anonymous
  • anonymous
Fan and Medal!! The area of a rectangular piece of land is 240 square meters. If the length of the land was 5 meters less and the width was 3 meters more, the shape of the land would be a square. Part A: Write an equation to find the width (x) of the land. Show the steps of your work. Part B: What is the width of the land in meters? Show the steps of your work.
Mathematics
katieb
  • katieb
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DanJS
  • DanJS
A square would be X by X This rectangle is said to be (X-5) by (X+3)
DanJS
  • DanJS
(X-5)(X+3) = 240
anonymous
  • anonymous
(x+3)(x-5)=240?

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anonymous
  • anonymous
Okay I got that
DanJS
  • DanJS
yes
anonymous
  • anonymous
What do I do now?
anonymous
  • anonymous
do you know how to find the area of a rectangle
DanJS
  • DanJS
Solve for X, you will get 2 answers, the positive one is correct
anonymous
  • anonymous
do I FOIL (x+3)(x-5)?
DanJS
  • DanJS
yes
anonymous
  • anonymous
I ended up getting x^2-2x-15
DanJS
  • DanJS
move the 240 over now to get x^2 - 2x - 255 = 0
DanJS
  • DanJS
factor that, or use the quadratic formula , since it is a book prob, it will probably factor nice
anonymous
  • anonymous
Do I make that into two binomials?
DanJS
  • DanJS
yep (x-17)(x+15)=0
anonymous
  • anonymous
Wait how did you get the 17 and 15?
DanJS
  • DanJS
255 = 17 * 15 and 15 - 17 = -2 (middle number)
DanJS
  • DanJS
If you multiply that out, you get back to the original ax^2 + bx + c = 0
anonymous
  • anonymous
Ohhh okay I understand that
DanJS
  • DanJS
or you could always just apply the quadratic formula, and you would get the X values
DanJS
  • DanJS
so now you have (x-17)(x+15)=0 which means either term can be zero, so (x-17)=0 or (x+15)=0 X=17 or X=-15
DanJS
  • DanJS
The problem is a physical measure, so the positive value is the one that makes sense... X=17
anonymous
  • anonymous
What do I write for part A and for Part B?
DanJS
  • DanJS
First Part... Area of Land = Length * Width = 240 240 = (X-5)(X+3)
anonymous
  • anonymous
And do I work it out until I get (x-17)(x+15) = 0?
DanJS
  • DanJS
right, for the second part you solve it
anonymous
  • anonymous
Thank you sososo much! You really helped a lot.
DanJS
  • DanJS
yw
anonymous
  • anonymous
Do you think you can check over some of my answers? If you have the time of course
DanJS
  • DanJS
sure
anonymous
  • anonymous
Thanks so much! They're quite long, so do you want me to screenshot it and attach it?
DanJS
  • DanJS
Sure, i have a bit of time
anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous
And that's it, since I don't want to have you check all of them, haha
DanJS
  • DanJS
The first one looks good, what is the prob with that one?
anonymous
  • anonymous
I just wanted to see if I got it correct or not
DanJS
  • DanJS
That one looks good to me
anonymous
  • anonymous
Thank you (:
DanJS
  • DanJS
second one looks good too
anonymous
  • anonymous
yay ^-^
DanJS
  • DanJS
For the last one part C, it asks if they all have a common factor
anonymous
  • anonymous
Yes, is it wrong?
DanJS
  • DanJS
I don't see a common factor btw all 3 of those
anonymous
  • anonymous
So it would be no because no common factor is consistent between the three polynomials?
DanJS
  • DanJS
yeah i think so
anonymous
  • anonymous
Do you think you could check 2 more?
DanJS
  • DanJS
k, real quick, then i have to go... you can fan me for help later if you want
anonymous
  • anonymous
Alright! Once I finish with these questions, I'll be done with Algebra for the year, aha
DanJS
  • DanJS
haha
anonymous
  • anonymous
anonymous
  • anonymous
And that's it!
DanJS
  • DanJS
For the first, for the domain, be sure to call the variable 't' and not x, Since y is a function of t, in S(t)
anonymous
  • anonymous
Okay
anonymous
  • anonymous
anything else?
DanJS
  • DanJS
nope, looks good to me
anonymous
  • anonymous
Yay!
anonymous
  • anonymous
Did you check the last one? or
DanJS
  • DanJS
Part b asks what the maximum profit is, you dont say what that is
anonymous
  • anonymous
How do I find the maximum?
DanJS
  • DanJS
it would be at the vertex of the parabola, or axis of symmetry value
anonymous
  • anonymous
How do I find that? Did my steps correspond to the question at all?
DanJS
  • DanJS
It looks like you have P(n) written in vertex form in part b right... so you can use that to extract the vertex coordinate (h,k)
anonymous
  • anonymous
Huh?
DanJS
  • DanJS
vertex point - (h,k) Vertex Equation - y = a(x-h)^2+k
anonymous
  • anonymous
Do I need to rewrite anything?
DanJS
  • DanJS
so the vertex from your equation is at the point, (5, 2250)
anonymous
  • anonymous
This is so confusing ._. I'm sorry that I'm so difficult to work with
DanJS
  • DanJS
sorry i said year... the most profit is at (5,2250) price 5 and prfit 2250
anonymous
  • anonymous
How do I find that with the steps I wrote down?
DanJS
  • DanJS
which is also on the axis of symmetry
DanJS
  • DanJS
The last thing you wrote, is the vertex equation for the parabola. vertex point - (h,k) Vertex Equation - y = a(x-h)^2+k The maximum profit 'k' is at that vertex point, you can just read it from your equation.
anonymous
  • anonymous
Ahhh okay! So now I write that the maximum profit is 2250 ?
DanJS
  • DanJS
yes, The vertex is at point (5,2250) When the tickets are sold at 5 dollars each, the profit is the most at 2250 dollars.
anonymous
  • anonymous
Thank you sosososo much!! You're truly a lifesaver, I wish I could give you a thousand medals , haha
DanJS
  • DanJS
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DanJS
  • DanJS
welcome,
anonymous
  • anonymous
Take care!!

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