Question

Need help please (: medal + fan
(attached image) I really need to finish this and i dont get it.

Answer 1

is there an answer choice

Answer 2

no its worded

Answer 3

hm let me see

Answer 4

okay thanks

Answer 5

sorry i have no idea how to do this :/

Answer 6

its okay

Answer 7

Here you need to complete the square. This will allow you to express the equation in y = a(x - h)^2 + k form, which gives you the vertex easily.

To complete the square, consider the first 2 terms on the right side, -250n^2 and 2500n. We want to add a third term to create a perfect trinomial, which is a trinomial whose two factors are the same. First thing to do is factor out -250 from both to make things a bit easier: -250(n^2 - 10n). Now we need that third term. To find it, divide the coefficient of second term by half and square it: (-10)/2 = -5, and (-5)^2 is 25.

This means our perfect trinomial is n^2 - 10n + 25. If you factor this, you get (n - 5)^2. However, we just added 25 to the equation! to keep the equation the same, we need to subtract 25 as well: (n - 5)^2 - 25. Keep in mind though, that this is is only part of the story - the full equation right now actually looks like this:

P(n) = -250[(n - 5)^2 - 25] - 5250

This almost looks like y = a(x - h)^2 + k form, but we need to do one more thing - let's take that -25 out of the brackets! If we do that though, we need to multiply it by -250 (remember, everything in the brackets was factored by -250). (-250) x (-25) = 6250, so now we have:

P(n) = -250(n - 5)^2 - 5250 + 6250
P(n) = -250(n - 5)^2 + 1000

There we go! We have the form we want! The coordinates of the vertex are (h,k) which in this case are (5,1000). We know this function has a maximum because the parabola opens downwards (a is negative). Therefore, the maximum profit in this case is 1000.

The axis of symmetry is the vertical line that goes through the vertex, dividing the parabola into two equal (symmetrical) halves. The vertex of the parabola has an x-value of 5, so the axis of symmetry is x = 5.

If anything is unclear please let me know! Hope this helps!

Answer 8

Thank you! (: and can you help me with one more question?

Answer 9

Sure

Answer 10

We have two variables here, length and width, and so we need 2 equations to figure out what they are. Let's find those first!

The area of a rectangle is given by length (L) times width (W). In this case, L x W = 260. We can rewrite this equation as L = 260/W. There's our first equation!

We know that in a square, all sides are equal (i.e. length = width). If a square is formed when the length and width are changed in the way that it says in the question, then we know that L - 5 = W + 2. You can rewrite this equation as well as an equation to find the width of the land: W = L - 7. Here's our second equation!

We know from the first equation that L can be expressed in terms of W. Let's sub this into our second equation: W = 260/W - 7. Now we just need to solve for W! Can you take it from there?

Answer 11

Thank you! (: