Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)?

Answers

Answer 1

The required equation of the hyperbola is expressed as

[tex]\frac{x^2}{10}- \frac{y^2}{15}=1 \\[/tex]

The standard form for calculating the equation of a parabola along the x-axis is expressed as:

[tex]\frac{(x-k)^2}{a^2}-\frac{(y-h)^2}{b^2} = 1 \ ............. 1[/tex] where:

(h, k) is the center

(k±c, h) are the foci

[tex]x=h\pm\frac{a^2}{c}[/tex] is the directrix

From the question given, we can see that foci = (±5, 0)

k±c, h = ±5, 0

k = 0

h = 0

c = 5

From the directrix,

[tex]x=h\pm\frac{a^2}{c}\\x =0\pm\frac{a^2}{5}\\\pm2 = \pm\frac{a^2}{5}\\a^2 = 10\\[/tex]

Also, we need to know that;

a²+b² = c²

10 + b² = 5²

b² = 25 - 10

b² = 15

Substituting the gotten values into the equation of a hyperbola;

[tex]\frac{(x-0)^2}{10}- \frac{(y-0)^2}{15} =1\\\frac{x^2}{10}- \frac{y^2}{15} =1\\[/tex]

This gives the required equation of the hyperbola

Learn more on the equation of hyperbola here: https://brainly.com/question/20409089

Answer 2

Answer:

The answers are between C and D

Step-by-step explanation:

It can't be A or B because they create a horizontal hyperbola, when the directrices are vertical.


Related Questions

Chanel found a used bookstore that sells pre-owned DVDs and CDs. DVDs cost $9 each, and CDs cost $6 each. Chanel can spend no more than $108.

Answers

The question is incomplete. Kindly see the correct question below

Chanel found a used bookstore that sells pre-owned DVDs and CDs. DVDs cost $9 each, and CDs cost $6 each. Chanel can spend no more than $108 Write an inequality that represents this

Answer:

9D +6C < 108

Step-by-step explanation:

Let the price of Dvd be D

Let the price of CDs be C

Hence the inequality can be represented as follows

9D + 6C < 108

Help me ASAP!!
Find the area of the whole blue triangle.
8.5 m
10 m
8 m
3 m
6 m

Answers

I believe you would add the 6m and 3m to make 9m then do the area equation which is a=1/2bh so 1/2 times 9 times 8 you would get 36 so that should be the answer 36

Rocco has a weekly reading schedule, reading for 4.5 hours per day on some days and 3.5 hours per day on the other days. He reads a total of 25.5 hours in a seven-day week. On how many days does he read for 4.5 hours?

Answers

Answer:

x = days he reads for 4.5 hours = 1 day

y = days he reads for 3.5 hours = 6 days

Step-by-step explanation:

Let

x = days he reads for 4.5 hours

y = days he reads for 3.5 hours

x + y = 7 (1)

4.5x + 3.5y = 25.5 (2)

From (1)

x = 7 - y

Substitute x = 7 - y into (2)

4.5x + 3.5y = 25.5 (2)

4.5(7 - y) + 3.5y = 25.5

31.5 - 4.5y + 3.5y = 25.5

- 4.5y + 3.5y = 25.5 - 31.5

-y = -6

y = 6

Substitute y = 6 into (1)

x + y = 7 (1)

x + 6 = 7

x = 7 - 6

x = 1

x = days he reads for 4.5 hours = 1 day

y = days he reads for 3.5 hours = 6 days

please help me dont add a link you'll get reported

Answers

Answer:

D, 245.0 in^2

Step-by-step explanation:

Formula for the surface area of a cylinder: A=2πrh+2πr^2

A = 2πrh + 2πr^2

A = 2π(3)(10) + 2π(3)^2

A = 60π + 18π  

A = 245.044

Answer:

???/

Step-by-step explanation:

Solve log2 x = log5 3+1 by graphing. round to the nearest tenth

Answers

Answer:

the answer is 3.2

Step-by-step explanation:

x≈3.2

it is multiple choice and i know 100% that the answer is no, but i dont know the answer for the solution part

Answers

Answer:

NO

NO SOLUTION

Step-by-step explanation:

2t + 2e = 11  eqn 1

t + e = 6.5 eqn 2

this can be solved using simultaneous  equation

Multiply eqn 2  by 2

2t + 2e = 13

subtract eqn 1 from2

0 + 0 = 2

there is no solution

A hospital recorded the weights, in ounces, of newborn babies for two weeks. The

results are listed below.

