Find the center, vertices, and foci of the ellipse with the given equation. (x+4)2/400 + (y+3)2/144 = 1

Answers

Answer 1

[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{(x+4)^2}{400}~~ + ~~\cfrac{(y+3)^2}{144}~~ = ~~1\implies \cfrac{[x-(-4)]^2}{20^2}~~ + ~~\cfrac{[y-(-3)]^2}{12^2}~~ = ~~1 \\\\\\ \begin{cases} h=-4\\ k=-3\\ a=20\\ b=12 \end{cases}\qquad \qquad c=\sqrt{20^2-12^2}\implies c=\sqrt{256}\implies \boxed{c=16} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{center}{(-4,-3)}\qquad vertices \begin{cases} (\stackrel{-4-20}{-24}~~,~~-3)\\\\ (\stackrel{-4+20}{16}~~,~~-3) \end{cases}\qquad foci \begin{cases} (\stackrel{-4-16}{-20}~~,~~-3)\\\\ (\stackrel{-4+16}{12}~~,~~-3) \end{cases}[/tex]


Related Questions

A company logo is made up of a square and two identical triangles, as shown in this image.

What is the area of the logo?

Enter your answer in the box.

cm2

Square with side length of 9 cm. The top and bottom sides of the square form the base of a triangle with a height of 6 cm.

Answers

The area of the company's logo is  135 square cm

Area of composite figure

Composite figures are figures that are made up of two or more shapes

The area of the given logo = Area of square + Area of 2 triangles

A = l² + bh

A = 9² + (9)(6)

A = 81 + 54

A = 135 square cm

Hence the area of the company's logo is  135 square cm

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Find the volume of the cone in terms of pi.
A) 324π cm^3
B) 405π cm^3
C) 72π cm^3​

Answers

Answer:

A. 324π cm^3

Step-by-step explanation:

I took the test and go it right.

Answer:

A. 324π cm^3

Step-by-step explanation:

took test

The clown at the birthday party made balloon animals for 8 children. Each animal used 4 balloons. The clown still has 24 balloons left. How many balloons did the clown start with?

Answers

Answer: 8

Step-by-step explanation:


4x8 gives you 32

Then you subtract:
32-24 =8

Which angles are adjacent to each other? Select all that apply. ​

Answers

dhc and chf
because adjacent means a pair of angles formed on the same side of a straight line when intersected by another line

Select the correct
function
that represents
this data.

Answers

Answer:

f(x) = -5x - 2

Step-by-step explanation:

Plug in the first set of values into each possible equation. Whichever equation yields the correct ouputs (y-values) for ALL input (x-values) is the correct answer. For the function f(x) = -5x - 2,  f(-2) = 8, f(-1) = 3 and so on... So f(x) = -5x - 2 is the correct answer!

Hope this helps!

Find the domain and range of the graph below.

Answers

Answer:

8

Step-by-step explanation:

the answer is 8 because the answer is 8

What is the minimum number of classes a customer can take for Rebekah to meet her goal?

Answers

Answer:

6

Step-by-step explanation:

Use the information to find and compare Δy and dy. (Round your answers to three decimal places. )
y = 0. 8x5 x = 1 Δx = dx = 0. 1
Δy = dy =

Answers

The computation shows that the values of Δy and dy will be 0.572 and 0.4 respectively.

How to compute the values?

The value of Δy will be computed thus:

Δy = y(x + Δx) - y(x)

= y(1.1) - y(1)

= 0.5(1.1)⁸ - 0.5(1)⁸

= 0.572

The value of dy will be:

= y'(x)dx

= (0.5)⁸ × x⁷(0.1)

= 0.4 (1)⁷

= 0.4

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Help please ASAP this is confusing first correct answer gets brainleist ​

Answers

8cm

First we need to look at the side opposite to the missing side

which it is 12cm

now we can see that on the missing side 4cm is right below it

so we do

12cm-4cm

this gives you

8cm

a) 12-4=8

b) 5+4+4+12+9=34

The perimeter is 34cm and the missing length is 8cm.

Or it could be 38 since this unknown length was determined.

Find each lettered angle measure A through H

(20 points)

Answers

The angles of the triangle can be found using angle on a straight line theorem, isosceles triangle theorem, sum of angles in a triangle, sum of angles in a quadrilateral, vertical angle theorem etc.

Angles in a triangle

The sum of angles in a triangle is equals to 180 degrees. Therefore, let's find the angles in the triangle

2a = 180 - 58(base angles of isosceles triangle)

a = 122 / 2

a = 61°

b = 180 - (180 - 90 - 40) = 130° (angle on a striaght line)

c = 130° (Known angles)

d = 180 - 33 - 88 = 59°(sum of angles in a triangle)

e = 180 - 69 = 111° (external triangle theroem)

f = 86° (vertically opposite angles)

g = 83° (vertically opposite angles)

h = 180 - 36 = 144° (sum of angles on a straight line)

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b.Mogan is playing mini goll. She has a mean of 7 shots after 3 holes. If after 4 holes, she has a mean
6 shots, how many times did she shoot on the 4th hole?

