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Sauron [17]
3 years ago
13

write an equation of a parabola with vertex at origin (0,0) with the given focus, and find the directrix. given the focus at (0,

-4)
Mathematics
1 answer:
pickupchik [31]3 years ago
8 0

<u>Directrix:</u>

If the vertex of the parabola is at (0, 0) and the focus is (0, -4) <em>which is 4 units down</em><em> </em>then the directrix will be the line 4 units UP.

Answer: y = 4

<u>Equation of parabola:</u>

y = \frac{1}{4p}x^{2}  ; where p is the distance from the vertex to the focus.

As stated above, the focus is 4 units down, so p = -4

y = \frac{1}{4(-4)}x^{2}

y = \frac{1}{-16}x^{2}

Answer: y = -\frac{1}{16}x^{2}


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Which of the following statements are true of the graph of the function f(x)=(x+5)(x-3)?
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Answers: b, d and e

b.The graph has a relative minimum

d. The graph has an x intercept at 3,0

e. the graph has an y intercept at 0,-15

f(x)=(x+5)(x-3)

The given equation is in the form of f(x) = a(x-b)(x-c)

If 'a' is positive then graph has a relative minimum

If 'a' is negative then graph has a relative maximum

Here a=1 that is positive so graph has a relative minimum .

To find x intercept we set f(x) =0 and solve for x

0=(x+5)(x-3)

x+5 =0 -> x = -5 so x intercept is (-5,0)

x - 3=0 -> x= 3 so x intercept is (3,0)

To find y intercept we plug in 0 for x

y=(x+5)(x-3)

y=(0+5)(0-3) = -15

so y intercept is (0,-15)



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3 years ago
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A Candy contains 300 pieces of which 28% are wet how many pieces are red
Dmitrij [34]
I assumed you meant red instead of wet.

To calculate this, multiply 28% (which is the same as .28) times 300.

300 x .28 = 84
8 0
3 years ago
The useful life of a radial tire is normally distributed with a mean of 30,000 miles and a standard deviation of 5000 miles. The
otez555 [7]

Answer:

  empirical rule: 81.5%

  table or calculator: 81.9%

Step-by-step explanation:

The lower limit of the life range of interest has a z-score of ...

  z = (x -μ)/σ = (20,000 -30,000)/5,000 = -2

The upper limit has a z-score of ...

  z = (35,000 -30,000)/5,000 = 1

<u>Empirical rule solution</u>

The empirical rule tells you that 95% of the distribution lies within 2 standard deviations of the mean, so (100% -95%)/2 = 2.5% lie below z = -2. It also tells you 68% lie within 1 standard deviation of the mean, so (100% -68%)/2 = 16% lie above z = 1.

The fraction that lies within -2 to 1 standard deviations of the means is thus ...

  (100% -2.5% -16%) = 81.5%

The probability the tire has a life in the desired range is about 81.5%.

__

<u>Calculator solution</u>

A probability calculator for the Normal distribution tells you that ...

  P(-2 < z < 1) ≈ 0.8185946

The probability the tire has a life in the desired range is about 81.9%.

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The angles in the new triangle is the same as the original triangle.

The angles are the same, they are not multiplied by the factor of 1.5





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