MA1210
Module 3 exercise

1) 3x+5=50
3x+5-5=50-5
3x=45
3x/3=45/3
X=15
3x+5=80
3x+5-5=80-5
3x/3=75/3
X=25 2) F(x)=-x^2+2x+2
X=-b+/-sqrt(b^2-4ac)/2a
X=-2+/-sqrt(2^2-4*-1*2)/2*-1
X=-2+/-sqrt(4+8)/-2
3-(-4)
3+4
2^2-4*-1*2
4-(-8)
4+8
X=-2+/--sqrt(4+8)/-2
X=-2+/-sqrt(12)/-2
Sqrt12
Sqrt(4*3)
2sqrt(3)
X=-2+/-SQRT(12)/-2
X=-2+2sqrt(3)/-2
2(-1+sqrt 3)/-2
-1+/- sqrt (3)/-1
3) f(x)=16^2+200x+4
X=b/2a
X=200/2*-16
X=-200/-32
X=6.25
F(x)=-16x^2+200x+4
F(6.25)=-16*(6.25)^2+200*6.25+4
=16*39.0625+1250+4
=-625+1250+4
=-625+1254
= 629 feet 4) F(x)=2^x+1
6=2^x+1
6=2^7
6=128
5) P(x)=x^2-4000x+7,800,000
X^2-4000x+7,800,000-3,800,000=3,800,000-3,800,000
X^2-4000x+4,000,000=0
X^2-2*2000*x+(2000)^2=0
(x-2000)^2=0 x-2000=0 x-2000+2000=0+2000 x=2000 6) F(x)=20,000(1/2)^x
3=20,000(1/2)^3
3=20,000*1/8
3=2500
7) F(x)=-x^2+3x+6
X=-b/2a
X=-3/2*-1
X=-3/-2
X=1.5
1.5=-1.5^2+3*1.5+6
=-2.25+4.5+6
=-2.25+10.5
=8.25 8) X+y=210
X=y^2
Y^2+y=210
Y^2+y-210=210-210
Y^2+y-210=0
(y+15)(y-14)=0
Y+15=0
Y+15-15=0-15
Y=-15 y-14+14=0+14 y=14 x+y=210 x-15=210 x+15+15=210+15 x=225
(225,15)
X+y=210
X+14=210
X+14-14=210-14
X=196
(194,14)
(225,15),(196,14)
9) 12=x*y
X=5+2*y
X=5+2y
12=(5+2y)*y
12=5*y+2y*5
12=5*y+2y*y
12=5y+2y^2
2y^2+5y=12
2y^2+5y-12=12-2
2y^2+5-12=0
2*12=24
24=2*2*2*3
(8.3)
(2y-3)(y+4)
2y*y+3y*4-3*y-3*4
2y^2+8y-3y-12
2y^2+5y-12=0
(2y-3)(y+4)=0
2y-3=0
2y-3+3=0+3
2y=3
2y/2=3/2
Y=3/2
Y+4=0
4+4-4=0-4
Y=-4
10) 28=x*y
X=8+3y
28=(8+3y)*y
28=8*y+3y*y
28=8y+3y^2
3y^2+8y=28
3y^2+8y-28=28-28
3y^2+8y-28=0
3*28=84
84
84=2*2*3*7
(14,6)
(3y+14)(y-2) y-2=0 y=2+2=0+2 y=2 3y+14=0
3y+14-14=0-14
3y=-14
3y/3=-14/3
Y=-14/3
X=8+3y
X=8+3*2
X=8+6
X=14