Richard has 5 markers in a backpack. One of them is black and one is red. Find the probability Richard will reach into the backpack without looking and grab the black marker and then reach in a second time and grab the red marker. Express your answer as a fraction in simplest form.

The standard form of the equation of the hyperbola:

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:

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:

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

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.

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Answer:

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

Step-by-step explanation:

Plato

Answer:

To find the composite function (f ◦ g)(x), we need to substitute g(x) into f(x) and simplify.

Given:

f(x) = x

g(x) = -2x + 3

To find (f ◦ g)(x), we substitute g(x) into f(x):

(f ◦ g)(x) = f(g(x))

Substituting g(x) into f(x), we get:

(f ◦ g)(x) = f(-2x + 3)

Since f(x) = x, we replace f(-2x + 3) with (-2x + 3):

(f ◦ g)(x) = -2x + 3

Therefore, the composite function (f ◦ g)(x) is -2x + 3.

Answer:

y=3/2

Step-by-step explanation:

This line's slope is perpendicular to -2/3 and its y intercept is 0.