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Angles/344286: an angle meausuring 51 what is the measure of its supplementary angle
1 solutions

Answer 246316 by Fombitz(13828) About Me  on 2010-09-16 22:33:18 (Show Source):


Complex_Numbers/344305: Find the solutions of the equation.
x^3-125= 0
x^3= 125 x= 5
How can I find the COMPLEX solutions? I believe you have to use the quadratic equation but I'm not really sure how to factor x^3-125.
Thanks!
1 solutions

Answer 246315 by Fombitz(13828) About Me  on 2010-09-16 22:32:38 (Show Source):
You can put this solution on YOUR website!
No, you can't use the quadratic formula on a cubic equation.
Recognize that this is the difference of two cubes.
x%5E3-125=%28x-5%29%28x%5E2%2B5x%2B25%29=0
One solution is x-5=0
highlight%28x=5%29
.
.
.
Now find the root of the quadratic equation with the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A25+%29%29%2F2+
x+=+%28-5+%2B-+sqrt%28+25-100+%29%29%2F2+
x+=+%28-5+%2B-+sqrt%28+-75%29+%29%29%2F2+
highlight%28x+=+%285%2F2%29%28-1+%2B-+sqrt%28+3+%29i%29%29+ where i=sqrt%28-1%29


Age_Word_Problems/344330: 3 to the second power times 5 times what = 315
1 solutions

Answer 246314 by Fombitz(13828) About Me  on 2010-09-16 22:27:28 (Show Source):


Linear-equations/344292: passes through (0,3), parallel to graph of 6y-10x = 30
1 solutions

Answer 246313 by Fombitz(13828) About Me  on 2010-09-16 22:26:26 (Show Source):
You can put this solution on YOUR website!
Parallel means the left hand side of the equation is identical.
Use the point to find the right hand side.
6y-10x=6%283%29-10%280%29=18-0=18
highlight%286y-10x=18%29


Exponents-negative-and-fractional/344309: How would you solve x to the negative third power times x to the negative fourth power?
1 solutions

Answer 246312 by Fombitz(13828) About Me  on 2010-09-16 22:24:56 (Show Source):
You can put this solution on YOUR website!
Use the law of exponents, same base, multiplication, exponents add.
x%5E%28-3%29%2Ax%5E%28-4%29=x%5E%28-7%29=1%2Fx%5E7


Equations/344328: what is w-(-5)=4
1 solutions

Answer 246311 by Fombitz(13828) About Me  on 2010-09-16 22:23:57 (Show Source):
You can put this solution on YOUR website!
Negative times a negative is a positive.
w-%28-5%29=4
w%2B5=4
w=-1


Radicals/344326: Hi,
How do you solve: x^3 - 2x^2 + 9x - 18 = 0
the teacher has given us one solution, 3i/square root of -9.
i need two other solutions and am not sure how to obtain them.
i have tried rational root theorem/ long division but do not know how to do it with square roots and imaginary numbers.
thanks
1 solutions

Answer 246310 by Fombitz(13828) About Me  on 2010-09-16 22:23:17 (Show Source):
You can put this solution on YOUR website!
Complex solutions always come in complex conjugate pairs.
So, if 3i is a solution, then -3i is also a solution.
%28x-3i%29%28x%2B3i%29=x%5E2%2B9
You can then use polynomial long division to find the last root,
You can then get %28x%5E3-2x%5E2%2B9x-18%29%2F%28x%5E2%2B9%29
Also, since only one root remains you know it must be real.
You could graph the equation and find it that way too.
.
.
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3-2x%5E2%2B9x-18%29
.
.
Looks like x=2 might be a number to stick in the function to see if f%282%29=0.


Complex_Numbers/344327: what does an imaginery number mean?? like in the equation (3+2i)+(5-4i). i dont understand the purpose of the "i".
1 solutions

Answer 246309 by Fombitz(13828) About Me  on 2010-09-16 22:18:16 (Show Source):
You can put this solution on YOUR website!
i was invented for equations like this x%5E2%2B1=0.
Since real numbers square can only take positive values, then no real number can solve that equation.
Complex numbers were created just for that reason.
In this case, if x=i=sqrt%28-1%29 I know that,
x%5E2=-1 so then x%5E2%2B1=-1%2B1=0.


