(30PTS) What are the slopes of the asymptotes of a hyperbola with equation x^2/2^2-y^2/6^2=1

Answers

Answer 1

Answer:

2x2−3y2=6or2x26−3y26=1 or. x23−y22=1or(x−0)2(√3)2−(y−0)2(√2)2=1. This is standard form of the equation of a hyperbola with center.

Step-by-step explanation:

c2 = a2 + b2. Every hyperbola has two asymptotes. A hyperbola with a horizontal transverse axis and center at (h, k) has one asymptote with equation y = k + (x - h) and the other with equation y = k - (x - h).

Answer 2

The slopes of the asymptotes of the hyperbola are +3 and -3.

What is an equation?

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The standard equation for a hyperbola with a horizontal transverse axis is:

[tex](x-h)^2/a^2 - (y-k)^2/b^2 = 1[/tex]

where (h,k) is the center of the hyperbola, "a" is the distance from the center to the vertices along the x-axis, and "b" is the distance from the center to the vertices along the y-axis.

Comparing this to the given equation:

[tex]x^2/2^2 - y^2/6^2 = 1[/tex]

We can see that h = k = 0, a = 2, and b = 6.

The slopes of the asymptotes are given by:

±(b/a)

So, the slopes of the asymptotes are:

±(6/2) = ±3

Therefore,

The slopes of the asymptotes of the hyperbola are +3 and -3.

Learn more about equations here:

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Related Questions

Solve this equation with ÷, ×, -, or +.
18 _ 2 × 4 = 26

Answers

Answer:

+

Step-by-step explanation:

b/c

18+2×4

18+8

26

hope it's helpful ❤❤❤

THANK YOU.

Write an expression for the sequence of operations described below.
q more than the quotient of 10 and p
Do not simplify any part of the expression.

Answers

More than means addition
Quotient means division

Q plus 10/p

I think this is the answer I hope this helps

9. What is the best model for the data?
Answer choices:
Linear
Exponential
Quadratic

Answers

Answer:

Exponential

Step-by-step explanation:

I think this is the answer but not correct me if I'm wrong

Please help I’ll mark you as brainliest if correct!

Answers

Answer:

304

Step-by-step explanation:

The area of the square is 12 x 8 = 96.

There are two triangles with area (11x8)/2=44. 44x2=88.

There are two triangles with area (10x12)/2=60. 60x2=120.

96+88+120=304

Hope I helped!

Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to adulthood. Assume this estimate is
correct. Suppose researchers choose 7 baby elk at random to monitor. Let X = the number that survive to adulthood.
What is the probability that more than 4 elk in the sample to survive to adulthood?
O 0.6294
O 0.2304
0.8598
0.1402
O 0.3706

Answers

Answer:

0.1402

Step-by-step explanation:

For each baby elk, there are only two possible outcomes. Either they survive adulthood, or they do not survive. The probability of an elk surviving adulthood is independent of other elks. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Biologists estimate that a randomly selected baby elk has a 44% chance of surviving to adulthood.

This means that [tex]p = 0.44[/tex]

Suppose researchers choose 7 baby elk at random to monitor.

This means that [tex]n = 7[/tex]

What is the probability that more than 4 elk in the sample to survive to adulthood?

This is:

[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7)[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{7,5}.(0.44)^{5}.(0.56)^{2} = 0.1086[/tex]

[tex]P(X = 6) = C_{7,6}.(0.44)^{6}.(0.56)^{1} = 0.0284[/tex]

[tex]P(X = 7) = C_{7,7}.(0.44)^{7}.(0.56)^{0} = 0.0032[/tex]

[tex]P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1086 + 0.0284 + 0.0032 = 0.1402[/tex]

0.1402 probability that more than 4 elk in the sample to survive to adulthood.

Using the concept of binomial probability, the probability that more than 4 survive is 0.1402

Using the binomial probability formula :

[tex] P(x = x) = nCx \times p^{x} \times q^{(n-x)} [/tex]

p = probability of success = 0.44q = 1 - p = 1 - 0.44 = 0.56 n = number of trials = 7

The probability that more than 4 survive can be defined thus :

[tex] P(x > 4) = p(x = 5) + p(x = 6) + p(x = 7) [/tex]

Using a binomial probability calculator :

[tex] P(x > 4) = 0.1086 + 0.0284 + 0.0032 [/tex]

[tex] P(x > 4) = 0.1402 [/tex]

Hence, the probability that more than 4 survive is 0.1402

Learn more : https://brainly.com/question/15929089

I will give brainiest to whoever answers correctly !!