Weights of babies born during week one: 128, 105, 80, 82, 96, 98, 87, 100, 112, 126

Weights of babies born during week two: 75, 85, 90, 97, 89, 105, 110, 127, 129, 130

Which statement is true?

Answers

Answer:

The standard deviation for week two was about 3 ounces more than the standard deviation for week one

Step-by-step explanation:

Given

[tex]Week\ 1: 128, 105, 80, 82, 96, 98, 87, 100, 112, 126[/tex]

[tex]Week\ 2: 75, 85, 90, 97, 89, 105, 110, 127, 129, 130[/tex]

See attachment for options

Required

The true statement

Checking the standard deviation

For week 1

Calculate the mean:

[tex]\bar x = \frac{\sum x}{n}[/tex]

[tex]\bar x = \frac{128+ 105+ 80+ 82+ 96+ 98+ 87+ 100+ 112+ 126}{10}[/tex]

[tex]\bar x = \frac{1014}{10}[/tex]

[tex]\bar x_1 = 101.4[/tex]

Then standard deviation

[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]

[tex]\sigma_1 = \sqrt{\frac{(128 - 101.4)^2 +............+ (126- 101.4)^2}{10}}[/tex]

[tex]\sigma_1 = \sqrt{\frac{2522.4}{10}}[/tex]

[tex]\sigma_1 = \sqrt{252.24[/tex]

[tex]\sigma_1 = 15.88[/tex]

For week 2, we have:

[tex]\bar x = \frac{75+ 85+ 90+ 97+ 89+ 105+ 110+ 127+ 129+ 130}{10}[/tex]

[tex]\bar x = \frac{1037}{10}[/tex]

[tex]\bar x_2 = 103.7[/tex]

Then standard deviation

[tex]\sigma_2 = \sqrt{\frac{(75 - 103.7)^2 +................+ (130- 103.7)^2}{10}}[/tex]

[tex]\sigma_2 = \sqrt{\frac{3538.1}{10}}[/tex]

[tex]\sigma_2 = \sqrt{353.81[/tex]

[tex]\sigma_2 = 18.81[/tex]

Compare the standard deviations

[tex]\sigma_1 = 15.88[/tex]

[tex]\sigma_2 = 18.81[/tex]

Calculate the difference:

[tex]d = \sigma_2 - \sigma_1[/tex]

[tex]d = 18.81 - 15.88[/tex]

[tex]d = 2.93[/tex]

[tex]d \approx 3[/tex]

This implies that option (b) is true

-2/3m = 12 solve for m

Answers

Step-by-step explanation:

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow \dfrac{-2}{3m}=12[/tex]

use cross multiplication

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow -2=3m\times 12[/tex]

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow -2=6m[/tex]

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow m=\dfrac{-2}{6}[/tex]

[tex]\\ \:\:\:\:\sf {:}\dashrightarrow{\underline{\boxed{\bf{ m=-\dfrac{1}{3}}}}}[/tex]

If a town with a population of 2000 doubles in size every 89 years what will the population be 267 years from now

Answers

Answer:

8,000 or 8·10³

Step by Step:

2000+2000=4000

4000+4000=8000

8000 or 8·10³

Answer:

16000

Step-by-step explanation:

This is essentially is asking 'What is 2000 * 2 * 2 * 2?'.

May I have Brainliest?

Hope that this helps!

PLEASEEEE HELPPP MEEE.
DUE RIGHT NOW!!

Topic: Math
Solve all the questions

Answers

Answer:

1. x= 9

2. x= −2

3. 51 inches

4. $213.11 each month

Step-by-step explanation:

1. Simplify both sides of the equation.

x + 7 + 7x= 25 + 6x

Combine Like Terms

(x + 7x) + (7)=6x + 25

8x + 7= 6x + 25

8x + 7= 6x + 25

Subtract 6x from both sides.

8x + 7 − 6x= 6x + 25 − 6x

2x + 7= 25

Subtract 7 from both sides.