Complex_Numbers/344307: Find the solutions of the equation.
4x^4 + 37x^2 +9 = 0
I need to find both the real and complex solutions!
Thanks!
1 solutions

Answer 246308 by Fombitz(13828) About Me  on 2010-09-16 22:15:35 (Show Source):
You can put this solution on YOUR website!
4x%5E4+%2B+37x%5E2+%2B9+=+0
You can factor this equation.
%284x%5E2%2B1%29%28x%5E2%2B9%29=0
Two solutions:
4x%5E2%2B1=0
4x%5E2=-1
x%5E2=-1%2F4
highlight%28x=0+%2B-+%281%2F2%29i%29 where i=sqrt%28-1%29
.
.
.
x%5E2%2B9=0
x%5E2=-9
highlight%28x=0+%2B-+3i%29 where i=sqrt%28-1%29


Geometric_formulas/344323: if UY = 4x - 3 and YV = x, Find UY and UV. Please show the work.
1 solutions

Answer 246307 by Fombitz(13828) About Me  on 2010-09-16 22:11:11 (Show Source):
You can put this solution on YOUR website!
Is there a relationship between Y, U, and V?
Is it the midpoint?
OK, Y is the midpoint.
So then,
UY=YV
4x-3=x
3x=3
highlight%28x=1%29
.
.
.
highlight%28UY=x=1%29
.
.
.
UV=UY%2BYV
UV=1%2B1
highlight%28UV=2%29


Exponents/344317: I am trying to figure out how to solve for "n" when it is 2 to the "n" power in the following equation:
2^n+6=14.
2^n+6-6=14-6
2^n=8
I am unclear where to go from here. How to I isolate the exponent "n" to find the solution?
1 solutions

Answer 246306 by Fombitz(13828) About Me  on 2010-09-16 22:08:18 (Show Source):
You can put this solution on YOUR website!
You could recognize that
8=2%5E3 and substitute.
2%5En=2%5E3
n=3
or take the log (base 2) of both sides.
log%282%2C%282%5En%29%29=log%282%2C%288%29%29
n=log%282%2C%288%29%29
n=log%2810%2C%288%29%29%2Flog%2810%2C%282%29%29
n=0.90309%2F0.30103
n=3


Sequences-and-series/344129: Solve the system of equations
3x + y =1
-x + 2y = 9
1 solutions

Answer 246229 by Fombitz(13828) About Me  on 2010-09-16 18:06:07 (Show Source):
You can put this solution on YOUR website!
Solve the system of equations
1.3x+%2B+y+=1
2.-x+%2B+2y+=+9
Multiply eq. 2 by 3 and add to eq. 1,
3x%2By-3x%2B6y=1%2B27
7y=28
highlight%28y=4%29
.
.
.
From eq. 2,
-x%2B8=9
-x=1
highlight%28x=-1%29


Complex_Numbers/344153: If x is a real number and x^64 = 64 and x^32 =32, what is x?
1 solutions

Answer 246228 by Fombitz(13828) About Me  on 2010-09-16 18:03:49 (Show Source):
You can put this solution on YOUR website!
By the law of exponents,
x%5E%2864%29%2Fx%5E%2832%29=x%5E%2864-32%29=x%5E%2832%29
So if you substitute the values,
64%2F32=32
2=32
Something's not right here.
Check your numbers.


Word_Problems_With_Coins/344080: You have 30 coins. You have nickels, twice as many dimes as nickels and quarters. You have $5.50 total. How many of each coin do you have?
1 solutions

Answer 246179 by Fombitz(13828) About Me  on 2010-09-16 16:18:25 (Show Source):
You can put this solution on YOUR website!
1.N%2BD%2BQ=30
2.D=2N
3.5N%2B10D%2B25Q=550
Substitute eq. 2 into eq. 1 and eq. 3.
N%2B2N%2BQ=30
4.3N%2BQ=30
.
.
.
5N%2B10%282N%29%2B25Q=550
5N%2B20N%2B25Q=550
25N%2B25Q=550
5.N%2BQ=22
From eq. 4,
2N%2B%28N%2BQ%29=30
Substitute from eq. 5,
2N%2B22=30
2N=8
highlight%28N=4%29
.
.
.
D=2N
D=2%284%29
highlight%28D=8%29
.
.
.
Then from eq. 1,
4%2B8%2BQ=30
highlight%28Q=18%29


test/344086: Undefined and defined

1 solutions

Answer 246175 by Fombitz(13828) About Me  on 2010-09-16 16:14:03 (Show Source):
You can put this solution on YOUR website!
I know it's not Jeopardy but you need to form a question.


