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4 1727 Xwhen Y (2) 6 =...

Question

4 1727 Xwhen Y (2) 6 =

4 1727 X when Y (2) 6 =



Answers

$$\begin{aligned} 4 x-2 y &=8 \\-7 y &=-12 \end{aligned}$$

So for this problem, we know that we're going to be able to write a proportion between our two points. And this essentially comes from the fact that because y Berries directly with X, we know that why over X is equal to some constant K. So that means that if we plug in one number one set of points x y, this should be equal to another set of points x y that lie within the same direct variation. And so our problem gives us our first point it if y is equal to four, when X is equal to negative too. So that means that our first point is negative to four. I'm in her second point. That we want to solve for is, except to is equal to what when our second why is equal to six. And so if we plug these numbers into our direct proportion, I'm on the left side. Why one is for divided by X one is negative too should be equal to on the right side. Why, too, we're told, is six divided by our ex that we're solving for And so we know that we're going to have to Ah cross multiply to figure our proportion. And when we do that we get for X is equal to negative 12. So to solve for X will divide both sides of our equation by four. And we find that X is equal to negative three when y is equal to sit.

This graph is representing X squared equals four way. The center is at zero comma zero. As you can tell, to find the focus convert to standard form. The general form is for P times why minus K is equal to X minus h squared to find P. In this case, the P value is technically provided for us because four has been factored out. So that means we know that one is our p value. So rewrite this equation as four times one times why minus zero is equal to X minus zero squared. To find the focus, just add the P value to the y, coordinate of the vortex and that would be zero plus one. So our focus is simply zero comma. One defined the director X We know our P values one. The equation is why equal zero minus p plug in one for P. Why equals one is the direct tricks and we're done

We need to match the equation why squared is equal to negative four -4 times x. So since this is why squared instead of being X squared, we know that the problem is going to be either open it right or left, so we can throw out all the problems that open up or down. So that throws out be throws out, see throws up deep. And because it's Y squared equals negative for X. Since the number in front of the X is a negative sign is going to open to the left. So that throws out A. So when we look at our values, the ones that match up closer our letter E. So letter E is the one that matches why squared is equal to negative four times X.

Okay, so here were provided a system of equations were asked to solve S So I think the best way to do this would be the substitution method. Let's go ahead and solve a four hour Ah, why, in our second inclusion, by dividing by X on both sides, why equals four over X And then let's plug that into our first equation. So we're gonna have X squared equals Sorry. Plaice 44 X squared equals 20 X squared plus four squared the inside. So that's gonna be 16 over X squared. I was 20 and let's go ahead and distribute that foreign to our parentheses. So four times 16 a 64 over X squared I was 20. And let's get the X squared out of our denominator by multiplying it out. Just get rid of that fraction. So we have X to the fourth plus 64 equals 20 x squared. Let's get everything on the same side of our equation by subtracting 20 x Credible sides soar equations gonna look like X to the fourth minus 20 x squared plus 64 that's equal to zero. So let's go ahead and factor this. So now we're gonna have X squared on both sides. Only need something when multiplied together. Equal 64 out of together equal 20. I only know 16 and four do just that. We want them to be negative because their twenties negative But are 64 so positive and then we can then factor these out a little bit further. We can have x minus for an X plus four for our X squared minus 16. And we can have X minus two X plus two for our expert menace. For have we saw all of our X is equal to zero. Our solutions or answers for X are gonna be four negative for two in negative too. Let's go ahead and plug that into our why equation? So we're gonna have why equals 4/4. Why equals four over negative for why equals four over to and why equals four over native to So are why solutions? Well four divided by four is one four divided by negative force. Native one four, divided by two is two and four divided by negative. Two is negative. Two. So when our X is four are wise one when our ex is negative for our wise negative one when her ex is to our white is too on The X is a negative to our white is negative two Here is our set of solutions.


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