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Linear-systems/298223: the following system of equations is a dependent system.
x - 6y = 8
5x - 30y = 40
what is the correct way to write the solution?
a) no solution
b) x - 6y = 8
c) 0
d) all numbers
1 solutions
Answer 214599 by Fombitz(13828) on 2010-04-29 08:25:44 (Show Source):
You can put this solution on YOUR website!b) Since the second equation is the first equation multiplied by 6 (hence dependent), every solution of the first equation will also solve the second equation, since they're the same equation.
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Quadratic-relations-and-conic-sections/298218: Write an equation for an ellipse with center(-4,2) and a horizontal major axis?
(Thats all the information given in the book) 1 solutions
Answer 214596 by Fombitz(13828) on 2010-04-29 08:16:07 (Show Source):
You can put this solution on YOUR website!The general equation for an ellipse centered at (h,k) is,

Substituting,

You are free to choose  and  .
The only other restriction is regarding the horizontal axis which means that

.
.
.
So here's one example (of many) with  and  ,
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Probability-and-statistics/297867: A bag contains 3 nickels, 4 dimes, and 5 quarters. If two coins are selected at random without replacing the first one selected, what is the probability that the two coins match? 1 solutions
Answer 214454 by Fombitz(13828) on 2010-04-28 16:29:15 (Show Source):
You can put this solution on YOUR website!3 nickels
4 dimes
5 quarters
12 total coins
P(N)=3/12
P(D)=4/12
P(Q)=5/12
Once one coin is chosen then the total number of coins drops to 11 and the probability of each coin is adjusted.
P(N if nickel is chosen first)=2/11
P(D if dime is chosen first)=3/11
P(Q if quarter is chosen first)=4/11
Since each event is independent, multiply the probabilities.
P(nickel then nickel)=(3/12)(2/11)=1/22
P(dime then dime)=(4/12)(3/11)=1/11
P(quarter then quarter)=(5/12)(4/11)=5/33
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Geometry_proofs/297859: Hello,
I have 4 points given to me and I have to prove algebraically whether the figure is a kite. I can't just plot the points. How would I go about doing that? 1 solutions
Answer 214423 by Fombitz(13828) on 2010-04-28 16:05:25 (Show Source):
You can put this solution on YOUR website!Given 4 points, divide them into two sets.
One set is the lengthwise component on the kite (line AB below).
The other set is the transverse (sideways) component of the kite (line CD).
Calculate the eqaution of the line using the slope and the point-slope form of a line for the length wise component.

Then convert to slope-intercept form

Do the same for the transverse component to get its equation,

If it's a kite, the lines will be perpendicular and the relationship between the two slopes will be,

If that's not the case, then stop there. It's not a kite.
.
.
.
If it is true then find the intersection point, I, between the two lines.
Solve the system of equations.

Since they both equal y, set them equal to each other.

Solve for x.
Then solve for y using either equation.
Now you have the point of intersection (xi,yi) of the two components of the kite.
If it's a kite, the distance from the intersection point (xi,yi) to the ends of the transverse components (C and D) must be identical.

If that's the case, then you've proven that the points form a kite.
If it's not true, then you don't have a kite.
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Linear-systems/297817: Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent.
y = x + 4
3y - 5x = 6
1 solutions
Answer 214411 by Fombitz(13828) on 2010-04-28 15:43:37 (Show Source):
You can put this solution on YOUR website!1. 
2. 
Substitute eq. 1 into eq. 2 directly and solve for x,

Now use eq. 1 to solve for y.

.
.
.
Graphical check of the solution.
Independent.
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test/297603: Could any one pls help to solve this -How do you solve an equation like x3 + 2x2 – 88x + 200 = 0 1 solutions
Answer 214333 by Fombitz(13828) on 2010-04-28 10:28:24 (Show Source):
You can put this solution on YOUR website!First step is to graph it.

Yikes, unfortunately this equation does not have simple (integer or rational)
roots. I suggest using www.1728.com/cubic.htm which has a cubic equation solver. From that site,
x=6.687,x=-11.327,x=2.640 are roots for this equation.
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