PLEASE HELP WILL MARK BRAINLIEST
Which is the equation of a hyperbola with directrices at x = ±2 and foci at (4, 0) and (−4, 0)?

x squared over 8 minus y squared over 8 equals 1
x squared over 8 minus y squared over 16 equals 1
y squared over 8 minus x squared over 8 equals 1
y squared over 16 minus x squared over 8 equals 1

Answers

Answer 1

The equation of the hyperbola is:

[tex]\frac{x^2}{8} - \frac{y^2}{8} = 1[/tex]

-----------------------------------------

Directrices at [tex]x = \pm 2[/tex]Foci at [tex]x = \pm 4[/tex]

They are both in the x-axis, and the center is (0,0), which means that the equation is:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

-----------------------------------------

Directrices at [tex]x = \pm 2[/tex] means that:

[tex]\frac{a^2}{c} = 2[/tex]

-----------------------------------------

Foci at [tex]x = \pm 4[/tex] means that:

[tex]c^2 = 4^2 = 16 \rightarrow c = 4[/tex]

Thus:

[tex]a^2 = 2c = 2(4) = 8[/tex]

-----------------------------------------

For b, we have that:

[tex]a^2 + b^2 = c^2[/tex]

[tex]8 + b^2 = 16[/tex]

[tex]b^2 = 8[/tex]

-----------------------------------------

Thus, since a and b have been found, the equation of the hyperbola is:

[tex]\frac{x^2}{8} - \frac{y^2}{8} = 1[/tex]

A similar problem is given at https://brainly.com/question/20409089


Related Questions

What is a simpler form of the following expressions?
(7m2 - 5)(7m2 + 5)
(This is a rushed one so pls help?)

Answers

Answer:

49m^4 - 25

Step-by-step explanation:

The simpler expression can simply be found by expanding

The kind of expansion we have here is the difference of two squares

(a + b)(a-b) = a^2 - b^2

Thus, we have it that;

(7m^2-5)(7m^2 + 5)

=

49m^4 - 25

Explain ASAP PLEASE!!!!!!

Answers

Answer:

C

Step-by-step explanation:

you can make a right triangle from the center of one base to the edge of that circle, and then up to a point on the circumference of the other base

the bases of the triangle would be 2 and 5

so that gives sqrrt 29

What type of triangle is this

Answers

Answer:

isosceles

Step-by-step explanation:

Answer:

An isosceles

Help quick!!!

What is the distance between the following points:

A ( 25,20 ) B ( 5, 20 )

Answers

Answer:

(20,0)

Step-by-step explanation:

I think that's it sorry if I am wrong:(

Will Mark Brainliest

Solve each system by elimination. Show your work

3х – 10 y = 14
3х – 9y = 15

Answers

Answer:

subtracting both equations

3x-10y=14

3x-9y=15

- - =-

_________

0-y=-1

y=1

then putting the value of y in first eqn

3x-10×1=14

3x=24

x=8

so x is 8and y is 1

In AGHI, h = 300 inches, ZG=30° and ZH=29º. Find the length of i, to
the nearest inch.

Answers

The answer is Stan twice ZG=30

34.23 times one year is ....

Answers

Answer:

410.76

Step-by-step explanation:

34.23 * 12= 410.76

1 year = 12 months

410.76

34.23 times 12, because there are 12 months in one year, and the calculator shows 410.76!

Tisha wants to plant a garden in the widest corner of her triangular backyard. The backyard is bordered by
the back of the house that is 50 feet long, fence A that is 27 feet long, and fence B that is 35 feet long. Which corner has the widest measure?

Answers

Answer:

in think it's fence b okm

Enter your answer and show all the steps that you use to solve this problem in
the space provided.


The two figures shown above are congruent. Identify the corresponding sides and
angles.

Answers

Answer:

Step-by-step explanation:

they're the same figure but turned 90 deg

congruent sides:

AD and RQ

BA and SR

BC and SP

PQ and CD

congruent angles:

D and Q

R and A

B and S

C and P

haven't done this in a minute sorry if this is wrong

what is the slope of the line?

