Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of the minor axis: (1, 7), (7, 7)

Answers

Answer 1

Answer:

The standard form of the ellipse is [tex]\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1[/tex].

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

[tex](h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)[/tex] (1)

If we know that [tex]V_{1} (x,y) = (4,0)[/tex] and [tex]V_{2}(x,y) = (4, 14)[/tex], then the coordinates of the center are, respectively:

[tex](h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)[/tex]

[tex](h,k) = (2,0) + (2, 7)[/tex]

[tex](h, k) = (4, 7)[/tex]

The length of each semiaxis is, respectively:

[tex]a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}[/tex]

[tex]a = 3[/tex]

[tex]b = \sqrt{(4-4)^{2}+(0-7)^{2}}[/tex]

[tex]b = 7[/tex]

The standard equation of the ellipse is described by the following formula:

[tex]\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1[/tex]

Where:

[tex]h[/tex], [tex]k[/tex] - Coordinates of the center of the ellipse.

[tex]a[/tex], [tex]b[/tex] - Length of the orthogonal semiaxes.

If we know that [tex]h = 4[/tex], [tex]k = 7[/tex], [tex]a = 3[/tex] and [tex]b = 7[/tex], then the standard form of the ellipse is:

[tex]\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1[/tex]


Related Questions

a bookstore sells 9 books for $90. Which table represents the relationship between number of books and the total price?​

Answers

Answer:

   

Step-by-step explanation:

Answer:

Table B

first find cost of 1 book

cost of 1 book=$90/9

=$10

now cost cost of 10 books

cost of 11 books=$10*10

=$100

cost of 11 book =$10*11

=$110

Step-by-step explanation:

since the cost of 10 and 11 books match in  table B ,it is the correct answer

(Please answer) Octavia is going to buy milkshakes for her friends. Small milkshakes cost $2.50 and large milkshakes cost $6.00. She needs to buy at least 20 milkshakes and she can spend no more than $90. How many small milkshakes Octavia should buy to serve her friends but stay on budget?
Octavia should buy less than 8 milkshakes.


Octavia should buy at least 8 small milkshakes.


Octavia should buy less than 12 milkshakes.


Octavia should buy at least 12 small milkshakes.

Answers

Answer:

Step-by-step explanation:

In this scenario, Octavia should buy at least 12 small milkshakes. At $2.50 each small milkshake, buying 12 would be a total of $30. Since she needs to buy atleast 20 total milkshakes, she would need to buy 8 large milkshakes which at $6 each would cost her a total of $48. Together this would sum up to be $78 for the 20 milkshakes which would mean that Octavia is still under her budget.

What is the next term in the geometric sequence below?
3, -6, 12, -24, _, ...
A. 48
B. -48
C. -36
D. 36

Answers

The answer to your question is 36

Answer:

a. 48

Step-by-step explanation:

first of all find the num that can divide through equally

for ex. 3 x -2 = -6

-6×-2=12

12×-2=-24

-24×-2=48

therefore the num divisible is -2

what's the answer for this question​

Answers

Answer:

B(3/4*1/2)

Step-by-step explanation:

So lets see, we have:

3/4 divded by 2

Any whole number, such as 2, will have a denominator like this:

2/1

So we can rewrite this as:

3/4 divided by 2/1

Now, we can actually rewrite this division as multipication. To do this, you must flip the dividing fraction, which was 2/1.

So now it is 1.2:

3/4*1/2

Looking at the anwers, this should be the seocnd one down.

Hope this helps!

Meh need help, Im so confued

Answers

The answer is #2 (3/6 = 4/8) because both are equal to 1/2 therefore they are equal to each other. Hope this helps!

Answer:

3/6=4/8

Step-by-step explanation:

2/6=3/8

2*4 6*4=8/24

3*3 8*3=9/24

2/6 does not equal 3/8

3/6=4/8

3*4 6*4= 12/24

4*3 8*3=12/24

3/6=4/8 is true

WILL GIVE U BRAINLIEST!!!
What is an alternate exterior angle to angle 2?
A. 7
B. 6
C. 5
D. 4

Answers

Answer:

A. 7

Step-by-step explanation:

Alternate exterior angles are formed when we have two parallel lines that are intercepted by a transversal line in such a way that the exterior angles formed is outside the two parallel lines and they alternate each other along the transversal line.

