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Elena-2011 [213]
2 years ago
7

William has $7.50 to spend at the store. A large pretzel costs $1.25, and a soda costs $0.25. He buys two sodas and x pretzels.

What equation shows the number of pretzels, x, that William can buy?
Mathematics
1 answer:
zvonat [6]2 years ago
4 0
7.50-((2• .25) + (1.25•x))
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SHOW ALL WORK BUT KEE IT SIMPLE AND EASY TO UNDERSTAND:)
7nadin3 [17]
To do this problem, you need to use a process called completing the square. Let me explain:  

To complete the square on the function f(x) = x² + 8x +13, first group the first two terms in (  )  and leave some space at the end as follows:
f(x) = (x² + 8x          ) + 13  Now our next step is to fill in the space and adjust our expression on the right hand side of the function.  To do this, we take half of the middle number 8 and then square it:  so 4² = 16 and we fill in our space inside the ( ) with this value 16;   
f(x) = (x² + 8x + 16) + 13  now what we have done is to increase the overall value of our expression on the right by 16, but we want the overall value to remain the same.  To fix this we simply need to subtract 16 at the end like this:  f(x) = (x² + 8x + 16) + 13 -16   we can simplify and get the following.
f(x) = (x² + 8x + 16) - 3   At this point we're almost done.. All we need to do now is to rewrite the what is in the parentheses in a slightly different form.  Here is what it will look like:  f(x) = (x + 4)² - 3  notice all I did was take the sum of the square root of x² and the square root of 16 originally in the (  ) to get then new expression inside the ( ) and then square that  ( )²

Now this is a nice form to have because you can get the vertex straight from this form.. IN FACT this is called vertex form or (h,k) form for short.  In general the form is f(x) = a(x - h)² + k  don't worry about the 'a'  for now.. you might see that in our case it is just 1 and will not effect our equation.  You only have to consider this if the original leading coefficient of the quadratic is not 1 to begin with...

So you can see that our vertex is (-4,-3)  
Hope this is helpful, but if you have questions let me know.
5 0
3 years ago
Hey can someone please help me with just number 13 ?
Fudgin [204]
THE ANSWER IS B! YOUR WELCOME!
7 0
3 years ago
Tony separates a number of paintbrushes, x, into 3 equally sized groups. He claims that this is the same as making a group 1/3 t
DochEvi [55]

Answer:

Size of each group = \frac{x}{3}

Step-by-step explanation:

Total number of paint brushes = x

Since each the three groups are equally sized, to get the number of paintbrushes in a group, we will have to divide the total number of paint brushes by 3

∴ We have, number of paint brushes in a group = \frac{Total number of paintbrushes}{3}\\

= \frac{x}{3}

this is also the same thing as saying \frac{1}{3}×\frac{x}{1}

This shows that the size of the new group is the same as \frac{1}{3} the size of the original group

4 0
3 years ago
1- Random response The question on the right appears on a survey. Why are people told to roll a dice? It makes the survey more f
stellarik [79]
The answer would be 14 because I don’t know how to explain it
6 0
2 years ago
A rectangular tank with a square​ base, an open​ top, and a volume of 8 comma 7888,788 ft cubedft3 is to be constructed of sheet
Vlad [161]

Answer:

  26 ft square by 13 ft high

Step-by-step explanation:

The tank will have minimum surface area when opposite sides have the same total area as the square bottom. That is, their height is half their width. This makes the tank half a cube. Said cube would have a volume of ...

  2·(8788 ft^3) = (26 ft)^3

The square bottom of the tank is 26 ft square, and its height is 13 ft.

_____

<em>Solution using derivatives</em>

If x is the side length of the square bottom, the height is 8788/x^2 and the area is ...

  x^2 + 4x(8788/x^2) = x^2 +35152/x

The derivative of this is zero when area is minimized:

  2x -35152/x^2 = 0

  x^3 = 17576 = 26^3 . . . . . multiply by x^2/2, add 17576

  x = 26

_____

As the attached graph shows, a graphing calculator can also provide the solution.

5 0
3 years ago
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