Answers

Slope:0
Y intercept: -2
Do you still need help my guy?

Find the value of x that makes m || n

Answers

Answer:

x = 60

Step-by-step explanation:

if m and n are parallels, that means that x and 2x would be same side interior angles.

same side interior angles add up to 180

x + 2x = 180

3x = 180

x = 180/3

x = 60

From the graph shown, what is an approximate solution of the system of equations?

Answers

Where is the graph? It is a a black screen

PLEASE HELP ASAP!!!!!!!

Answers

Answer:

[tex]\frac{9}{16}[/tex]

Step-by-step explanation:

[tex]\frac{1 \frac{1}{2} * \frac{3}{4}}{2}=\frac{9}{16}[/tex]

What is the difference between a system of equations and a system of inequalities?

Answers

The graph of linear inequalities include a dashed line if they are greater than or less than but not equal to. Linear equations, on the other hand, include a solid line in every situation. Moreover, linear inequalities include shaded regions whereas linear equations do not.

Expressions can be expressed as equations or as inequalities.

The difference is that the variables in a system of equation have one solution each, while in a system of inequalities, the variables have a range of values.

Let the system of equation be:

[tex]\mathbf{ax + by = c}[/tex]

[tex]\mathbf{dx + ey = f}[/tex]

Let the system of inequality be:

[tex]\mathbf{ax + by < c}[/tex]

[tex]\mathbf{dx + ey > f}[/tex]

Both systems can be solved using the same method, such as: graphs, substitution and elimination.

However, the difference is that:

In a system of equation, the variables can have one solution each, while in a system of inequalities, the variables have a range of values.

Read more about system of equations and inequalities at:

https://brainly.com/question/11476486

3. Abdoul has $100 in his bank account and he adds $50 each month.

Answers

Answer:

$600

Step-by-step explanation:

Multiply 50, 12 times, you get 600. Add 100, and you get 700.

Answer is $700

A group of seven friends went out for dinner together and they each paid the same amount for their meal. Their total bill was $68.95 what was the cost of one meal
Please answer I really need it <3

Answers

Answer:

9.85

Step-by-step explanation:

$68.95 Divided by seven friends = 9.85

You're Welcome :D

Solve for X.

x+3
4
8

Answers

Answer:

First find the hypotenuse of the small triangle then use that value as the base of the upper triangle. Evaluate the equation formed with the “x"

Work out the area of this circle with radius 11.2 take pie to be 3.142 and give your answer to 2 decimal places

Answers

Answer:

394.13 to 2 D.P.s

Step-by-step explanation:

Area = pi r^2

= 3.142 * 11.2^2

= 394.132.

The area of this circle up to 2 decimal places will be 394.13 square units.

What is the area of the circle?

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The radius of the circle is 11.2 units and takes π to be 3.142. Then the area is given as,

A = π x (11.2)²

A = 3.142 x 125.44

A = 394.13 square units

The area of this circle up to 2 decimal places will be 394.13 square units.

More about the area of a circle link is given below.

https://brainly.com/question/11952845

#SPJ5

Classify the triangles as acute obtuse or right

Answers

Answer:

Acute

Obtuse

Right

Acute

Step-by-step explanation:

To see if a triangle is acute, right, or obtuse, you use something similar to the pythagorean theorem:

Let a and b be the shorter sides, c be the longest side.

If a^2+b^2 > c^2, then the triangle is acute.

If a^2+b^2 = c^2, then the triangle is right.

If a^2+b^2 < c^2, then the triangle is obtuse.

Dario increased his savings from $350 to $413. What is Dario's percent increase in
savings?

