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Katarina [22]
3 years ago
9

3. Write the equation of a parabola with focus (-2, 4) and directrix y = 2. Show your work, including a sketch.

Mathematics
1 answer:
aleksklad [387]3 years ago
5 0
To solve this problem you must apply the proccedure shown below:

 1. (x0,y0) is any point of the parabola.

 2. You have that the distance between (x0,y0) and the the focus (-2,4) is:

 √(x0-(-2))²+(y0-4))²
 √((x0-+2)²+(y0-4))²

 3. The distance between (x0,y0) and the directrix y=2, is:

 |y0-2|

 4. Then, you have:

 √((x0-+2)²+(y0-4))²= |y0-2|

 5. When you simplify it and you clear y0, you obtain:

 y0=(x0²/4)+x0+4

6. Therefore, <span>the equation of the parabola with focus (-2, 4) and directrix y = 2, is:
</span>
 y=(x²/4)+x+4

 7. The graph is shown in the figure attached.

 The answer is: y=(x²/4)+x+4 

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Given f(x)= -x+15, what is f(-3) A.-45 B.12 C.18 D.45
lina2011 [118]
So you just subsitute -3 for x
f(-3)=-(-3)+15
f(-3)=3+15
f(-3)=18
answer is C
18
8 0
3 years ago
Select all expressions that represent a correct solution to the equation 6(x+4)=20
Sergeeva-Olga [200]

Answer:

D. 20 ÷ 6 − 4

E. 1/6(20 − 24)

F. (20−24) ÷ 6

Step-by-step explanation:

6(x + 4) = 20

6(x) + 6(4) = 20

6x + 24 = 20

     - 24  - 24

6x = -4

/6    /6

x = -4/6 or x = -2/3

D. 20 ÷ 6 − 4

20/6 - 4

20/6 - 24/6

-4/6 = -2/3

E. 1/6(20 − 24)

1/6(-4)

-4/6 = -2/3

F. (20 − 24) ÷ 6

- 4 / 6

-4/6 = -2/3

Hope this helps!

3 0
2 years ago
The U.S. and many other countries have recently tightened airport security. A sociologist is interested in estimating the propor
melisa1 [442]

Answer:

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

Step-by-step explanation:

Conduct a test to determine whether the true proportion of interest is higher than 0.7.

This means that the null hypothesis is: H_{0}: p = 0.7

And the alternate hypothesis is: H_{a}: p > 0.7

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

0.7 is tested at the null hypothesis:

This means that \mu = 0.7, \sigma = \sqrt{0.7*0.3}

The sociologist found that 375 of the 500 travelers randomly selected and interviewed indicated that the airports were safe.

This means that n = 500, X = \frac{375}{500} = 0.75

Value of the z-statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.75 - 0.7}{\frac{\sqrt{0.7*0.3}}{\sqrt{350}}}

z = 2.44

P-value of the test:

Probability of z being larger than 2.44, that is, a proportion larger than 0.75.

This is, looking at the z-table, 1 subtracted by the pvalue of Z = 2.44. S

Z = 2.44 has a pvalue of 0.9927

1 - 0.9927 = 0.0073

0.0073 < 0.05, which means that we reject the null hypothesis and conclude that the true proportion of interest is higher than 0.7.

8 0
3 years ago
How do you find a volume of a cube and Rectangular prism and a cylinder? PLEASE HELP ASAP ASAP PLEASSEEEEEEE I BEG YOU
Nat2105 [25]

Of course!

Cube: side length * side length * side length

So if it's a 6x6x6 cube, it's 6*6*6 = 216

Rectangular Prism: side length * side height * base width

So if it's a 6x7x8 prism, it's 6*7*8 = 336

Cylinder: π * (radius squared) * height

So if the base's radius is 6 and the height is 7, it's π*6^2*7 = 252π

5 0
3 years ago
Read 2 more answers
Can i get some help... CAN I PLEASE GET SOME HELP
miskamm [114]
-11+square root of 19/ 20   ,     -11- square root of 19/ 20
7 0
3 years ago
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