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Nuetrik [128]
3 years ago
13

Problem situation: Bernie spends $6.50 on ingredients and cups for his lemonade stand. He charges $1.50 for each cup of lemonade

. How many cups, x, will Bernie need to sell to make a profit of at least $20? Inequality that represents this situation: 20≤1.50x−6.50 Drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution.

Mathematics
1 answer:
salantis [7]3 years ago
3 0

Answer:

Answer:

18 cups.

Step-by-step explanation:

We are given that Bernie spends $6.50 on ingredients and cups for his lemonade stand. He charges $1.50 for each cup of lemonade. Inequality that represents this situation: .

To find number of cups x to make a profit of at least  $20 we will use our given inequality.

Therefore, in order to make a profit of at least $20 Bernie need to sell 18 cups of lemonade.

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The boundary of the lawn in front of a building is represented by the parabola . The parabola is represented on the coordinate p
Colt1911 [192]
The boundary of the lawn in front of a building is represented by the parabola

y = (x^2) /16 + x - 2

And you have three questions which require to find the focus, the vertex and the directrix of the parabola.

Note that it is a regular parabola (its symmetry axis is paralell to the y-axis).

1) Focus:

It is a point on the symmetry axis => x = the x-component of the vertex) at a distance equal to the distance between the directrix and the vertex).

In a regular parabola, the y - coordinate of the focus is p units from the y-coordinate of the focus, and p is equal to 1/(4a), where a is the coefficient that appears in this form of the parabola's equation: y = a(x - h)^2 + k (this is called the vertex form)

Then we will rearrange the standard form, (x^2)/16 + x - 2 fo find the vertex form y = a(x-h)^2 + k

What we need is to complete a square. You can follow these steps.

1) Extract common factor 1/16 => (1/16) [ (x^2) + 16x - 32]

2) Add (and subtract) the square of the half value of the coefficent ot the term on x =>

16/2 = 8 => add and subtract 8^2 => (1/16) [ (x^2) + 16 x + 8^2 - 32 - 8^2]

3) The three first terms inside the square brackets are a perfect square trinomial: =>

(1/16) [ (x+8)^2 - 32 - 64] = (1/16) [ (x+8)^2  - 96] =>

(1/16) [(x+8)^2 ] - 96/16 =>

(1/16) (x +8)^2 -  6

Which is now in the form a(x - h)^2 + k,
where:

a = 1/16 , h = - 8, and k = -6

(h,k) is the vertex: h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.

=> a = 1/16 => p =1/4a = 16/4 = 4
 
y-componente of the focus = -6 + 4 = -2

x-component of the focus = h = - 8

=> focus = (-8, -2)

2) Vertex

We found it above, vertex = (h,k) = (-8,-6)


3) Directrix

It is the line y = p units below the vertex = > y = -6 - 4 = -10

y = -10   

 


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3 years ago
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o-na [289]

Answer:

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Step-by-step explanation:

3 0
3 years ago
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Karra is at the dollar store buying bags of chips for her sleepover party. For every 5 bags of chips she buys, she pays $6. What
Alexus [3.1K]

Answer:

$1.20

Step-by-step explanation:

Given that:

Price paid to buy 5 bags of chips = $6

To find:

Price per bag of chips in two digits after the decimal.

Solution:

To find the price of each bag of chips, we need to divide the price of 5 bags of chips with 5.

i.e. we need to divide $6 with 5, then we will get the price of each bag of chips.

\text{Price of each bag of chips}=\dfrac{\text{Price of 5 bags of chips}}{5}\\\Rightarrow \dfrac{\$6}{5} = \bold{\$1.2}

Therefore, the answer is:

Price of each bag of chips is <em>$1.2.</em>

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Answer:

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Step-by-step explanation:

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Answer: I haven't been in Geometry in a while but watch this video. It should help you.


Step-by-step explanation:


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