Thus,

Angle 2 is an exterior angle along the transversal line and alternates angle 7, which is another exterior angle.

Therefore, an alternate exterior angle to angle 2 is angle 7.

A fair coin is flipped three times. Events A and B are defined as: A: there are at least two consecutive heads somewhere in the sequence B: at least one flip comes up tails What is p(A | B)?

Answers

Answer:

2 / 7

Step-by-step explanation:

Coin flipped 3 times has following outcomes, of heads 'H' & Tails 'T'

HHH , TTT , HTT, THT , TTH , THH , HTH , HHT  = total outcomes

P (A) = 2 consecutive heads , P (B) = atleast one tail

P (A) = 2 outcomes ( HHH , HHT , THH ) / total 8 outcomes = 3 / 8

P (B) = 7 outcomes (all except HHH) / total 8 outcomes = 7 / 8

P (A | B) = P ( A ∩ B ) / P (B)

P ( A ∩ B ) = P ( 2 consecutive heads & atleast one tail) / Total outcomes =   2 outcomes ( HHT , THH ) / total 8 outcomes = 2 / 8

So, P (A | B) = ( 2 / 8 ) /  ( 7 / 8 ) = 2 / 7

Find f(3) please. I need help. Thank you

Answers

Answer:

f(3) = -4

Step-by-step explanation:

3 is between 2 and 5 so we use the second piece of the function

f(3) = -4

Answer: f = 0

Step-by-step explanation:

f(3) = 0

f•(3) = 0

3f = 0

f = 0

WILL GIVE U BRAINLIEST
What is the value of X by CPCTC?
A. 11
B. 8
C. 3
D. 7
E. Not enough info

Answers

The value of x by CPCTC is 3.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

We need to find the value of x.

CPCT theorem states that if two or more triangles which are congruent to each other are taken then the corresponding angles and the sides of the triangles are also congruent to each other.

The side x is congruent to the quadrilateral having length 3.

the value of x is 3

Hence, the value of x by CPCTC is 3.

To learn more on Triangles click:

https://brainly.com/question/2773823

#SPJ1

No links!!! A student population in a school was 972. Next year they are projected to have a 25% increase in student population. How many students will they have next year?

Answers

Answer:

1215

Step-by-step explanation:

If you have a 25% or 1/4 increase, this would mean that you divided the total number of students and add the quotient to the main thing.

So: 972 divided by 1/4 = 972/4 = 243.

972 + 243 = 1215.

Answer:

1215 Students

Step-by-step explanation:

25% is equal to 1/4 correct? (It is :D) So divide 972/4 to know what 25% of the school's population is. 972/4 = 243. So then 243 is 25% of the students. To get the 25% increase add 972 (for the students that will be back next year) and 243 (for the new students). I may have explained this in a really detailed way but it isn't that hard when you think about it!

1. 972/4 (to find 25%)

2. 25% = 243

3. 974 + 243 (old + new)

4. 1215 Students

A man bought a house for 3600 Naira he repairs the house with 150 Naira if he sold the house for 4950 Naira . Find his percentage profit

Answers

Step-by-step explanation:

profit%=

[tex] \frac{selling \: price - cost \: price}{cost \: price} \times 100\%[/tex]

[tex] \frac{4950 \: naira - 3600 \: naira + 150 \: naira}{3750 \: naira} \times 100\%[/tex]

[tex] \frac{4950 - 3750}{3750} \times 100\%[/tex]

[tex] \frac{1200}{3750} \times 100\%[/tex]

=36%

pls help ASAP!! person who gives correct answer will be marked brainliest

Answers

Answer:

w+76=180(being supplementary angle)

w=180-76

w=104

please help me i’m like so over this.

