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sophadof
 one year ago
Find the point(s) of intersection of the line X + Y = 5 and the circle x2 + y2 = 25 by solving the system of equations.
sophadof
 one year ago
Find the point(s) of intersection of the line X + Y = 5 and the circle x2 + y2 = 25 by solving the system of equations.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My geometry is very rusty, but I'll give it a shot... If I remember correctly, you will need to put both equations into slopeintercept forum. Doing this, you will get y= x+5 and y= x+5 ( someone may want to double check this). After this, you use trace the two equations and will get an intersection of y=5. Again, my geometry is rusty and someone may want to double check.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Iehmad is close. The idea is to solve the first equation for y. 1) This gives y = x + 5. 2) You will then plug this into the second equation x^2 + y^2 = 25, to get x^2 + (x + 5)^2 = 25. 3) Solve this for x. 4) You can then use the x's you find to solve for y. 5) Your final answer will be coordinates (x,y).

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0wait..so @jtvatsim after i plug it in the step after would be x+(5)^2=25?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3The second equation is x^2 + y^2 = 25. We will replace y with y = x + 5. That makes the equation: x^2 + (x + 5)^2 = 25. Be careful to factor the entire parentheses. You should get x^2 + (x + 5)*(x + 5) = 25 which simplifies to x^2 + (x^2  5x  5x + 25) = 25, x^2 + x^2  10x + 25 = 25. Does that make sense?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Of course, there is still work to do from where I left off, but hopefully that gets you started. :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3You can check your answer against this graph I did on Desmos.com

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0I am completely lost :( @jtvatsim

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0it makes sense..it's just moving on from what you did is losing me.. @jtvatsim

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3No problem. Here's how I would do it. After simplifying the work I did above you should get: 2x^2  10x + 25 = 25. Did you get that?

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0yes!!(: @jtvatsim i actualy did haha

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3OK, great! Now, let's subtract 25 from both sides leaving us with: 2x^2  10x = 0

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3I can factor out a 2 (not essential, but why not?) to get 2(x^2  5x) = 0 then, x^2  5x = 0 (after dividing by 2). Factoring, gives me x(x  5) = 0. so x = 0, or x = 5.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Now WAY BACK in the beginning, we said that y = x + 5. So we can plug in our new found values of x to get the y values. x = 0, means y = 0 + 5 = 5. This is the point (0,5). x = 5, means y = 5 + 5 = 0. This is the point (5,0). We are done. Yay! :)

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0haha hang on..just gonna try it(: @jtvatsim

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for staying in this with me though!!!!(: @jtvatsim

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3No worries, glad to help if I can. :)

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0yeah i got x=5 @jtvatsim

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3And you should also get x = 0 as another solution.

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0oh! @jtvatsim gotcha!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Great! If you had done something like x^2 = 5x and divided by x, you would get x = 5, but dividing by x accidentally causes you to miss the x = 0 solution. Just wanted to be sure you saw that. :)

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0yes thank you!!!!! @jtvatsim I hate to ask you this but...do you have email, I have another math question and its with triangles..

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3No worries, feel free to post it on OpenStudy just in case I have to run here soon. At least someone else would be able to jump in. :)

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0yes thank you!!!!! @jtvatsim I hate to ask you this but...do you have email, I have another math question and its with triangles..

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3And we are to find the value of x correct?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Alright, first question, do you know what the ~ symbol means?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3So, that basically means the triangles have the same shape (maybe not the same size).

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3The problem is that the picture didn't really do a good job at showing this (especially since one is upside down!). I'll go ahead and fix that.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433640781894:dw That's better.

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Now, whenever we have similar triangles, we like to notice the sides that match and set up a "proportion". Something like these fractions: (big triangle side 1)/(big triangle side 2) = (small triangle side 1)/(small triangle side 2) Make sense so far?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Cool! So, now let's pick some sides! What would you like to pick for "big triangle side 1"? You can pick whatever you like (based on the drawing of course). :)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3OK, so right now we have: 75/(big triangle side 2) = (small triangle side 1)/(small triangle side 2). We need to keep going though. I would suggest that we pick "small triangle side 1" now. We need to pick the same part of the smaller triangle. (In this case the bottom). What would that be for the small triangle?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3We now just repeat the process for the other sides we know. We should get something like this...

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.375/30 = (4x  10)/(x + 5) Looks a little scary, but we have now got the question ready to solve. Any questions so far before we go on?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Right now, cross multiplication is your friend (or if you prefer multiply each fraction by the bottoms) and this gives us: 75*(x + 5) = 30*(4x  10)

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Very important step right there, are you ok with that?

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0yes! then do i solve?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Yes! Now you have a "nice" looking equation (you do have some distributing to do, so be careful).

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0so...75x+375=120x300?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Yes, that is correct!

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0yay!!!!!!!!!(: thank you!

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0then subtract 75 from 120?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Sure, that leaves you with 45x I believe.

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0yay!!!!! Thank you soooo much!!(: do i ned to plug in x for those equations or no?

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Only if the question wanted you to find the actual sides of the unknown triangle. Sometimes they do want you to find that.

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0oh alrighty!!! thank you so much!!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3That's easy to find though based on the information we now have.

sophadof
 one year ago
Best ResponseYou've already chosen the best response.0Have a good night? day? haha

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3More like evening. :) You too!
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