1. (x^2+1)*(x^3+2*x)*(x^2-64)
=(x^2+1)*x*(x^2+2)*(x+8)(x-8)
Solving for each factor in turn, for example,
x^2+1=0 => x^2=-1 => x=+i, x=-i
x=0 => x=0
x^2+2=0 => x^2=2 => x=+sqrt(2)i, -sqrt(2)i
x+8=0 => x=-8
x-8=0 => x=+8
we have solution set
S, whereS={+i, -i, 0, +sqrt(2)i, -sqrt(2)i, -8, +8)
2. A.
x^4-81=0 => x^4=81 => x^2=+9 or x^2=-9
x^2=+9 => x=+3, -3
x^2=-9 => x=+3i, -3i
S={+3i, -3i, +3, -3}
B.
x^4+10x^2+25=0 => (x^2+5)^2=0 => ± (x^2+5)=0 => x^2=-5
=> x=+sqrt(5)i (multiplicity 2 and x=-sqrt(5)i (multiplicity 2)
S={+sqrt(5)i (multiplicity 2) -sqrt(5)i (multiplicity 2)}
C.
x^4-x^2-6=0 => (x^2-3)(x^2+2)=0 => x^2=3 or x^2=-2
S={+sqrt(2)i,-sqrt(2)i, +sqrt(3), -sqrt(3) }
3.
x^4+3x^2-4=0 = (x^2-1)(x^2+4) => x^2=1 or x^2=-4
S={+2i, -2i, +1, -1}
Simple interest is given by the formula:
S.I=PRT/100
where:
P=principle
R=rate
T=time
From the information given:
P=$200, r=5%, t=3 years.
Plugging into the formula we obtain:
A=200×5/100×3
simplifying we obtain:
A=$30
Answer is: A] $30
Answer:
2
Step-by-step explanation:
1/4= .25
1/8= .125
so 1/4÷ 1/8=2
Answer:
x>3
Step-by-step explanation:
We are given with the inequation 3(8-4x) < 6(x - 5)
Dividing both sides in the above in equation by 3 we get
(8-4x)<2(x-5)
Distributing 2 over (x-5)
(8-4x)<2x-10
8-4x<2x-10
adding 10 and 4x on both hand sides we get
8+10<2x+4x
18<6x
Dividing both sides by 6 we get
3<x
Hence the solution to the given in equation is x>3
The options are;
1) AB is bisected by CD
2) CD is bisected by AB
3) AE = 1/2 AB
4) EF = 1/2 ED
5) FD= EB
6) CE + EF = FD
Answer:
Options 1, 3 & 6 are correct
Step-by-step explanation:
We are told that Point E is the midpoint of AB. Thus, any line that passes through point E will bisect AB into two equal parts.
The only line passing through point E is line CD.
Thus, we can say that line AB is bisected by pine CD. - - - (1)
Also, since E is midpoint of Line AB, it means that;
AE = EB
Thus, AE = EB = ½AB - - - (2)
Also, we are told that F is the mid-point of CD.
Thus;
CF = FD
Point E lies between C and F.
Thus;
CE + EF = CF
Since CF =FD
Thus;
CE + EF = FD - - - (3)