Answers

We need a clear picture

Plz help me well mark brainliest if correct

Answers

all of the above which is e

all of the above is the correct answer i believe

Please help me! I will give branliest if it’s correct :)

Answers

Answer:

the answer is in the picture

Answer:

[tex]\frac{z^{2} }{25}[/tex]

Step-by-step explanation:

In order to write the expression in the form of [tex]\frac{z^{2} }{k}[/tex] we simply have to open up the brackets. We do that the following way...

[tex](\frac{z}{5} )^{2} =( \frac{z}{5} )( \frac{z}{5}) = \frac{z^{2} }{25}[/tex]

someone tell me 1+1= 11 and not 2 - -

Answers

⇛ ANSWER ⇚

Conventional - 1+1=2 ( sometimes )Binary 1+1=10 There is no 2 in binary Boolean logic 1 And 1 = 1 This means True and True is True ( see below ) ⟱Roman and egyptian 1 + 1 = 11 In unary number systems , two is represented by the symbol for one twice

HOPE U understood!!!!!(:

Please help me I am super confused I would really appreciate it ♥️♥️

Answers

the answer is f(x)=710x4^t

what are adjacent angles​

Answers

Answer:

Two angles having the same vertex and having a common side between them.

Which point is the image of point R(4, -7) first reflected across the x-axis and then across the y-axis?

Answers

Answer:

(-4, 7)

Step-by-step explanation:

It would be the exact opposite of point R because it was rotated about 180 degrees from it's original location

I’m kinda stuck on this question, can y’all please help me?

Answers

Points J, K and M form a triangle.

In this triangle you are given the angles for JKM (50) and KJM (60)

The 3 inside angles of a triangle need to equal 180.

The third angle JMK would be 180 minus the two given angles:

JMK = 180 - 50 - 60 = 70

JMK = 70 degrees

PLEASE HELP
Find the measure of angle.

Answers

Answer:

39

Step-by-step explanation:

180-73-68

Can someone give me the answer to this plz

Answers

Answer:

X>Dy+c

Step-by-step explanation:

I did this question before

I need help asap. Evaluate Expressions

Answers

Answer:

1:

p-r/6=-6-(-6)/6=-6+1=-5

2:

p-(m-n)= -1-(-4-4)=-1-(-8)=-1+8=7

3:

(z+y)/2)3=(-5-4)/3=-9/3=-3

4:

m/6-n=6/6-6=1-6=-5

5:

k³-h=3³-(-2)=27+2=29

6:

p-(p-(m-3))=5-(5-(4-3))=5-(5-1)=5-4=1

7:

(k)(k-j)+3=(5)(5-5)+3=5*0+3=3

8.

p²/6-q=6²/6-4=6-4=2

9;

zx+3³=6*4+3³=24+27=51.

10:

y+z-(y-x)=5+4-(5-2)=9-3=6

Some basic rules:

+. +. +=+

+. * +=+

+. ÷ +=+

+. - +=+

and

+. +. -=add and put sigh of greater one.

-. * +=-sigh

-÷-=+sigh

- - -=add and put - sigh

-7= y/7? Solve the Equation.

Answers

y = -49

multiply 7 on both sides

-7*7 = y/7*7

-49 = y

Answer:

y = -49

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

-7 = y/7

Step 2: Solve for y

[Multiplication Property of Equality] Multiply 7 on both sides:                      -49 = yRewrite:                                                                                                             y = -49

Which matrix equation can be used to solve the system?
(2x+ 5y = 15
X + 3y = 18

Answers

THE CORRECT OPTION IS A where the input data is correct

Answer:

option 3

Step-by-step explanation:

[tex]AX = B\\X = A^{-1}B\\\\A = \left[\begin{array}{CC}\\2&5\\1&3\end{array}\right]\\\\\\B =\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\X =\left[\begin{array}{C}\\x&y\end{array}\right][/tex]

[tex]det A = 1\\\\adj A = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right][/tex]

[tex]A^{-1} = \frac{1}{det A} \times Adj A[/tex]

      [tex]= 1 \times \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\\\\\\= \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right][/tex]

Therefore,

      [tex]X = A^{-1}B\\\\\\\left[\begin{array}{C}\\x&y\end{array}\right] = \left[\begin{array}{CC}\\3&-5\\-1&2\end{array}\right]\left[\begin{array}{C}\\15&18\end{array}\right]\\\\\\[/tex]

At a carnival entrance, tickets are assigned seven-digit numbers using the digits 0-5. If one ticket number is chosen randomly for a prize, what is the probability that every number on the ticket is even

Answers

Answer:

"0.0041" is the right answer.

