Questions on Algebra: Complex Numbers answered by real tutors!

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It is not real clear what you are asking but I have a feeling you were given a solution set of x =6 and -1 and were asked to form a quadratic equation from this solution set...So we must work backward remember a quadratic equation takes the form of and when factored each factor is set to zero and the solution is found. In this case we are working backward
so....x=6...in order to make x term = to zero we must subtract 6 so x-6=0....now for x=-1 we must add 1......and get x+1=0 now these two terms can be multiplied together and set equal to zero
:
(x-6)(x+1)=0--->now multiply this out using foil
:
combine like terms
:
is our quadratic equation
If this doesnt answer your question you will have to re write your question and make it more clear....
:

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-1+i
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Do you have a question?

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(1/2)-(1/3)/(3/4)+(1/6)
1/2-(1/3)(4/3)+1/6
1/2-4/9+1/6
--------------------------
Checkley77, I really appreciate your help on this complex fractions.
Could you eplain how you got step 4- which is (9-4*2-3)/18. I got lost on this step.I really appreciate your help.
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In order to add fractions you need to have a common denominator.
The common denominator is any number evenly divisable by 2, 9 & 6.
A good way to do this is to see if the largest number is divisable by the other two. 9 is not divisable by 2
Next multiply the largest number (9) by (2)=18 and try again.
18 is divisable by both 2 & 6.
Now you need to change 1/2 to 9/18 by multiplying both numerator & denominator by 9, change 4/9 to 8/18 by multiplying both numerator & denominator by 2 & 1/6 to 3/18 by multiplying both numerator & denominator by 3.
Now you have a 'common denominator' and can add the numerators.
-----------------------------------------
(9*1-4*2+3*1)/18 multiply numerator terms.
(9-8+3)/18 combine numerator terms.
4/18 now reduce.
2/9 ans.

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vertex form is y=a(x-h)^2+k, where (h,k) is the vertex

y=x^2-16x+56 __ subtracting 56 __ y-56=x^2-16x

completing the square by adding half of the x coefficient, squared __ y-56+(-16/2)^2=x^2-16x+(-16/2)^2

y-56+64=x^2-16x+64 __ y+8=(x-8)^2 __ subtracting 8 __ y=(x-8)^2-8

the vertex is (8,-8)

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Remember ---->
Via Pyth. Theorem:



2 values:


Let's check, use



, close enough amigo (rounding off)
Thank you,
Jojo

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Whenever a polynomial has complex roots, the roots come in complex conjugates pairs.
So if (0-i) is a root, then so is (0+i).
and if (1+i) is a root, then so is (1-i).
The five roots are then 2,i,-i,1+i,1-i.

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Any help with the folllowing assignment question would be most appreciated. I am doing an electrical degree course which is moving too fast over the quantitative analysis section and I am struggling to take basics for each topic.
two coils connected in parrallel
r1= 12 ohm L1= 24mH
r2= 6 ohm L2=30mH
given that f = 50Hz calculate the values of impedance for each coil Z1 and Z2 and the total impednace for two impedances in parrallel in both polar form and rectilinear form.
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Start with the formula for inductive reactance, which corresponds to resistance of the inductor at a specific frequency:
X = 2*pi*f*L where f is in Hz and L is in Henries
L1 = 0.024 Henry
X1 = 2*pi*50*0.024 = 7.54 ohms
r1 = 12 ohms (I assume this is the resistance of the coil) so it's in parallel with the coil.
That's 4.63 ohms (at 50 Hz)
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L2 = 0.03 Henry
Same as above, X2 = 9.24 ohms
In parallel with 6 ohms gives 3.71 ohms.
---------------------
In parallel, their reactance at 50 Hz is 2.06 ohms.
I don't see anything to be plotted in rectilinear or polar form, it's just a number of ohms.

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3(x+jy)=9-j27
then
3x+3jy=9-27j
3x+(3y)j=9-(27)j
then
3x = 9 then x = 3
3y =-27 then y = -9
Answer: x=3, y=-9

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Let take
Let take
Note that w-z = -12y
then

then


then

then

then



then

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1. simplify:
:

-------------

:
Square the denominator fraction

-------------

:
Invert the dividing fraction and multiply, cancel like terms
* =
:
2. Simplify
:
+
:
Factor, then put over a common denominator:
+ = = =

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here's how i would do it.
original equation:
x^2+2y^2=18 and x=2y.
since x = 2y, equation becomes:
(2y)^2 + 2y^2 = 18
this becomes:
4y^2 = 2y^2 = 18
this becomes:
6y^2 = 18
divide both sides by 6 to get:
y^2 = 3
y = +/- sqrt(3)
-----
if y = +/- sqrt(3), then x = 2y = +/- 2*sqrt(3)
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to prove the answer is correct, substitute in original equation.
original equation is:
x^2+2y^2=18
substitute 2*sqrt(3) for x and sqrt(3) for y:
(2*sqrt(3))^2 + 2*(sqrt(3))^2 = 18
this becomes:
4*3 + 2*3 = 18
which becomes:
12 + 6 = 18
which becomes:
18 = 18 proving answer is correct.
it doesn't matter if + or - sqrt(3) is used since when you square it, it comes out positive either way.