Answers

Answer:

18%

Step-by-step explanation:

63/350 × 100 = 18

hope this helps

Will mark as brainliest

Answers

Answer:

p = 1

Step-by-step explanation:

Δ JKH ≅ Δ JIH

therefore KJ corresponds with IJ so you can set both sides equal to each other

10p = p+9

9p = 9

p = 1

Let u=-4i-5j and v=3i-6j

Answers

The answer is 2244. Because ghgfgggggffgfhfghfgh

Solve the following proportion for u.
3/17 = u/13

Answers

Answer:

2.294117647

Step-by-step explanation:

3/17  =  u/13

Cross multiply:

3 * 13 = 17 * u

Simplifying

3 * 13 = 17 * u

Multiply 3 * 13

39 = 17 * u

Solving

39 = 17u

Move all terms containing u to the left, all other terms to the right.

Add '-17u' to each side of the equation.

39 + -17u = 17u + -17u

Combine like terms: 17u + -17u = 0

39 + -17u = 0

Add '-39' to each side of the equation.

39 + -39 + -17u = 0 + -39

Combine like terms: 39 + -39 = 0

0 + -17u = 0 + -39

-17u = 0 + -39

Combine like terms: 0 + -39 = -39

-17u = -39

Divide each side by '-17'.

u = 2

Simplifying

u = 2.294117647

3/17=u/13
3*13=17u
39=17u
U=39/17=2.29

Question 4 Given: f(x) = -3x – 3 and g(x) = x2 + 5 Find (f - g) ().​

Answers

Answer:

We get [tex]\mathbf{(f-g)(x)= -x^2-3x-8}[/tex]

Step-by-step explanation:

We are given:

[tex]f(x) = -3x - 3\\ g(x) = x^2 + 5[/tex]

We need to find (f-g)(x) (assuming there is x in the bracket, i.e. (f - g) () should be (f-g)(x))

We would simply subtract f(x) and g(x)

[tex](f-g)(x)\\= -3x-3-(x^2+5)\\Multiply\:minus\:sign\:with\:terms\:inside\:the\:bracket\\=-3x-3-x^2-5\\Combining\:like\:terms:\\=-x^2-3x-3-5\\=-x^2-3x-8[/tex]

So, We get [tex]\mathbf{(f-g)(x)= -x^2-3x-8}[/tex]

find the equation of the line shown​

Answers

Answer:

[tex]y = - 1x + 9[/tex]

Step-by-step explanation:

Remmeber:

[tex]Slope = \frac{rise}{run} [/tex]

Find:-
1) Complement of 75 degree
2) Complement of 40 degree
3) Complement of 71 degree
4) Complement of 101 degree ​

Answers

Given :

Some angles in degree.

To Find :

1) Complement of 75 degree

2) Complement of 40 degree

3) Complement of 71 degree

4) Complement of 101 degree ​

Solution :

We know, two angles are complement when their sum is 90 degree.

1) Complement of 75 degree is, 90 - 75 = 15 degree.

2) Complement of 40 degree is, 90 - 40 = 50 degree.

3) Complement of 71 degree is, 90 - 71 = 19 degree.

4) Complement of 101 degree is, 90 - ( -101 ) = 191 degree.

Hence, this is the required solution.

This is some question pizza circles in math

Answers

Step-by-step explanation:

Diameter : 10

Radius : 5

Area :

[tex]\pi {r}^{2} = \pi{5}^{2} = 78.54[/tex]

Diameter: 18

Radius : 9

Area :

[tex]\pi {9}^{2} = 254.47[/tex]

Diameter: 11

Radius: 5.5

Area:

[tex]\pi {5.5}^{2} = 95.03[/tex]

Diameter: 12

Radius : 6

Area:

[tex]\pi {6}^{2} = 113.09[/tex]

Factor each polynomial: 9x-6

Answers

Answer:

3(3x−2)

Step-by-step explanation:

CAN YOU PLEASE HELP ME!!....

Answers

Answer:

I have no idea sorry :c

Step-by-step explanation:

Could you help me on this, I need to submit soon as well :)

Answers

Answer:

6

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

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