Step-by-step explanation:

According to the question,

The total possible number of tickets will be:

= [tex]6^5[/tex]

= [tex]7776[/tex]

here,

The total even numbers are:

= [tex]2[/tex]

i.e., (2, 4)

now,

With even numbers, the total number of tickets are:

= [tex]2^5[/tex]

= [tex]32[/tex]

hence,

The probability will be:

= [tex]\frac{32}{7776}[/tex]

= [tex]0.0041[/tex]

The probability is the ratio of the favorable event to the total number of events. Then the probability is 0.0041.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. I

At a carnival entrance, tickets are assigned seven-digit numbers using the digits 0-5.

If one ticket number is chosen randomly for a prize.

Then the probability that every number on the ticket is even will be

The total possible number of tickets will be

⇒ 6⁵ = 7776

The total even numbers will be

⇒ 2 {2, 4}

With even numbers, the total number of tickets will be

⇒ 2⁵ = 32

Then the probability will be

[tex]\rm P = \dfrac{32}{7776}\\\\P= 0.0041[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Find the integration of (1-cos2x)/(1+cos2x)

Answers

Given:

The expression is:

[tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex]

To find:

The integration of the given expression.

Solution:

We need to find the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex].

Let us consider,

[tex]I=\int \dfrac{1-\cos 2x}{1+\cos 2x}dx[/tex]

[tex]I=\int \dfrac{2\sin^2x}{2\cos^2x}dx[/tex]         [tex][\because 1+\cos 2x=2\cos^2x,1-\cos 2x=2\sin^2x][/tex]

[tex]I=\int \dfrac{\sin^2x}{\cos^2x}dx[/tex]

[tex]I=\int \tan^2xdx[/tex]                      [tex]\left[\because \tan \theta =\dfrac{\sin \theta}{\cos \theta}\right][/tex]

It can be written as:

[tex]I=\int (\sec^2x-1)dx[/tex]             [tex][\because 1+\tan^2 \theta =\sec^2 \theta][/tex]

[tex]I=\int \sec^2xdx-\int 1dx[/tex]

[tex]I=\tan x-x+C[/tex]

Therefore, the integration of [tex]\dfrac{1-\cos 2x}{1+\cos 2x}[/tex] is [tex]I=\tan x-x+C[/tex].

Please help I will give brainliest!!!!!

Answers

Answer:

Step-by-step explanation:

[tex]sin^2\theta+cos^2\theta=1~=>sin\theta=\pm\sqrt{1-cos^2\theta}\\\\cos\theta=\frac{\sqrt{2}}{2}[/tex]

we'll took the negative solucion of sin because sin is negative in IV cuadrant

[tex]sin\theta=-\sqrt{1-(\frac{\sqrt{2}}{2})^2}=-\frac{1}{\sqrt{2}}=-\frac{\sqrt{2}}{2}[/tex]

[tex]tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]  => [tex]tan\theta=-1[/tex]

so, the right option is the last one

Melanie moved to Denver on October 13 and returned home for a visit fourteen months later. When did she return home?

Answers

Answer:

She arrived home in December

Step-by-step explanation:

Add 14 months to October

Answer:

she returned home in December just add 14 months to October

In a survey conducted at a pet store, 150 customers were asked if they owned
birds or fish. The survey data are shown in the relative frequency table.
What percentage of the people surveyed own fish?
A. 10%
B. 6%
C. 4%
D. 0.1%

Answers

Answer: the answer should be 10%

Step-by-step explanation:

Answer:

10% is correct!

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