2x + 7 − 7= 25 − 7

2x= 18

Divide both sides by 2.

2x/2= 18/2

2.  Subtract 5x from both sides.

x − 5x= 5x + 8 − 5x

−4x= 8

Divide both sides by -4.

−4x/−4= 8/−4

3. First find the perimeter of the trapezoid

4 + 3 + 4 + 8= 19

A square has all equal sides

8 * 4= 32

Add them together

19 + 32 = 51 inches

4. Subtract the amount she put for finance from the total

1598.66 - 320 = 1278.66

Then divide that amount by the 6 months

1278.66 divided by 6 = 213.11

$213.11 each month

Jeffrey's recipe for oatmeal muffins calls for 2 3/4 cups of oatmeal and makes one dozen muffins. If he makes 2 dozen muffins for a club meeting and 1 1/2 dozen muffins for a family reunion, how much oatmeal will he use?

Answers

Answer:

                              5

Jeffrey will use 9  __ cups of oatmeal

                              8

Step-by-step explanation:

2.75 cups of oatmeal per 1 dozen

2.75 x 2 = 5.5

2.75 + 2.75(1/2) = 4.125

add

5.5 + 4.125 =

9.625 cups of oatmeal

              or

9 5/8 cup

PLEEEEASEEE HELP ASAP

In the diagram, the measures of ∠1 and ∠4 are 105°. The measures of ∠5 and ∠8 are 115°. Are lines c and d parallel

a p e x

Answers

Answer:

a

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

I just got done with this same quiz and i got a 100 .

please find the missing side of this triangle

Answers

The answer is 15.01

First you need to find the other angle of the triangle so you do 90+25 which gives you 115 and subtract that by 180 because all angles of a triangle add up to 180. That gives you 65 then you will use TAN(65) and get 2.144506920509559 which you will then multiple by 7 to get 15.01154844356691 which you then round to get 15.01!

Liam bought a sandwich for $4.75, a bag of chips for $2.30, and a drink for $1.15. The tax was $0.65. He gave the cashier $10.00. How much change should Liam have receive

Answers

answer:
$1.15

step-by-step explanation:
4.75 + 2.30 + 1.15 + 0.65
8.85
10.00 - 8.85
1.15

Can you solve this for x? 7x-1

Answers

Answer 1/7 hope it helps

Lena has two coupons for pants.
Coupon A: 45% off of $47 pants
Coupon B: $25 rebate on $47 pants
Choose the coupon that gives the lower price.

Answers

Answer:

coupon A

Step-by-step explanation:

coupon A 45%÷100=0.45 so 0.45×47= gives 21.15. coupon B 25÷2=23.50 so that the solution the lower price is coupon A $21.15


A. 65
B. 30
C. 10
D. 50

Answers

Answer:

50

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

D. 50

Step-by-step explanation:

∠CGF and ∠AFG add up 180° because they are same side interior angles. We can write an equation to model the situation:

m∠CGF + m∠AFG = 180°

And, we can substitute:

3x - 20 + x = 180

4x - 20 = 180

4x = 200

x = 50

Can someone help me out my grads are bad

Answers

Answer:

50 m^2

Step-by-step explanation:

3cm = 5 m

6 cm = 10 m

5 x 10 = 50 m^2

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

50 [tex]m^{2}[/tex]

Step-by-step explanation:

3cm = 5m

6cm = 10m

5x10 = 50

Jenna multiplied four numbers together and then divided by -2. The result was a positive value.

Which of the following statements MUST be true?

A) An odd number of factors were negative.
B) None of the factors were negative.
C) An even number of factors were negative.
D) All of the factors were negative.

Answers

Answer:

c

Step-by-step explanation:

What is the probability of rolling a 6 and then a 7 on a number cube?

NO LINKS PLEASE!​

Answers

Answer:

the probability of rolling 6 is 16 or 16.7%.

the probability of rolling 7 is 0.

Step-by-step explanation:

7 is 0 because its impossible to roll a 7 on one number cube.

Find the missing values in the Table of Values. Write your numbers from top to bottom in the space below with a comma between each value.

PLEASE DON'T GIVE A LINK OR DELETE THE ANSWER BECAUSE THIS IS MY SECOND TIME POSTING THIS SO PLS PLS PLS GIVE A PROPER ANSWER TO ALL OF THE PICTURES.

