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notka56 [123]
2 years ago
8

Jacob made 93 cups of lemonade.

Mathematics
1 answer:
Greeley [361]2 years ago
5 0

Answer:

I think it's 87.5 or 87½

Step-by-step explanation:

I hope it helps you.

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Part 1: Identify the vertex, focus, and directrix of each. Then sketch the graph.
Lina20 [59]

Answer:  \bold{1.\quad \text{Vertex}:(4,-1)\qquad \text{Focus}:\bigg(4,-\dfrac{9}{8}\bigg)\qquad \text{Directrix}:y=-\dfrac{7}{8}}

                \bold{2.\quad \text{Vertex}:(2,1)\qquad \text{Focus}:\bigg(\dfrac{9}{4},1\bigg)\qquad \text{Directrix}:y=\dfrac{7}{4}}            

<u>Step-by-step explanation:</u>

The vertex form of a parabola is y = a(x - h)² + k  or  x = a(y - k)² + h

  • (h, k) is the vertex
  • p is the distance from the vertex to the focus
  • -p is the distance from the vertex to the directrix

    \bullet\quad a=\dfrac{1}{4p}

1) y = -2(x - 4)² - 1     →      a = -2   (h, k) = (4, -1)

a=\dfrac{1}{4p}\quad \rightarrow \quad -2=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{8}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{-8}{8}+\dfrac{-1}{8}\\\\.\qquad =-\dfrac{9}{8}\qquad \rightarrow \qquad \text{Focus}=\bigg(4,-\dfrac{9}{8}\bigg)\\\\\\\text{Directrix: y=Vertex - p}\\\\.\qquad \qquad y=\dfrac{-8}{8}-\dfrac{-1}{8}\\\\.\qquad \qquad y=-\dfrac{7}{8}

*******************************************************************************************

2) x = (y - 1)² + 2     →      a = 1   (h, k) = (2, 1)

a=\dfrac{1}{4p}\quad \rightarrow \quad 1=\dfrac{1}{4p}\quad \rightarrow \quad p=-\dfrac{1}{4}\\\\\text{Focus = Vertex + p}\\\\.\qquad = \dfrac{8}{4}+\dfrac{1}{4}\\\\.\qquad =\dfrac{9}{4}\qquad \rightarrow \qquad \text{Focus}=\bigg(\dfrac{9}{4},1\bigg)\\\\\\\text{Directrix: x=Vertex - p}\\\\.\qquad \qquad x=\dfrac{8}{4}-\dfrac{1}{4}\\\\.\qquad \qquad x=\dfrac{7}{4}

6 0
3 years ago
Jason and his 3 roommates share the cost of the electric bill evenly
Law Incorporation [45]
To figure out how much every person would pay for electricity, divide the cosy by 4.
7 0
3 years ago
Read 2 more answers
Examine the graph at right. Then in a sentence suggest why the graph rises at 11:00am and drops at 1:15pm
makkiz [27]
The x-axis of the graph is the time while y-axis of the given plot is the money inside Lucy's purse in dollars. we can see that from 6 am to 11 am, Lucy's money is equal to about $60 while around 11 am it rose up to around $125 and then decreased to $100. This means that in the given range of time, only one transaction per time range was done by Lucy. One scenario here was that before lunch, say 11 am, her money was $60 and found out that she has to buy something after work, in which her money was not enough. She went to withdraw some cash that's why she had $125 in total and has to spend a portion of it at lunch with the remaining cash of $100. 
6 0
3 years ago
The function y=−0.25x+0.7 represents the percent y (in decimal form) of battery power remaining x hours after you turn on a lapt
mel-nik [20]

Answer:

x-intercept: 2.8 hours

y-intercept: 0.7 . . . . fraction of power remaining

Step-by-step explanation:

The equation is in slope-intercept form, so the y-intercept can be read directly: 0.7.

To find the x-intercept, set y=0 and solve for x:

0 = -0.25x +0.7

0.25x = 0.7 . . . . . add .25x

x = 2.8 . . . . . . . . . multiply by 4 (that is, the reciprocal of 0.25)

The x-intercept is 2.8; the y-intercept is 0.7.

7 0
3 years ago
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Please help I need to pass this test so I can bring my grades up!
Marianna [84]

Answer:

8. 24

9. 10

2. 72

1. 113

5. 7.96 = <u>8</u>

11. 30.19 = <u>30.2</u>

6. 28.27 = <u>28</u>

That's all I can answer right now, maybe study a bit more and your grades will get better! Good luck!

4 0
3 years ago
Read 2 more answers
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