Write the standard form of the equation of the hyperbola 4x2 − 9y2 − 16x − 36y − 56 = 0.

Answers

Answer 1

Answer:

The standard form of the equation of the hyperbola:

$((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1$

How did we get the values?

To write the standardform of the equation of a hyperbola, you need to rearrange the given equation into the following form:

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

Where (h, k) is the center of the hyperbola, and "a" and "b" are positive constants related to the shape and size of the hyperbola.

Start by completing the square for both the x and y terms:

1. Group the x terms and y terms separately:

4x² - 16x - 9y2 - 36y - 56 = 0

2. Complete the square for the x terms by adding and subtracting the appropriate constant inside the first bracket:

4(x² - 4x + 4) - 9y² - 36y - 56 = 0

3. Complete the square for the y terms by adding and subtracting the appropriate constant inside the second bracket:

4(x² - 4x + 4) - 9(y² + 4y + 4) - 56 + 36 = 0

4. Now, rewrite the equation and simplify:

4(x² - 4x + 4) - 9(y² + 4y + 4) - 20 = 0

5. Factor the squares:

4(x - 2)² - 9(y + 2)² - 20 = 0

6. Divide both sides by the constants to isolate the equation:

$((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1$

Now, you have the standard form of the equation of the hyperbola:

$((x - 2)^2)/(5) - ((y + 2)^2)/(20/9) = 1$

The center of the hyperbola is at (h, k) = (2, -2), "a" is the square root of 5, and "b" is the square root of 20/9.

learn more about standard form: brainly.com/question/19169731

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Answer 2

Answer:

(x-2)^2/3^2 - (y+2)^2/2^2 =1

Step-by-step explanation:

Plato

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A jar contains 4 red marbles, numbered 1 to 4, and 11 blue marbles numbered 1 to 11. A marble is chosen at random. If you're told the marble is red, what is the probability that it has the number 2 on it?

Answers

Answer:

25%

Step-by-step explanation:

So there are four marbles that are red.

It doesnt matter if we have a probability of picking blue because the question says you are picking red.

There are four possible outcomes and one favorable outcome so it is 1/4 of 25/100 or 25%

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x + 6y = 7.50 10x + 5y = 8.75

Answers

Given:
let x = apples
let y = oranges

Equation 1: 6x + 6y = 7.50
Equation 2: 10x + 5y = 8.75

Equation 1 - Equation 2
6x + 6y = 7.50
- (10x + 5y = 8.75)
-4x+ y = -1.25
y = -1.25 + 4x

6x + 6y = 7.50
6x + 6(-1.25 + 4x) = 7.50
6x - 7.50 + 24x = 7.50
30x = 7.50 + 7.50
30x = 15
x = 15/30
x = 1/2 or 0.50 cost of one apple

y = -1.25 + 4x
y = -1.25 + 4(0.50)
y = -1.25 + 2
y = 0.75 cost of one orange

6x + 6y = 7.50
6(0.50) + 6(0.75) = 7.50
3 + 4.5 = 7.50
7.50 = 7.50

10x + 5y = 8.75
10(0.5) + 5(0.75) = 8.75
5 + 3.75 = 8.75
8.75 = 8.75

Answer:

The cost of one apple would be 0.5 :)

Step-by-step explanation:

Just took the test, hope this helps :)

If the points show below are collinear, what can you conclude about the lengths AB, BC, and AC? SOMEONE PLEASE ANSWWR THIS WILL GIVE BRAINLIEST!!!!

Answers

Answer:

$\sf\nAB+BC=AC$

Explanation:

$\sf\n\textsf{This is because the lengths of line segments AB, BC and AC are the distances}\n\textsf{between the points A,B and C respectively. And since A, B and C are collinear,}\n\textsf{these distances must add up to the total distance between A and C.}$

$\textsf{Here is a simple explanation:}\n\rightarrow \textsf{Suppose you are standing at point A and you want to walk on point C. You }\n\textsf{\ \ \ \ can either walk directly to point C (along line segment AC), or you can}\n\textsf{\ \ \ \ first walk to point B and then from point B to point C (along line segments}\n\textsf{\ \ \ \ AB and BC).}$

$\rightarrow \textsf{The total distance you walk in either case is the same. So, AB+BC=AC.}$

HELP ME PLEASE!!What are the domain and range of the function f(x)=1/4(x^3+6x^2+5x-4)

choices:
domain: (-5,0)
range: (-2,0.5)

domain: (-3.5, 2.5)
range: (-0.5, -1.3)

domain: (infin., 1/4)
range: -4, infin.)

domain: (-infin., infin.)
range: (-infin., infin.)

Answers

Answer:

domain: (-infin., infin.)

range: (-infin., infin.)

Step-by-step explanation:

This is an odd degree polynomial which forms a sideways S shape starting low and ending high. Since nothing restricts the function from having an output for every real number input, the domain and range are (-infin., infin.).

Can anybody help e with this question ?? 9! - 5!

Answers

9! - 5!
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362880 - 120
362760

What is the answer for N+4=6

Answers

The answer would be n=2

6-4=2 so n must be 2

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