Answers

Answer:

Alright, with this, its essentially asking for you to plug in X into each equation for the answer.

With the first box, it asks for y = 5 - x, given the x = -2.

y = 5-x

y=5-(-2)

y=5+2

y=7

With the second box down, it wants things a bit differently, it gives you the y value, and wants for you to find the x. Given this, this question can be done backwards for the x value.

y = 5-x

6 = 5-x

x+6= 5

x=-1

With the third one, its the same thing as with the first box.

y = 5-x

y = 5-0

y = 5

Same thing with the fourth one.

y = 5-1

y = 4

If you have any question about the process or the answer, please comment below and I can help explain on what you're stuck on.

Answer:

Picture 1: (-2, 7), (-1,6), (0,5), (1,4)

Picture 2: (-2, -6), (4,6), (0,-2), (1,0)

Picture 3: (-1, -4), (8,5), (1,-2), (5,2)

Help me plsssssssssssssssss

Answers

THE ANSWER TO X IS 14

1-3x+15
-3x=12/3=4
2-5x-45
+5=50/5=10
3-4+10=14

Can someone help me

Answers

Answer:

b. the slopes of both functions are positive

Step-by-step explanation:

hope this helps :)

Answer:

C. The slope of function A is positive and the slope of function B is negative.

Step-by-step explanation:

For this problem, you need to determine the slope of each function.

For function A:

You're given y = (1/4)x - 2/3, which is in slope-intercept form y = mx + b. The slope of an equation in slope intercept form is given by m.

So the slope for function A is 1/4.

For function B:

You're given a list of (x, y) points, so use the definition of the slope = [tex]\frac{y2-y1}{x2-x1}[/tex], which gives you the slope from any two (x, y) points on the line. Let's take the first and second points (2, -8) and (4, -9)

Slope = [tex]\frac{-9-(-8)}{4-2} = \frac{-1}{2}[/tex].

Therefore, the slope of function A is positive and the slope of function B is negative.

HELP IM GOING TO HAVE A MENTAL BREAKDOWN
Find the values of x and y that make these triangles congruent by the HL Theorem.

Answers

Answer:

x = 3 ; y=2

Step-by-step explanation:

to simplify the work we can build a system of two equations

2x+3 = 3y+3

x = y+1

we can now substitute the value of x in the first equation

2(y+1)+3 = 3y+3

2y + 2 + 3 = 3y+3

2y + 5 = 3y+3

y = 2

now we can subisitute the value of y in the first equation

x = 2 + 1 = 3

Verify

2(3)+3 = 6+3 = 9

3(2) + 3 = 6 + 3 = 9

3

2+1 = 3

Evaluate the expression for a = 10 and b = 12.


a+4(b−3)

Answers

Answer:

46

Step-by-step explanation:

a + 4(b - 3)

Substitute the values for a and b.

10 + 4(12 - 3)

Subtract inside the parenthesis.

10 + 4(9)

Multiply.

10 + 36

Add.

46

Logan has $63 and would like to purchase as many packs of baseball cards as possible to add to her collection. Part A An advertisement in the newspaper shows that each pack of cards costs $1.75. At this price, how many packs of cards can Logan buy? Write the answer in the box. packs

Answers

Answer:

36 card

Step-by-step explanation:

because 1 card cost $1.75 and Logan has $63, just divide 63 by 1.75 to get the answer

63÷1.75 =36

problem of volume that equals 9 work please

Answers

Step-by-step explanation:

l=1

b=3

h=3

l×b×h

9 is the vol

What is the solution to the inequality -3x - 5 < -20?

Answers

Answer: x>5

Step-by-step explanation: Hope this help :D

PLS HELP DUE ASAP! WILL MARK BRAINLIEST

Answers

Answer:

24º

Step-by-step explanation:

C = (1/2)(56 + 116)

C = 86

4x - 10 = 86

4x = 96

x = 24

URGENT THIS IS FOR FINALS CAN SOMEONE PLZ SOLVE IT I will brain list​

Answers

Answer:

were is the line

Step-by-step explanation:

Answer:

1- y=2x-5

2- y=-1/6x-5

Hope this helps you!!

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