Exponents/344075: (x2y2)2
(x-1)
in the parethesis the number after the x and y are exponents
I dont know how to type the problem correctly
How do I show a exponent on the keyboard
1 solutions

Answer 246170 by Fombitz(13828) About Me  on 2010-09-16 16:08:53 (Show Source):
You can put this solution on YOUR website!
Using the caret "^".
(x^2y^2)^2=%28x%5E2y%5E2%29%5E2
What's your question?


Word_Problems_With_Coins/344077: A pharmacist has 20 L of a 10% drug solution. How many liters of 5% solution must be added to get a mixture that is 8%?
1 solutions

Answer 246168 by Fombitz(13828) About Me  on 2010-09-16 16:07:32 (Show Source):
You can put this solution on YOUR website!
Let A be the amount of 5% solution.
10%2820%29%2B5%28A%29=8%2820%2BA%29
200%2B5A=160%2B8A
3A=40
highlight%28A=40%2F3%29liters.


Radicals/344071: what is radical 9ab raised to the third power?
1 solutions

Answer 246163 by Fombitz(13828) About Me  on 2010-09-16 15:50:48 (Show Source):


Angles/344065: Proof: given: angle 1 is congruent to angle 2
Prove: angle 3 is congruent to angle 4
What is the proof?
1 solutions

Answer 246159 by Fombitz(13828) About Me  on 2010-09-16 15:45:59 (Show Source):
You can put this solution on YOUR website!
Do you have a diagram to describe the relationship between angles 1,2,3 and 4??


Trigonometry-basics/344068: Solve for Y : 9x-6xy=30
1 solutions

Answer 246158 by Fombitz(13828) About Me  on 2010-09-16 15:45:16 (Show Source):


Numbers_Word_Problems/344066: what 2 numbers(1-9) equal 18 when added together?
1 solutions

Answer 246156 by Fombitz(13828) About Me  on 2010-09-16 15:43:51 (Show Source):


Quadratic_Equations/343971: A parabola with the equation of the form y = ax^2 + bx + c has the point (3, 1) as its vertex. If (1, 3) also lies on the parabola, which of the following is another point on this parabola?
(A)(-3, -1) (B) (-1,-3) (C) (2, 2)(D) (2, 6) (E) (5, 3)
1 solutions

Answer 246154 by Fombitz(13828) About Me  on 2010-09-16 15:42:32 (Show Source):
You can put this solution on YOUR website!
In vertex form,
y=a%28x-3%29%5E2%2B1
Using (1,3),
3=a%281-3%29%5E2%2B1
a%28-2%29%5E2=2
4a=2
a=1%2F2
.
.
.
highlight_green%28y=%28x-3%29%5E2%2F2%2B1%29
Now that you have the equation, test all of the points.
I'll do one, you do the remaining four.
A) (-3,-1):-1=%28-3-3%29%5E2%2F2%2B1
-1=%28-6%29%5E2%2F2%2B1
-1=36%2F2%2B1
-1=18%2B1
-1=19
False, so (-3,-1) is not a point on the parabola.
Continue with the remaining points in the same manner.
.
.
.


Linear-systems/344051: I bought 10 lbs. of Stayman apples and x lbs. of golden delicious apples at the orchard. What was the combined weight of the apples?

1 solutions

Answer 246153 by Fombitz(13828) About Me  on 2010-09-16 15:37:58 (Show Source):


Equations/344063: 2/3+3y=5y-2/15
1 solutions

Answer 246151 by Fombitz(13828) About Me  on 2010-09-16 15:37:15 (Show Source):
You can put this solution on YOUR website!
2%2F3%2B3y=5y-2%2F15
Multiply both sides by 15.
10%2B45y=75y-2
-30y=-12
y=12%2F30
highlight%28y=2%2F5%29


Linear_Equations_And_Systems_Word_Problems/344052: Problem solving using linear equation
problem question : Zara works part-time at a flower shop. She is making a flower arrangement for a customer with a total of 30 flowers, using two types of flowers. she asked to use four times as many carnations as roses. how many of each will be in the arrangement?


i tried to solve this question many times but couldn't get the right answer
so please can you help me?
1 solutions

Answer 246150 by Fombitz(13828) About Me  on 2010-09-16 15:34:11 (Show Source):
You can put this solution on YOUR website!
The total number of carnations and roses is 30.
1.C%2BR=30
There are four times as many carnations as roses.
2.C=4%2AR
Substitute eq. 2 into eq. 1,
4R%2BR=30
Now solve for R.
.
.
.
Once you have R, use either equation to solve for C.