Answers

Answer:

45

Step-by-step explanation:

7x3=21

6x4=24

21+24=45

Factor x3 – 4x2 7x – 28 by grouping. what is the resulting expression? (x2 – 4)(x 7) (x2 4)(x – 7) (x2 – 7)(x 4) (x2 7)(x – 4)

Answers

An expression has numbers, variables, and mathematical operations. The factors of the expression x³-4x²+7x-28 are (x²+7)(x-4).

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The factors of the expression x³-4x²+7x-28 can be written as,

[tex]x^3-4x^2+7x-28\\[/tex]

Take x² as the common factor from the first two terms while 7 as the common factor from the last two terms.

[tex]x^3-4x^2+7x-28\\\\=x^2(x-4)+7(x-4)\\\\=(x^2+7)(x-4)[/tex]

Hence, the factors of the expression x³-4x²+7x-28 are (x²+7)(x-4).

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Gary, the technology coordinator of a high school, is planning to

purchase one memory stick for each of the teachers. There are 86

teachers at the school. The English teachers requested memory sticks

that have a capacity of 32 gigabytes. Gary determines that $600 is the

maximum amount that can be spent for all of the memory sticks. Gary

finds the following prices for the purchases from Computer City.

Option

Memory Stick

Capacity

Cost Each

A

16 gigabyte

$5. 99

B

32 gigabyte

$9. 99

Free shipping for any order $35 or more.

1

If a represents the number of 16-gigabyte memory sticks

and b represents the number of 32-gigabyte memory sticks,

which equation represents the number of each kind of

memory stick that should be purchased for the teachers?

A a + b = 86

C 16a + 32b = 86

B a + b = 600

D 16a + 32b = 600

Answers

Answer:

D

Step-by-step explanation:

Some please help me bruuh

Answers

Answer:

[tex]m\angle QPO + (2x+16)^\circ = 180^\circ[/tex]

Step-by-step explanation:

In a cyclic quadrilateral, opposite angles add up to 180 degrees. Therefore, our answer would be the third answer, [tex]m\angle QPO + (2x+16)^\circ = 180^\circ[/tex], where QPO and QRO are opposite of each other.

Draw the image of \triangle ABC△ABCtriangle, A, B, C under a dilation whose center is PPP and scale factor is \dfrac{1}{3} 3 1 ​ start fraction, 1, divided by, 3, end fraction.

Answers

Dilating the triangle ABC would create another triangle whose size is different from the triangle ABC

How to dilate the triangle?

From the complete question, we have the following coordinates:

Point A = (-4,5)Point B = (7,-7)Point C = (-2,2)Point P = (1,-4)Scale factor, k = 1/3

The dilation rule across the center P is:

(x, y) --> (1/3x – 1, 1/3y + 4)

So, the coordinates of the image of the triangle are:

A' =  (-1/3 * 4 – 1, 1/3 * 5 + 4)

A' =  (-7/3, 17/3)

B' =  (1/3 * 7 – 1, -1/3 * 7 + 4)

B' =  (4/3, 5/3)

C' =  (-1/3 * 2 – 1, 1/3 * 2 + 4)

C' =  (-5/3, 14/3)

From the above computation, the coordinates of the new triangle is:

A' =  (-7/3, 17/3)

B' =  (4/3, 5/3)

C' =  (-5/3, 14/3)

See attachment for the image of triangle ABC

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What is the absolute value of -7
Will mark brainlyest!!

Answers

Answer: 7

Step-by-step explanation:

The absolute value of -7 is 7 because to find the absolute value you take away the sign.

A rectangle measures 2
1
4
meters by 1
7
8
meters. What is its area?

Answers

Answer:

77/18 or 4 5/18

Step-by-step explanation:

Convert 2 1/3 and 1 5/6 into improper fractions then multiply:

7         11      77        5

--  x     --  =   --  = 4  --

3          6      18       18

Hopes this helps :)

What’s The Answer Of This? PLEASE HELP

Answers

Answer:

80.

Step-by-step explanation:

Angles of a triangle add up to 180. 180-80-20 is 80.

Isaiah buys a hat that normally costs $17.There is a sale for 15% off. How much
does he pay for the hat?
+

Answers

Answer:

$14.45

Step-by-step explanation:

15% of 17 is 2.55. 17 - 2.55 is 14.45

a father is 20 years older than his son 5 years ago he was 3 times as old as his son.find their prasent age​

Answers

Present ages: son 15, father 35.5
5 years ago : son 10, father 30

Answer:

Son -- 10

Dad -- 30

Step-by-step explanation:

5  years ago the dad was 15 years older than his son.15 / 3 = 5. The son was 5 five years ago he would be 10 now because 5 years ago he was 5. Since the son is 10 the dad must be 30. I know this because the dad is 20 years older than his son.