Answers

Answer:

it is not clear .... please add the question and send the link of the question

Answer:

$712.79

Step-by-step explanation:

What is the distance between the points (-9,5) and (8,5)

Answers

Answer:

17 units

Step-by-step explanation:

Use distance formula, [tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], to find the distance between (-9, 5) and (8, 5):

Let,

[tex] (x_1, y_1) = (-9, 5) [/tex]

[tex] (x_2, y_2) = (8, 5) [/tex]

Plug in the values into the distance formula:

[tex] d = \sqrt{(8 - (-9))^2 + (5 - 5)^2} [/tex]

[tex] d = \sqrt{(17)^2 + (0)^2} [/tex]

[tex] d = \sqrt{(289 + 0)} [/tex]

[tex] d = \sqrt{289} [/tex]

[tex] d = 17 [/tex]

Plz help due tomorrow

Answers

Answer:

Step-by-step explanation:

1/6 x 1/5 + 1/30

= 1/30 + 1/30

= 2/30

=1/15

Okay the equation is 1/6x + 1/30

It is asking us to plug in 1/5 so let’s plug it in

1/6(1/5) + 1/30 = 1/30 + 1/30 = 2/30

So we reduce the fraction and the answer is 1/15

Which one is a better deal? Deal 1: $7.65 for 9 iTunes songs Deal 2: $6.93 for 7 iTunes songs

Answers

Umm I think the deal 7 sure it’s more money but I think it better or just get Apple Music

Answer:

yeah I would say deal #1 is better

which of the following are functions.

Answers

Answer:

Graph ii and iii

Step-by-step explanation:

In graph ii and iii, every input has one and only output. Another way to check is by doing the vertical line test.

The answer is
ii and iii

https://brainly.com/question/20659247 Someone please help I seriously need it just use the link know what here you go if you dont wanna use the link

Answers

6•6=24 then dived by 3

Ana completed 40% of her math test yesterday. She completed 12 math problems. How many math problems are on her test?

Answers

Answer:  30

Step-by-step explanation:

as you see i kinda need help lol

Answers

Answer:

i believe the answer is C

Step-by-step explanation:

so do I lol I can’t finish my math test due by 12

Question 5
Evaluate:
Five cubed.
Write the numerical answer only.

Answers

Answer:

125

Step-by-step explanation:

..................

Answer:

pretty sure it's 125

Step-by-step explanation:

hope this helps!

i need help with finding area whats the area of a 3m an 7m regtangle​

Answers

Answer:

34

Step-by-step explanation:

Answer:

Area of rectangle =LXB

L=7m

B=3m

so 7m multiply by 3m gives 21 so the area is 21

solve the equation 1/2x+7=18

Answers

Answer: 22

Step-by-step explanation:

Solve for x

   1/2x + 7 = 18

Combine 1/2 and x.

  x/2+ 7 = 18

Move all terms not containing x to the right side of the equation.

Subtract 7 from both sides of the equation.

  x/2= 18 − 7

  x/2 = 11

Multiply both sides of the equation by 2.

  2 ⋅ x/2 = 2 ⋅ 11

Simplify both sides of the equation.

Cancel the common factor of 2.

  x = 2 ⋅ 11

Multiply 2 by 11.

  x = 22

Find the rule and the graph of the function whose graph can be obtained by performing the translation 2 units left and 3
units up on the parent function f(x)=x?

Answers

Answer:

b.

Step-by-step explanation:

1. You have the following parent function given in the problem above:

f(x)=x³ (This is the simplest form. We need to translate it 3 units left and 2 units down)

2. If you take the parent function and make y=f(x+3), then you have:

(The function is shifted 3 units left on the x-axis).

3. Then you if you make y=f(x+3)-2, as following, you obtain:

(The function is shifted 2 units down on the y-axis).

4. Therefore, that is how you obtain the final function.

The answer is the graph shown in .b

Please help. The few questions I need help with are in the image below. Thanks.

Answers

Answer:

3) 21/60= 0.35

4) 5/4= 1.25

5) 9/15= 0.6 or 2/3

6) 378/15= 25.2 or 25 and 1/5

7) 1 1/2/ 2/3= 2.5

8) 28 1/3 / 3 1/3= 8.5

Step-by-step explanation:

hope this helps!

mark me brainliest please!

