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3 years ago

HELP ME PLZ I WILL GIVE 30 POINTS!!!!!

Mathematics

1 answer:

arsen [322]3 years ago

4 0

Answer:

Step-by-step explanation:

Step-by-step explanation:

Using Pythagoras' identity on the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² = 7² + 4² = 49 + 16 = 65 ( take the square root of both sides )

AB = \sqrt{65} → D

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Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).

olya-2409 [2.1K]

Answer:

The equation of the hyperbola is (y + 5)²/16 - (x - 3)²/81 = 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 vertices of the hyperbola are (3 , -1) , (3 , 9)

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

∴ h = 3

∴ k + a = -1 and k - a = -9

∵ The co-vertices of it are (-6 , -5) and (12 , -5)

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

∴ k = -5

∴ h + b = -6 and h - b = 12

∵ h = 3

∴ 3 + b = -6 ⇒ subtract 3 from both sides

∴ b = -9

∵ k + a = -1

∵ k = -5

∴ -5 + a = -1 ⇒ add 5 to both sides

∴ a = 4

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

∵ a = 4 , b = -9 , h = 3 , k = - 5

∴ The equation of the hyperbola is (y - -5)²/(4)² - (x - 3)²/(-9)² = 1

∴ The equation of the hyperbola is (y + 5)²/16 - (x - 3)²/81 = 1

5 0

3 years ago

A number x is no more than 9 units away from 8. Write and solve an absolute-value inequality to show the range of possible value

Montano1993 [528]

The answer is a (|x - 8| ≤ 9 and -1 ≤ x ≤ 17) Because the difference between x and 8 can't be greater than 9, but it can be less than or equal to it, and because the range that x could be would be -1 to 17, since 8 + 9 = 17 and 8 - 9 = -1.

7 0

3 years ago

Read 2 more answers

Find the percent of the number <br>105% of 400

just olya [345]

Answer:

105% of 400 is 420, the percent is 42000%

Step-by-step explanation:

6 0

3 years ago

The table shows the first five terms for two number sequences with different rules. Select the coordinate plane that has the ord

Nookie1986 [14]

The linear function of the table of values is y = -1.5x + 25

<h3>How to plot the ordered pairs?</h3>

The table of values is given as:

<u>Sequence One Sequence Two Ordered Pair </u>

6 16 (6, 16)

8 13 (8, 13)

10 10 (10, 10)

12 7 (12, 7)

14 4 (14, 4)

From the above table of values, we can see that:

As x constantly increases by 2 i.e. +1
y constantly decreases by 3 i.e. -3

This means that the table represents a linear function, and the slope of the function is

m = -3/+2

This gives

m = -1.5

A linear function is represented as:

y = mx + c

This gives

y = -1.5x + c

Using the table of values, we have

16 = -1.5 * 6 + c

Evaluate the product

16 = -9 + c

Add 9 to both sides

c = 25

Substitute c = 25 in y = -1.5x + c

y = -1.5x + 25

Hence, the linear function of the table of values is y = -1.5x + 25

See attachment for the graph of the table

Read more about linear functions at:

brainly.com/question/4025726

#SPJ1

8 0

2 years ago

Convert 0.39 to fraction

aliina [53]

0.39 as a fraction will be 39/100

7 0

3 years ago

Read 2 more answers