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lesantik [10]
3 years ago
10

Knowledge, intensify, skills and grow net work​

Mathematics
2 answers:
aleksley [76]3 years ago
5 0

Answer:Active listening

Step-by-step explanati

frosja888 [35]3 years ago
4 0

Answer:

u nice keep goin.

sry lol

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What is the coordinates of the center of an ellipse defined by the equation 16x^2 + 25y^2 + 160x - 200y + 400 = 0 ? Please give
pickupchik [31]

16x^2 + 25y^2 + 160x - 200y + 400 = 0     Rearrange and regroup.

(16x^2 + 160x) + (25y^2 - 200y ) = 0-400.     Group the xs together and the ys together.

16(X^2 + 10x) + 25(y^2-8y) = -400.     Factorising.

We are going to use completing the square method.

Coefficient of x in the first expression = 10.

Half of it = 1/2 * 10 = 5. (Note this value)

Square it = 5^2  = 25.     (Note this value)


Coefficient of y in the second expression = -8.

Half of it = 1/2 * -8 = -4. (Note this value)

Square it = (-4)^2  = 16. (Note this value)


We are going to carry out a manipulation of completing the square with the values

25 and 16.  By adding and substracting it.


16(X^2 + 10x) + 25(y^2-8y) = -400

16(X^2 + 10x + 25 -25) + 25(y^2-8y + 16 -16) = -400

Note that +25 - 25 = 0.    +16 -16 = 0. So the equation is not altered.

16(X^2 + 10x + 25) -16(25) + 25(y^2-8y + 16) -25(16) = -400


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = -400 +16(25) + 25(16)    Transferring the terms -16(25) and -25(16)

to other side of equation.  And 16*25 = 400


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = 25(16)


16(X^2 + 10x + 25) + 25(y^2-8y + 16)  = 400

We now complete the square by using the value when coefficient was halved.


16(x-5)^2 + 25(y-4)^2  = 400

Divide both sides of the equation by 400


(16(x-5)^2)/400 + (25(y-4)^2)/400  = 400/400              Note also that, 16*25 = 400.


((x-5)^2)/25 + ((y-4)^2)/16  = 1

((x-5)^2)/(5^2) + ((y-4)^2)/(4^2)  = 1


Comparing to the general format of an ellipse.

((x-h)^2)/(a^2) + ((y-k)^2)/(b^2)  = 1


Coordinates of the center = (h,k).

Comparing   with above   (x-5) = (x - h) , h = 5.

Comparing   with above   (y-k) = (y - k) , k = 4.

Therefore center = (h,k) = (5,4).

Sorry the answer came a little late.  Cheers.

3 0
3 years ago
A book contains 120 pages and each page 35 lines how many pages will the book contains if every page has 24 lines
hichkok12 [17]

Answer:

If there will be 24 lines on all pages, there will be 175 pages in the book

Step-by-step explanation:

First we have to find out how much lines does the book have in total, so we multiply the number of pages by the number of lines on the page. So we get.....

120 x 35 = 4200

Now in order to find out how much pages will the book have when a page will have 14 lines we divide the number of lines by 24 and we get......

4200 / 24 = 175

7 0
3 years ago
Jacob used 1/7 of a liter of water to fill 1/9 of the fish aquarium. How many liters of water are needed to fill the aquarium?
laila [671]
Jacob used 1/7 of a liter of water.
He needs to fill 1/9 of the fish aquarium.
Find how many liters would Jacob need to fill the aquarium
=> Let x = liters of water need to fill the aquarium
=> x/1 = 1/7 divided by 1/9
=> x = 1/7 x 9/1
=> x = 9/7, since this is an improper fraction, let’s convert it to mixed fraction
=> x  = 1 and 2/7
So, Jacob need 1 and 2/7 liter of water to fill the whole aquarium.



3 0
3 years ago
What was the first inverse operation to find the answer of -4(3x -5) < 2(3x+ 4)
Dovator [93]

Answer:

First operation is Parathenses or Grouping. In this case, you need to use distrubtion to go past this operation

Step-by-step explanation:

6 0
2 years ago
Which interval notation represents the set of all numbers less than or equal to -6 or greater than or equal to -2
Alik [6]

Answer: 1≤x<12

Step-by-step explanation:

The values that are greater than or equal 1 but less than 12 are values ranging from 1 to 11 i.e {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}. Note that 1 is included because the number is greater than or equal to 1 (1 included) and less than 12(12 not included).

x≥1 and x< 12

if x≥1, it means 1≤x

combining both inequality

1≤x and x<12

1≤x<12

The interval notation that represent the set S =  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} will be given as S = {x: 1≤x<12}

5 0
3 years ago
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