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1.
2.
Substitute eq. 2 into eq. 1, directly substitute for x and solve for y.
Then go back and find x.
1.





Then from eq. 2,
2.


.
.
.
When we graph the equations, you can see the solutions more clearly.
Equation 1 is the ellipse.
Equation 2 is the straight line.
.
.
.
(1.73,3.46) and (-1.73,-3.46)
.
.
.

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They probably want you to get rid of "i" in the denominator
Multiply by the conjugate of (5+i) which is (5-i) over itself, (same as mult by 1)
*
:
Multiply the numerators and FOIL the denominators. Remember i^2 = -1
= = = = +
:
Note that we can reduce both fractions, they both are multiples of 13
+ = is the form they want probably
;
Did this help?

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x^2-x-6
(x-3)(x+2)

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This question is incomplete.
Please, retype your question.

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(2/14x)/(4/7xy)
------------------
Invert the denominator and change to multiplication to get:
= [1/7x] * [7xy/4]
Cancel factors common to a numerator and a denominator to get:
= [1/1] * [y/4[
= y/4
==============
Cheers,
Stan H.

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imaginary
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Cheers,
Stan H.

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If the average cost per unit C(x) to produce x units of plywood is given by:
C(x) =
:
What do 600 units cost? Round your answer to the nearest cent.
;
You are looking for the total cost which is
no. of units sold (x) times cost/unit, which is the given equation
:
C(x) = x*
:
Substitute 600 for x in the given equation:
C(x) = 600*
:
C(x) = 600*
:
C(x) = 600 * 1.42857
:
C(x) = $857.14

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1. You don't need synthetic division to find f(-3). Just substitute.





.
.
.
2. Here you need the synthetic division.
Showing synthetic division is a little difficult.
The first part will show the factor (left hand column), then the factor times the divisor,
then the next line will show the subtraction.
Repeat.
Hopefully it makes sense.
.
.
.
..........._______________
(x+4)|x^3+x^2-22x-40
x^2:...x^3+4x^2
..................-3x^2-22x-40
-3x:..........-3x^2-12x
.............................-10x-40
-10:......................-10x-40

Now you can factor the quadratic,

and substitute back,

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C(60)=900/630 is the cost per unit
so the cost of 600 units is (900/630)600=857.14
then correct option is a)

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Please help me write 3(cos 60 degrees + i sin 60 degrees) in the form of a + bi!
Thank you, Tami
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3(cos 60 degrees + i sin 60 degrees)
cos(60º) = 1/2
sin(60º) = (1/2)sqrt(3)
= 3[(1/2) + i*sqrt(3)/2]
= 3/2 + i*(3*sqrt(3)/2)
a = 3/2
b = (3/2)*sqrt(3)

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An NFL kicker attempts a 41-yard field goal. The path of the football toward the uprights can be represented by the graph of the quadratic function f(x)= -.0625x²+2.7x, where x is the horizontal distance the football travels in yards and f(x) is the vertical distance the football travels. The bottom of the upright is 3.5 yards above the ground.
Assuming the kick is in between the uprights, did the kicker make the field goal? Why or Why not?
Find value of x (dist) when f(x) = 3.5 (height)
-.0625x² + 2.7x = 3.5
:
-.0625x² + 2.7x - 3.5 = 0
:
Use the quadratic formula:

In this problem a=-.0625; b=+2.7; c=-3.5

:

:

:


x = 1.33; not the solution we want here
and


x = 41.86 yds; clears the upright nicely
:
The ball had traveled almost 42 yds when it had descended to 3.5 meters

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Find: p(-3) if p(x)=x^5+3x^2
p(-3)=(-3)^5+3*(-3)^2
p(-3)=-243+3*9
p(-3)=-243+27=-216
YOU GAVE IT A GOOD SHOT BUT I THINK YOU MIGHT HAVE OVERLOOKED A MINUS SIGN

Hope this helps---ptaylor

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Start with the given expression


Factor the numerator. Note: use the Sum of Cubes formula to factor.


Factor the denominator.


Highlight the common terms.


Cancel out the common terms.


