maths

15.
a)
2x/5>4-6x/5
8x/5>4
x>5/2
b)
2(2p+3)/5>4-6(2p+3)/5
2p+3>5/2
2p>-1/2
p>-1/4
26.
H=2a+(b-a)/4c
21=2a+(-32-a)/(-8)
21=2a+(32+a)/8
168=16a+32+a
17a=136
a=8
20.
a)
5p-15q+10r=5(p-3q+2r)
b)
-bx+by+3bz=b(-x+y+3z)
21.
a)
-ax²+axy-axz=ax(-x+y-z)
b)
8mn+16n²-8mn²=8n(m+2n-mn)
22.
a)
x(a-6)-2y(6-a)
=x(a-6)+2y(a-6)
=(x+2y)(a-6)
b)
14p(s+t)-28q(s+t)
=(14p-28q)(s+t)
=14(p-2q)(s+t)
23.
a)
4u-12v-2(u-3v)
=4(u-3v)-2(u-3v)
=2(u-3v)
b)
2(x-y)²+(y-x)³
=2(y-x)²+(y-x)³
=(2+y-x)(y-x)²
24.
a)
(3x+6)/(2y-10)+(x²y+2xy)/(5y²-y³)
=3(x+2)/2(y-5)+xy(x+2)/y²(5-y)
=3y²(x+2)/2y²(y-5)-2xy(x+2)/2y²(y-5)
=[3y²(x+2)-2xy(x+2)]/2y²(y-5)
=(3y²-2xy)(x+2)/2y²(y-5)
=y(3y-2x)(x+2)/2y²(y-5)
=(3y-2x)(x+2)/2y(y-5)
b)
(pq+q²-qr)(p)(p-q)²/(pq-p²)(pr²+qr²-r³)
=pq(p+q-r)(q-p)²/pr²(q-p)(p+q-r)
=q(q-p)/r²
c)
2-20/(y-10)
=[2(y-10)-20]/(y-10)
=(2y-40)/(y-10)
=2(y-20)/(y-10)
d)
1/(m-n)-1/(n-m)-2n/(m+n)(m-n)
=1/(m-n)+1/(m-n)-2n/(m+n)(m-n)
=2/(m-n)-2n/(m+n)(m-n)
=2(m+n)/(m+n)(m-n)-2n/(m+n)(m-n)
=[2(m+n)-2n]/(m+n)(m-n)
=(2m+2n-2n)/(m+n)(m-n)
=2m/(m+n)(m-n)
=2m/(m²-n²)
25.
y=(2m+c)/(m-c²)
-2=(2m+1/2)/(m-1/4)
-2(m-1/4)=2m+1/2
-2m+1/2=2m+1/2
4m=0
m=0
18.
vA=50,vB=30
tA+tB=30
sA+sB≧1000
vAtA+vBtB≧1000
50tA+30tB≧1000
50tA+30(30-tA)≧1000
50tA+900-30tA)≧1000
20tA≧100
tA≧5
Ans:5 hours
19.
a)
area=3(x+5)/2≦4x
3x+15≦8x
15≦5x
x≧3
Ans:3
b)
area=6(y+8)/2≦4y
6y+48≦8y
48≦2y
y≧24
Ans:24

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