1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Anastasy [175]
3 years ago
14

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Mathematics
1 answer:
Artemon [7]3 years ago
6 0

Answer:

The equation y=\frac{-x^2-6x+31}{8} represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }, we find that the distance between (x, y) is

\sqrt{(x+3)^2+(y-3)^2}

and the distance between (x, y) and the directrix y = 7 is

\sqrt{(y-7)^2}.

On the parabola, these distances are equal so, we solve for y:

\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}

You might be interested in
Type the correct answer in the box,
HACTEHA [7]

<u>We'll assume the quadratic equation has real coefficients</u>

Answer:

<em>The other solution is x=1-8</em><em>i</em><em>.</em>

Step-by-step explanation:

<u>The Complex Conjugate Root Theorem</u>

if P(x) is a polynomial in x with <em>real coefficients</em>, and a + bi is a root of P(x) with a and b real numbers, then its complex conjugate a − bi is also a root of P(x).

The question does not specify if the quadratic equation has real coefficients, but we will assume that.

Given x=1+8i is one solution of the equation, the complex conjugate root theorem guarantees that the other solution must be x=1-8i.

3 0
3 years ago
Triangle LMN has coordinates L (0, 0), M (0, -2), and N (2, 0). If ΔLMN ≅ ΔXYZ, what is the measure of XZ?
salantis [7]

Check the picture below.

3 0
3 years ago
Suppose that the population mean for income is $50,000, while the population standard deviation is 25,000. If we select a random
Fudgin [204]

Answer:

Probability that the sample will have a mean that is greater than $52,000 is 0.0057.

Step-by-step explanation:

We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.

We select a random sample of 1,000 people.

<em>Let </em>\bar X<em> = sample mean</em>

The z-score probability distribution for sample mean is given by;

               Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean = $50,000

            \sigma = population standard deviation = $25,000

            n = sample of people = 1,000

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample will have a mean that is greater than $52,000 is given by = P(\bar X > $52,000)

  P(\bar X > $52,000) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{52,000-50,000}{\frac{25,000}{\sqrt{1,000} } } ) = P(Z > 2.53) = 1 - P(Z \leq 2.53)

                                                                    = 1 - 0.9943 = 0.0057

<em>Now, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.</em>

Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.

5 0
3 years ago
Which numbers are solutions of the inequality?<br><br> x &gt; –5; –7, –5, –1
yanalaym [24]

Answer:

-1 is the only answer that is greater than -5

3 0
3 years ago
4 x (2 x 7) = (4 x 2) x ___
natka813 [3]

Answer:

x=0

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Anca a citit 375 de pagini dintr-o carte. În fiecare zi, începând cu a doua zi, ea a citit cu 5 pagini mai mult decât în ziua pr
    13·1 answer
  • Solve for x<br> 3(X-5)-4X = 6(X-10) -(X+ 5)
    13·1 answer
  • 75 + 50x = 25 + 70x<br><br> a, 5<br> b, 5/6<br> c, 2<br> d, 2.5
    8·1 answer
  • Eli has saved $8 more than 1/3 of Angela's savings.If they each save $10 more Eli will have saved &amp;4 more than Angela's savi
    11·2 answers
  • 3. The difference of the squares of two positive consecutive odd integers is 32. Find the
    11·1 answer
  • HELP ASAP 30 POINTS WORTH !!!!! OωO
    8·2 answers
  • (20,-3),(19,-20) what is the slope of this
    7·2 answers
  • 6. Consider the diagram below.
    7·2 answers
  • Yo yo i need help trying to bring my grade up yo it would be helpful yo
    13·2 answers
  • What is the number that not the same in a fish
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!