Simplify


So simplifies to

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Note:




So

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For 3(p+1)^2=81
I would start by dividing both sides by 3
Therefore (p+1)^2=81/3 or (p+1)^2 = 27
I would then take the square root of each side
p+1 = radical 27
Then subtract 1
p=(radical 27) - 1 or p = -1 + (radical 27) or punch in radical 27 into a calculator and then subtract 1, which is 5.1961524 - 1 = approximately 4.196
For 5y^2+4=14
I would first subtract 4
so 5y^2=10
Then divide by 5
y^2=2
Take the square root
y= radical 2 or y= approximately 1.41421

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P(x)=5x^4-3x^3+ax^2+bx-7
i is a zero of P(x) then -i is a zero of P(x) too
Using synthetic division:
Please see source code
5 -3 a b -7
i 5i -5-3i -5i+3+ai 5+3i-a+bi
5 5i-3 -5-3i+a -5i+3+ai+b -2-a+(3+b)i=0
-i -5i 3i 5i-ai
5 -3 -5+a 3+b=0
-2-a+(3+b)i=0
3+b=0
then b=-3 and a=-2
P(x)=5x^4-3x^3-2x^2-3x-7

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The shape of a supporting arch can be modeled by h(x)=-0.03x^2+3x, where h(x) represents the height of the arch and x represents the horizontal distance from one end of the base of the arch in meters.
:
Solve the equation for x = 0;
-.03x^2 + 3x = 0
:
Factor out -.03x
-.03x(x - 100) = 0
x = 0
and
x = 100 meters is the width of the base of the arch
:
Find the maximum height of the arch.
:
Max height occurs halfway, at x = 50 (axis of symmetry)
:
Substitute 50 for x in the original equation
:
h(x) = -.03*50^2 + 3(50) = 0
h(x) = -75 + 150
h(x) = 75 meters is the height

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x = 6 x = -4
Once you get to
then more help can be found here
http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=algebra&s2=factor&s3=basic

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1. 2x+y-3z=-4
2. 4x-2y+z=9
3. 3x+5y-3z=5
--------------
Multiply eqn 2 by 3
12x-6y+3z=27
Add to eqn 1 and to eqn 3
1. 2x+y-3z=-4
12x-6y+3z=27
14x-5y = 23 No z term
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3. 3x+5y-3z=5
12x-6y+3z=27
15x-y = 32 No z here either
Now there are 2 eqns in 2 unknowns:
14x-5y = 23
15x- y = 32 Multiply this by 5 to get the same y coefficient
75x-5y = 160
14x-5y = 23 Subtract this from it
61x = 137
x = 137/61 Answer for x
Sub x into 15x -y = 32
15*(137/61) - y = 32
y = (15*137 - 32*61)/61
y = 103/61 Answer for y
Sub x and y into any of the 3 original eqns, I'll use #1
1. 2x+y-3z=-4
2*(137/61) + (103/61) - 3z = -244/61
-3z = (-244 - 274 - 103)/61
-3z = -621/61
z = 207/61

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Note: it's helpful to remember that


Start with the given function


Plug in . In other words, replace each "x" with "1+2i"


Break up to get


FOIL to get


FOIL to get


Distribute


Combine like terms.


So the answer is

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(3+[1/(x^2 -1)])/(2+[4/(x-1)])
=(3(x^2-1)+1)/(x^2-1))/...
=(3x^2-3+1)/(x^2-1)/...
=(3x^2-2)/(x^2-1)/...
=.../((2(x-1)+4)/(x-1))
=.../((2x-2+4)/(x-1))
=.../((2x+2)/(x-1))
=
=
=
.
Ed

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(-4+2i)-(7-3i) = -4+2i-7+3i
               = (-4-7)+(2i+3i)
               = -11+5i

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Start with the given equation.


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the answers are or

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Start with the given equation


FOIL


Combine like terms.


In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: .


Start with the given formula.


From , we can see that , , and .


Plug in and .


Negate to get .


Multiply 2 and to get .


Divide.


So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


Start with the given equation.


Plug in .


Square to get .


Multiply and to get .


Multiply and to get .


Combine like terms.


So the y-coordinate of the vertex is .


So the vertex is .

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Start with the given equation


FOIL


Combine like terms.

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Solve the quadratic equation
3(x-9)²=81
--------------
Divide by 3

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What does the quotient equal?

Form the conjugate of the denominator:

The denominator is  so to form
the conjugate we use the first term but
we change the sign of the term in ,
so the conjugate of  is 
Put that over itself. That is, we form the 
fraction  which is just  
in value.

Then we multiply the original expression by
this:



Put parentheses around everything:



Indicate the multiplication of numerators and denominators:



Use FOIL on the top and bottom:







Now replace the 's by 







Make two fractions:



To write it in the form ,



Edwin

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5x²-60x+180=0
Factor out a 5:
5(x²-12x+36)=0
Factoring:
5(x-6)(x-6)=0
.
solution:
x = 6

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(7-i)-(12-4i)
Distribute the neg sign to terms inside the parenthesis:
7-i-12+4i
7-12+3i
-5+3i

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.
Now, they want you to get rid of all radical signs in the denominator:

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Please state the problem.
Not all the tutors have all the books, so we can't help without the problem.
Thanks.

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i+1 =sqrt(2) [cos(pi/4) + isin(pi/4) ]
Now
(i+1)^6= (sqrt(2) )^6 [cos(pi/4) +isin(pi/4)]^6
By De Moivre's
(i+1)^6= 8 {cos (8pi/4) +isin(8pi/4) )
= 8*1
=8.

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Remember




So which is now in form where and