517 37/50 + 312 3/100

Answers

Answer: 829 3/4 or 829 75/100

Step-by-step explanation:

36 over 9 = g over 1​

Answers

Answer:

4/1

Step-by-step explanation:

g is 4

the product of two number is 20 and the sum of square is 41 find the number​

Answers

Let the two number is a and b

so,

product =ab=20

sum of square=[tex]\bold{a^2+b^2=41 }[/tex]

Then,

[tex]\bold{(a+b)^2=a^2+b^2+2ab }[/tex]

[tex]\bold{ (a+b)^2=41+2×40 }[/tex]

[tex]\bold{ (a+b)^2=81 }[/tex]

[tex]\bold{a+b=\sqrt{81} }[/tex]

[tex]\bold{a+b=9 }[/tex]•••••••••(equation I)

Now,

[tex]\bold{(a-b)^2=a^2+b^2-4ab }[/tex]

[tex]\bold{ (a-b)^2=41-4×20 }[/tex]

[tex]\bold{(a-b)^2=41-40 }[/tex]

[tex]\bold{a-b=\sqrt{1} }[/tex]

[tex]\bold{a-b=1 }[/tex]••••••••(equation II)

Now,combine the equation I and equation II

we,get

[tex]\bold{a+b+a-b=9+1 }[/tex]

[tex]\bold{a+\cancel{b}+a\cancel{-b}=10 }[/tex]

[tex]\bold{ 2a=10 }[/tex]

[tex]\bold{a=\dfrac{10}{2} }[/tex]

[tex]\blue{\boxed{ a=5 }}[/tex]

Then,

put the value of a in equation II.

we get that,

[tex]\bold{5-b=1 }[/tex]

[tex]\bold{b+1=5 }[/tex]

[tex]\bold{b=5-1 }[/tex]

[tex]\bold{\boxed{\blue{b=4}} }[/tex]

so,

The two number is 5 and 4.

Please help 30 points

Answers

Answer:

The total surface area is 973.89 ft

Step-by-step explanation:

The formula for the surface area of a cylinder is A=2πrh+2πr2.

The top cylinder has a radius of 5 ft, and height of 2 ft.

The bottom cylinder has a radius of 10 ft, and a height of 2 ft.

Plug in the numbers for each and you get:

Top Cylinder:

A=2π(5)(2)+2π(5^2)

A=2π(10)+2π(25)

A= 62.83185307 + 157.079327

A= 219.9111801

A≈ 219.91

Bottom Cylinder:

A= 2π(10)(2)+2π(10^2)

A= 2π(20)+2π(100)

A= 125.6637061 +  628.3185307

A= 753.9822368

A≈ 753.98

Combined:

753.98 + 219.91 = 973.89

Is this graph and example of sun or cos graph?

Answers

It is a cos graphhhh

Probability! Always struggled with these Plz Help

Answers

Answer:

B) The probability that the arrow will point to blue is more than 1/4

Step-by-step explanation:

The blue area makes up 1/3 of the pie chart, and 1/3 > 1/4

PLEASE HELP!!!!

A taxi charges $4.00 for the first mile plus $1.25 for each additional mile.
On a fare of $16.50, how long was the ride?

Answers

Work backwards $16.50 a $4.00 is $12.50. That got you the first mile.
The $12.50 / $1.25 per mile is ten more miles

Total length of ride is ten plus one or eleven miles

Order 0.5 , 0.66 , -1.5 , -1.25 from least to greatest

Answers

Answer:

-1.25, -1.5, 0.5, 0.66

hope it helps you

solve for x, x+25 70 degrees

Answers

Answer:

70-25=45

45+25=70

Step-by-step explanation:

28) Solve the inequality: 12x−10>170
A. x>15
B. x<−90
C. x<−58
D. x<15

Answers

Answer:

p=5x+3y

solve for x, number of cupcakes. isolate x

5x=p-3y

divide by 5

x=(p-3y)/5

Step-by-step explanation:

D. x<15

how do i the find the slope?
(btw i know how to do [m=change in y and x] thingy, but i just cant seems to get the right answer.)

Answers

Step-by-step explanation:

[tex]x ^{1} = - 5 \\ y ^{1} = - 2 \\ x {}^{2} = - 2 \\ y {}^{2} = 1 \\ then \: you \: solve \: with \: that \: formula \: you \: know[/tex]

5. Emma, Brandy, and Damian will cut a rope that is 29.8 feet long into
3 jump ropes. Each of the 3 jump ropes will be the same length. Write a
division sentence using compatible numbers to estimate the length of
each rope

Answers

Answer:

29.8÷3=9.93333333333

Step-by-step explanation:

*note* the 3 is a repeating number

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