I need help asap!!!!!!

Answers

Answer:

The Answer is C: [tex]y > x, y < 4[/tex]

Step-by-step explanation:

By looking at the graph the shaded area is the inequalities that you need to find.

[tex]y=4[/tex] is the lines on the y-axis. Below the y-axis is shaded [tex]y < 4[/tex].

From the [tex]y=x[/tex] is a linear line. Above the linear line is [tex]y > x[/tex]

5. Find the equation of the line that goes through the point (2.-3) and has a slope of -1.
y = -x-1
y = -x-3
y=2x-3
y=-x+2

6. Find the equation of the line that goes through the point (5.1) and has a slope of 0.
y = 5x + 1
y=5
y=1
x=5

Answers

Answer:Option AOption CSolution:First, let's write the equation of the line in point-slope form:y-y1=m(x-x1)y-(-3)=-1(x-2)y+3=-(x-2)y+3=-x+2y=-x=2-3y=-x-1Same with the next equation:y-1=0(x-5)y-1=0x-0y=1

Hope it helps.

Do comment if you have any query.

Answer:

A and C.

Step-by-step explanation:

The original price of a shirt is $16. 0. The price of the shirt is discounted by 20%, then a 4% sales tax is added. What is the

final price of the shirt after the discount is taken off and the sales tax is added?

NO LINKS!!!!

Answers

Answer: 13.312

Step-by-step explanation:

16 x 0.20 = 12.80

4% = 0.512

12.8 + 0.512 = 13.312

The Price of the shirt is now $13.312 .

Hope this helps answering your question !

how to find the axis of symmetry if the parabola doesn't cross the y axis
please i need help

Answers

Step-by-step explanation:

a parabolic graph is given by the equation ax^2 + bx + c

the axis of symmetry is equal to -b/(2a)

however it is worth noting that all parabolas have a y intercept since their domain is all real numbers.

make sure to inform me if you need further guidance.

What is the perimeter of the rectangle shown below? width 9 inches and length 13 inches

Answers

Answer:

44

Step-by-step explanation:

the formula for finding the perimeter of a rectangle is p=2(l+w)

if school starts at 8:15 am and ends at 3:31 pm when how long is the school day

Answers

Answer:

7hours and 16 minutes

Step-by-step explanation:

8:15-9:15 is one hour. 9:15-10:15 is two hours. 10:15-11:15 is three hours.11:15-12:15 is four hours. 12:15-1:15 is five hours. 1:15-2:15 is six hours. 2:15-3:15 is seven hours. 3:15-3:31 is 16 minutes.

The answer is 7 hours 16 minutes

HELP ME i think i get the idea but i need further evaluation.

Answers

Answer:

x = 4.28

Step-by-step explanation:

[tex]Given,\ To\ find\ for\ x,[/tex]

[tex]Let\ c\ be\ the\ centre\ of[/tex]

[tex]Circle,\ where[/tex][tex]AD=22.4\ (Diameter)[/tex]

[tex]AC=\frac{22.4}{2}=11.2\ (radius)[/tex]

[tex]AB=8.8[/tex]

[tex]In\ \Delta\ ABC, Right\ angled\ at[/tex]

[tex]B.\ USing Pythagoras\ theovem[/tex]

[tex](AB)^2+(BC)^2=(AC)^2[/tex]

[tex](8.8)^2+(BC)^2=(11,2)^2[/tex]

[tex](BC)^2=125.44-77.44=48[/tex]

[tex]BC=\sqrt{48}=6.92[/tex]

[tex]E_c=x+y\ \ \ \ \(Where\ Fc\ is\ also\ radius\ of\ arcle[/tex]

[tex]\therefore\ \ \ \ \11.2=x+6.92[/tex]

[tex]x=11.2-6.92=4.28[/tex]

[tex]Hence,\ x=4.28\ is\ the\ answer.[/tex]

I hope this helps you

:)

In one particular suburb, there are 18 families that own a pug. If there are a total of 24 families that own a dog in general, then what percentage of dog owners have a pug? Round your answer to the nearest whole number if necessary.​

Answers

Answer:

75% of people own a dog.

Step-by-step explanation:

We apply the percentage formula in this problem

Total People * X/100 = Groups of people

Fill in the values

24 * X/100 = 18

We now Simplify the equation.

After simplifying you should get X=75, meaning 75% of people own a dog.

75% of people own a dog

How many times can 3 go into 35

Answers

Answer: 11 times is the awnser

Step-by-step explanation:

Find the sum of the first 8 terms of the following series, to the nearest integer.
144, 36,9, ...

Answers

answer:

192

(the pattern is dividing each number by 4, if you need it)

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