All categories

2 years ago

Write 9x² - 36x = 4y² + 24y + 36 in standard form

Mathematics

1 answer:

Kisachek [45]2 years ago

5 0

Answer:

9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;

(x - 2)²/2² - (y + 3)²/3² = 1

Step-by-step explanation:

The standard form of a hyperbola is given as follows;

(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1

The given equation is presented as follows;

9·x² - 36·x = 4·y² + 24·y + 36

By completing the square, we get;

(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)

(3·x - 6)² - 36 = (2·y + 6)²

(3·x - 6)² - (2·y + 6)² = 36

(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1

(3·x - 6)²/6² - (2·y + 6)²/6² = 1

3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1

(x - 2)²/2² - (y + 3)²/3² = 1

The equation of the hyperbola is (x - 2)²/2² - (y + 3)²/3² = 1.

You might be interested in

Convert from $0.20 dollars to cents

Arada [10]

Since 100 cents = $1

Then to convert $20 to cents, all you have to do is multiply.

$20 × 100 cents

<em><u>=2000 cents. </u></em>

More examples to try:

Convert $0.10 dollars to cents.

$10 × 100 cents = 1000 cents.

Here is a guild for next time:

100 cents = $1
200 cents = $2
300 cents = $3
400 cents = $4
___ cents = $__

So.....now you can fill in the blanks by yourself. Tell me the answer if possible! :D

~Hope this helped!~

8 0

3 years ago

If using the method of completing the square to solve the quadratic equation x2 + 3x - 17 = 0, which number would have to be add

MatroZZZ [7]

Answer:

Step-by-step explanation:

To solve using completing square, we need to write the equation as x2+3x=17.

The next step is to add a number such that the square can be completed. The number must be equal to (b/2a)^2, so here it will be (3/2)^2 = 9/4

The equation then becomes x2+3x+(9/4)=17+(9/4).

Solving it further will get you the final answer

8 0

2 years ago

Juan bought 4 pounds of chocolate

Andru [333]

Answer:

Step-by-step explanation:

This is a system of equations. The 2 equations are:

4c + 2p = 16

2c + 3p = 12

Let's get rid of the p's first. Do this by multiplying the first equation by -3 and the second equation by 2 to get a new system that looks like this:

-12x - 6p = -48

4c + 6p = 24

Now add to get

-8c = -24 and

c = 3

That means that chocolate is $3 per pound. Now sub that back in to either one of the original equations to get the price for peanuts:

4(3) + 2p = 16 and

12 + 2p = 16 and

2p = 4 so

p = 2

The price for peanuts is $2 per pound.

6 0

3 years ago

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $4$ times as much

oksano4ka [1.4K]

Answer: 31 : 9

Step-by-step explanation:

Assume the following:

Alice's amount = P

Bob's amount = Q

Amount received = n

If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.

P + n = 4(Q - n)

P + n = 4Q - 4n

P = 4Q - 4n - n

P = 4Q - 5n - - - - (1)

If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob

P - n = 3(Q + n)

P - n = 3Q + 3n

P = 3Q + 3n + n

P = 3Q + 4n - - - - - - (2)

Equating both equations - (1) and (2)

4Q - 5n = 3Q + 4n

4Q - 3Q = 4n + 5n

Q = 9n

Express P in terms of n, use either equation (1) or (2)

From equation 2:

P = 3Q + 4n

Substituting Q = 9n

P = 3(9n) + 4n

P = 27n + 4n

P = 31n

Alice's amount = P, Bob's = Q

Ratio = P:Q

31 : 9

5 0

3 years ago

Write 64 in expanded from

lozanna [386]

Um im guessing 60 +4 or sixty four

3 0

3 years ago