(09.02 HC)The function f(x) = −x2 + 24x − 80 models the hourly profit, in dollars, a shop makes for selling coffee, where x is the number of cups of coffee sold, and f(x) is the amount of profit.


Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)


Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)


(10 points)

Answers

Answer 1
Answer:

Answer:

Vertex = (12,64)

The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.

X-intercepts: 4 and 20

The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.

Step-by-step explanation:

To find the vertex we can use the formula for the x-coordinate of the vertex:

x_v = -b/2a

Where a and b are coefficients of the quadratic equation (in this case, a = -1 and b = 24)

So we have that:

x_v = -24 / (-2) = 12

The vertex is 12 cups of coffee. Now we apply this value to find the y-coordinate of the vertex:

f(x) = -12^2 + 24*12 - 80 = 64

So the vertex is (12,64). The meaning of this pair of values is that the y-coordinate is the maximum profit obtainable, and the x-coordinate is how many cups sold will make the maximum profit.

To find the x-intercepts, we need to make f(x) = 0 and find the values of x:

-x2 + 24x - 80 = 0

Delta = 24^2 - 80*4 = 256

sqrt(Delta) = 16

x1 = (-24 + 16)/(-2) = 4

x2 = (-24 - 16)/(-2) = 20

The x-intercepts are 4 and 20. The meaning of theses values is that these amounts of cups sold (4 and 20) will make zero profit.


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Answers

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Answer:

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Step-by-step explanation:

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Answers

The number of boxes of chopsticks that the manager order will be 30.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A Chinese café utilizes around 225 sets of chopsticks every day the supervisor needs to arrange a multi-day supply of chopsticks the crates come in of 750 sets

The number of chopsticks required in a month is given as,

⇒ 225 x 30

⇒ 6750

Then the number of boxes of chopsticks is given as,

⇒ 6750 / 225

⇒ 30

The number of boxes of chopsticks that the manager order will be 30.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

750/30 = 25 - pairs of chopsticks in one box
225/25 = 9 - boxes should the manager order.

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Answers

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Answers

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 245.76
- 75.00
----------------
 170.76

n=$170.76

$245.76 = $75.00 + n
We are subtracted both side by 75.00 because when we write equation the sign with the front of 75.00 is positive the positive opposite is negative thats why we subtract it and n equal to 170.76.
245.76 = 75.00 + n
-75.00  = -75.00
--------------------------
170.76 = n

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Answers

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Answers

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