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
chubhunter [2.5K]
2 years ago
6

Find the standard form of the equation for the conic section represented by x^2 + 10x + 6y = 47.

Mathematics
1 answer:
Levart [38]2 years ago
7 0

Answer:

The standard form of the equation for the conic section represented by x^2\:+\:10x\:+\:6y\:=\:47 is:

4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2

Step-by-step explanation:

We know that:

4p\left(y-k\right)=\left(x-h\right)^2 is the standard equation for an up-down facing Parabola with vertex at (h, k), and focal length |p|.

Given the equation

x^2\:+\:10x\:+\:6y\:=\:47

Rewriting the equation in the standard form

4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2

Thus,

The vertex (h, k) = (-5, 12)

Please also check the attached graph.

Therefore, the standard form of the equation for the conic section represented by x^2\:+\:10x\:+\:6y\:=\:47 is:

4\left(-\frac{3}{2}\right)\left(y-12\right)=\left(x-\left(-5\right)\right)^2

where

vertex (h, k) = (-5, 12)

You might be interested in
Which statement is true?​
love history [14]
<h2>Hello!</h2>

The answer is:

The second option,

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

<h2>Why?</h2>

Discarding each given option in order to find the correct one, we have:

<h2>First option,</h2>

\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}

The statement is false, the correct form of the statement (according to the property of roots) is:

\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}

<h2>Second option,</h2>

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

The statement is true, we can prove it by using the following properties of exponents:

(a^{b})^{c}=a^{bc}

\sqrt[n]{x^{m} }=x^{\frac{m}{n} }

We are given the expression:

(\sqrt[m]{x^{a} } )^{b}

So, applying the properties, we have:

(\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }

Hence,

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

<h2>Third option,</h2>

a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}

The statement is false, the correct form of the statement (according to the property of roots) is:

a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}

<h2>Fourth option,</h2>

\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}

The statement is false, the correct form of the statement (according to the property of roots) is:

\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }

Hence, the answer is, the statement that is true is the second statement:

(\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }

Have a nice day!

6 0
3 years ago
The ratio of red pens to blue pens in a package is 2:5. If there are 35 ​blue ​pens in the package, how many ​red ​pens are in t
prisoha [69]

Answer:

10 red pens

Step-by-step explanation:

6 0
3 years ago
Thomas has four jugs of different sizes. One holds 1.2 liters, one
dimulka [17.4K]
I don’t know how to do these
7 0
3 years ago
What is the exact value of BC?<br>A. 3.16<br>B. 5\|2<br>C. 7.07<br>D. 25<br>​
Natalija [7]

Answer:

C. \:  \:  7.07

Step-by-step explanation:

Coordinates of B are

(5,5)

Coordinates of C are

(4, - 2)

Distance between two points

\sqrt{({x_2 - x _1 {)}^{2} + (y_2 - y_1 {)}^{2} }}

Distance of BC

\sqrt{(4 - 5) {}^{2} + (  - 2   - 5 {)}^{2}  }

\sqrt{ { (- 1}^{2})  +  ({ - 7}^{2}) }

\sqrt{1 +49 }

\sqrt{50}

7.07

3 0
2 years ago
The product of 9 and the quantity 5 more than a number t is less than 5
Lelechka [254]
9(t+5) \ \textless \  5\ \ \ |use\ distributive\ property:a(b+c)=ab+ac\\\\(9)(t)+(9)(5) \ \textless \  5\\\\9t+45 \ \textless \  5\ \ \ |subtract\ 45\ from\ bot\ sides\\\\9t \ \textless \  -40\ \ \ \ |divide\ both\ sides\ by\ 9\\\\\huge\boxed{t \ \textless \  -\dfrac{40}{9}\to t \ \textless \  -4\dfrac{4}{9}}
3 0
3 years ago
Other questions:
  • Find the volume of the cylinder.<br> Either enter an exact answer in terms of π or use 3.14
    13·2 answers
  • What is slope of the libe
    8·1 answer
  • Jacob bought some tickets to see his favorite singer he bought some adult tickets and some children tickets for a total of 9 tic
    13·1 answer
  • Write the equation of a line that is perpendicular to y = 5 y=5y, equals, 5 and that passes through the point ( − 7 , − 5 ) (−7,
    9·2 answers
  • Please solve the attached problem and chose from the answers below.
    11·2 answers
  • A bag of marbles contains 3 red marbles, 4 blue marbles, and 6 green marbles. If two are pulled out without replacement, find th
    15·1 answer
  • (08.01)Jenni is surveying shoppers about their use of the new customer service center in a store. Which question in her survey i
    10·1 answer
  • What is 3 numbers between 2.15 and 2.17
    12·1 answer
  • ∞ IS IT AN EVEN or odd
    5·1 answer
  • 5X-20 =18O what is x?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!