Angles/344061: angle A is 21 less than twice as large as its supplement angle B
1 solutions

Answer 246148 by Fombitz(13828) About Me  on 2010-09-16 15:31:05 (Show Source):
You can put this solution on YOUR website!
A%2BB=180
.
.
.
A=2B-21
Substitute,
%282B-21%29%2BB=180
3B=201
highlight%28B=67%29degrees
.
.
A=2%2867%29-21
highlight%28A=113%29degrees


Probability-and-statistics/344056: A certain diet claims to lower cholesterol by an average of 60 points with a standard deviation of 7. Find the probability that the mean amount lowered will be more than 75 points.
1 solutions

Answer 246147 by Fombitz(13828) About Me  on 2010-09-16 15:29:20 (Show Source):
You can put this solution on YOUR website!
Find the z-score.
z=%28x-mu%29%2Fsigma=%2875-60%29%2F7
z=2.14
P%28z%3C=2.14%29=0.983938
P%28z%3E2.14%29=1-P%28z%3C=2.14%29
P%28z%3E2.14%29=1-0.983938
highlight%28P%28x%3E75%29=P%28z%3E2.14%29=0.01606%29


Equations/344060: Solve the equation x^4-2⁢x^2-15=0
1 solutions

Answer 246145 by Fombitz(13828) About Me  on 2010-09-16 15:26:12 (Show Source):
You can put this solution on YOUR website!
x%5E4-2x%5E2-15=0
%28x%5E2%2B3%29%28x%5E2-5%29=0
Two solutions:
x%5E2%2B3=0
x%5E2=-3
highlight%28x=0+%2B-+sqrt%283%29i%29 where i=sqrt%28-1%29
.
.
.
x%5E2-5=0
x%5E2=5
highlight%28x=0+%2B-+sqrt%285%29%29


Radicals/344059: Solve by multiplying both side by the LCD.
x+3/x-1 + x+4/x+1 = 8x+5/x^2-1


My Work: (x+1)(x+3)+(x-1)(x+4)=8x+5
2x^2-7x-1=8x+5
2x^2-15x-6=0
no solution
Is this correct please help thanks
1 solutions

Answer 246144 by Fombitz(13828) About Me  on 2010-09-16 15:24:24 (Show Source):
You can put this solution on YOUR website!
%28x%2B1%29%28x%2B3%29%2B%28x-1%29%28x%2B4%29=8x%2B5
%28x%5E2%2B4x%2B3%29%2B%28x%5E2%2B3x-4%29=8x%2B5
2x%5E2%2B7x-1=8x%2B5 <--- You had (-7x)
2x%5E2-x-6=0
%282x%2B3%29%28x-2%29=0
Use the zero product property to solve for the two solutions.


Age_Word_Problems/344048: Melissa is 24 years younger than Joyce. In 2 years, Joyce will be 3 times as old at Melissa will be then. How old are they now?
1 solutions

Answer 246143 by Fombitz(13828) About Me  on 2010-09-16 15:18:09 (Show Source):
You can put this solution on YOUR website!
1.M=J-24
In two years, Melissa will be M%2B2, Joyce will be J%2B2.
J%2B2=3%28M%2B2%29
J%2B2=3M%2B6
2.J=3M%2B4
Substitute eq. 1 into eq. 2,
J=3%28J-24%29%2B4
J=3J-72%2B4
-2J=-68
J=34
Then
M=34-24=10
.
.
.
Joyce is 34 years old and Melissa is 10 years old.


Polynomials-and-rational-expressions/344050: Hello, I need to factor the Polynomial completely and I just don't get how to do it. If you can help me get started I might be able to figure it out. The problem is -x%5E4%2B10x%5E3-21x%5E2
Thank you for your help.
1 solutions

Answer 246141 by Fombitz(13828) About Me  on 2010-09-16 15:15:25 (Show Source):
You can put this solution on YOUR website!
First factor out the highest power of x and the -1 too.
-x%5E4%2B10x%5E3-21x%5E2=-x%5E2%28x%5E2-10x%2B21%29
You can further factor the quadratic equation.
Look at factors of 21 that sum to -10.