Molly has decided to set up a budget after

Write the equation of a hyperbola with a center at (-5, -3), vertices at (-5, -5) and (-5, -1) and co-vertices at (-11, -3) and

svet-max [94.6K]

Answer:

The equation is (y + 3)²/4 - (x + 5)²/36 = 1

Step-by-step explanation:

* Lets revise the equation of the hyperbola

- The standard form of the equation of a hyperbola with

center (h , k) and transverse axis parallel to the y-axis is

(y - k)²/a² - (x - h)²/b² = 1

# The length of the transverse axis is 2a

# The coordinates of the vertices are (h , k ± a)

# The length of the conjugate axis is 2b

# The coordinates of the co-vertices are (h ± b , k)

# The distance between the foci is 2c, where c² = a² + b²

# The coordinates of the foci are (h , k ± c)

* Lets solve the problem

∵ The center of the hyperbola is (-5 , -3)

∵ The coordinates of the its center is (h , k)

∴ h = -5 and k = -3

∵ Its vertices are (-5 , -5) and (-5 , -1)

∵ The coordinates of its vertices are (h , k + a) and (h , k - a)

∴ k + a = -5 and k - a = -1

∵ k = -3

∴ -3 + a = -5 and -3 - a = -1

∵ -3 + a = -5 ⇒ add 3 to both sides

∴ a = -2

∵ Its co-vertices are (-11 , -3) and (1 , -3)

∵ The coordinates of the co-vertices are (h + b , k) and (h - b , k)

∵ h = -5

∴ -5 + b = -11 and -5 - b = 1

∵ -5 + b = -11 ⇒ add 5 to both sides

∴ b = -6

∵ The equation of it is (y - k)²/a² - (x - h)²/b² = 1

∵ h = -5 , k = -3 , a = -2 , b = -6

∴ The equation is (y - -3)²/(-2)² - (x - -5)²/(-6)² = 1

∴ The equation is (y + 3)²/4 - (x + 5)²/36 = 1

7 0

3 years ago

Jan buys 3 bags of beads. Each bag contains 7 beads. Draw a bar diagram and write an addition equation and a multiplication equa

-Dominant- [34]

Answer:

- The diagram bar is attached.

- Addition equation: $7+7+7=21$

- Multiplication equation: $(3)(7)=21$

- How are the equation related? Each equation shows 3 groups of 7.

Step-by-step explanation:

We know that Jan buys 3 bags of beads and each bag contains 7 beads, then, you can draw the bar diagram shown attached.

Observe that the diagram has 3 blocks (each block represents a bag of bead) and there is a number 7 inside of each block (which is the number of beads contained in a bag).

Therefore:

- Add the numbers inside the blocks in order to get the addition equation that shows the number of beads Jan buys. This is:

$7+7+7=21$

- Multiply 3 blocks by 7 in order to get multiplication equation that show the number of beads Jan buys:

$(3)(7)=21$

The equations are related. Each one shows 3 groups of 7.

6 0

3 years ago

Which of the following describe an angle with a vertex at E?

Marianna [84]

Answer

B., C.

Step-by-step explanation:

Since the 'E' in the middle

it represents that the angle forms at the vertex E

3 0

4 years ago

Read 2 more answers

7. In the accompanying diagram of right triangle ABC, altitude BD divides hypotenuse

xxMikexx [17]

Answer:

A.

Step-by-step explanation:

5 0

3 years ago

A rectangle measures 2 2 /3 inches by 1 5/ 9 inches. What is its area?

KengaRu [80]

4.15

You take 2.6666 times 1.55555

8 0

4 years ago