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Lesechka [4]
1 year ago
7

Graph the hyperbola using the transverse axis, vertices, and co-vertices:

Mathematics
1 answer:
Reptile [31]1 year ago
4 0

See attachment for the graph of the hyperbola 12x^2 - 3y^2 - 108 = 0

<h3>How to graph the hyperbola?</h3>

The equation of the hyperbola is given as:

12x^2 - 3y^2 - 108 = 0

Start by calculating the transverse axis

So, we have:

<u>Transverse axis</u>

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

Where

a = 3 and b = 6

The transverse axis is calculated as:

y = ±b/a(x - h) + k

So, we have:

y = ±6/3(x - 0) + 0

Evaluate the difference and sum

y = ±6/3x

Evaluate the quotient

y = ±2x

This means that the transverse axes are y = 2x and y =-2x

<u>The vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

<u>The co-vertices</u>

In the above section, we have:

The vertices of the given hyperbola are (0, 0)

This means that

(h, k) = 0

And

a = 3 and b = 6

The co-vertices are

(h - a, k) and (h + a, k)

So, we have:

(0 - 3, 0) and (0 + 3, 0)

Evaluate

(-3,0) and (3, 0)

See attachment for the graph of the hyperbola

Read more about hyperbola at:

brainly.com/question/26250569

#SPJ1

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Answer:

x = 12.6

Step-by-step explanation:

Sum of measure of all the arcs of a circle = 360°

m(arc CD) + m(arc CED) = 360°

Since, m(arc CED) = (20x)°

And m(arc CD) = (8x + 6)°

By substituting these measures in teh expression,

(20x)° + (8x + 6)° = 360°

(20x + 8x) + 6 = 360

28x = 360 - 6

28x = 354

x = \frac{354}{28}

x = 12.64

x = 12.6

4 0
3 years ago
Suppose each license plate in a certain state has three letters followed by three digits. The letters and and the digits , , and
exis [7]

Answer:

17576000 different possible license plates

Step-by-step explanation:

Note that in the question, repetition is allowed for both the letters and digits.

For the first letter, there are 26  choices to make. For the each of the letters, there are 26 choices for the second letter, and for each of the letters, there are another 26 choices for the third letter.

Therefore, this gives us 26x26x26 = 17576 possible pairs of letters.

For the three numbers, we have ten possibilities for the first digit, ten possibilities for the second digit, and ten possibilities for the third digit.

Therefore, this gives us 10x10x10 =1000 possible numbers.

The combined possibility of the license plates in both three letters and three numbers is 17576 x 1000 = 17576000 different possible license plates.

7 0
3 years ago
What is the approximate volume of a cone with a height of 12 in. and radius of 9 in.?
swat32
The answer would be 1017.88 in³. Use the volume for cones ( 1/3 times pi times radius times height) so 1/3*3.14*9*12 in which would be 1017.88 in³ hope it helps!
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2 years ago
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If &lt;3 and &lt;4 are vertical angles and m&lt;3=9x+5 and m&lt;4=5x+33 find &lt;4
KatRina [158]

Answer:

<em>68 degrees</em>

Step-by-step explanation

If <3 and <4 are vertical angles, then <3 = <4

This means that

9x + 5 = 5x + 33

9x - 5x  = 33 - 5

4x = 28

x = 28/4

x = 7

Since <4 = 5x+ 33

<4 = 5(7) + 33

<4 = 35 + 33

<4 = 68 degrees

<em>Hence the measure of <4 is 68 degrees</em>

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