T8th=5/3*1/64=5/192..

7c) log x=3+log y.
Log x-log
y=3
x/y=2power3.   
x/y=8.

(N09ai )
dst bc=tita pieRcosa/180
=80times3.142times640cos2/180
=1452980.9/180=8099.9=8100km.
(N09ii)
Chord bc =2crostita /2
=2*64cos25sin40degree.

(N11a)
Log27base3=log64base1/4+nlog3 1/81
Log3^2base3=log4^3base1/4+-4nlog3base3
2=3log4base1/4-4n
4n=3log16base14-2
4n=12-2
4n=10
N=10/4
=2^1/2.

^ means raise to power

(11b)
<CTD=x
<ATB=36degree(base<sof 180CA)
<TAB+72degree=180degree
<TAB+36f36=180degree(sum of <s in D)
<ATB+72degree=180degree
<TAB=180degree-72degree=108
<BCD=180-108(suppl.<s=72degree
<BTC=72degree(base<s of asoseless triangle)<cbt=x(<S
<CBT=x(<s in aLTERNATIVE SEGMENT<CBT=180-144DEGRE
X=36DEGREE.

12. Abu=2/7
Abu=1/6
Ola=3/5
(abu)^1=5/7
(ola)^1=2/5
(a).pr(all score below 70%)
=5/7*5/16*2/5
=5/56.
(b).pr(at most score70%)
=(5/2*1/6*3/5)+(5/6*2/7*3/5)
+(2/5*2/7*1/6
5/70+10/70+20/70
5/70+10/70+20/70
15/70+2/70=17/70.
(c).pr (all score 70%)
=2/7*1/6*3/5
=2/70=1/35.

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