Which is the equation of a hyperbola with directrices at x = ±3 and foci at (4, 0) and (−4, 0)?​

Answers

Answer 1

Answer:

[tex]\frac{x^2}{12}-\frac{y^2}{4}=1[/tex]

Step-by-step explanation:

Since our foci are located on the x-axis, then our major axis is going to be the horizontal transverse axis of the hyperbola:

Formula for hyperbola with horizontal transverse axis centered at origin

[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]Directrices -> [tex]x=\pm\frac{a^2}{c}[/tex]Foci -> [tex](\pm c,0)[/tex] where [tex]a^2+b^2=c^2[/tex][tex]a>b[/tex]

Since we are given our directrices of [tex]x=\pm3[/tex] and foci of [tex](\pm4,0)[/tex], then we can set up the directrices equation to solve for [tex]a^2[/tex]:

[tex]x=\pm\frac{a^2}{c}\\ \\\pm3=\pm\frac{a^2}{4}\\ \\12=a^2[/tex]

Now we can determine [tex]b^2[/tex] to complete our equation for the hyperbola:

[tex]a^2+b^2=c^2\\\\12+b^2=4^2\\\\12+b^2=16\\\\b^2=4[/tex]

Therefore, our equation for our hyperbola is [tex]\frac{x^2}{12}-\frac{y^2}{4}=1[/tex]

Which Is The Equation Of A Hyperbola With Directrices At X = 3 And Foci At (4, 0) And (4, 0)?

Related Questions

please help me find total surface area

Answers

Answer:

190mm2

Step-by-step explanation:

8x6=48

8x7=56

8x7=56

6x5/2=15

6x5/2=15

48+56+56+15+15=190

The number of points scored by the bears, eagles, and cowboys last weekend was three consecutive odd numbers. the bears scored the least number of points and the cowboys scored the most. if the product of the points scored by the bears and cowboys was 37 more than the 8 times the sum of the points scored by the eagles and cowboys, how many points did the eagles score?
A) 13 points
B) 15 points
C) 17 points
D) 19 points
E) 21 points
Please show solution

Answers

Answer: The Philadelphia Eagles tried to blow a 19-point lead to the Chicago Bears, but managed to hold on for a 22-14 victory in a rematch of the NFC Wild Card Game to move to 5-4 on the year. Philadelphia allowed the Bears to score 14 unanswered points after taking a 19-0 lead in the third quarter, but put together one of their most impressive drives of the season in taking 8:14 off the clock in the fourth quarter, converting four consecutive third downs in the most critical junction of the game.

Chicago never got the ball back after Jake Elliott hit a 38-yard field goal with 26 seconds left to make it 22-14. Bears tight end Adam Shaheen muffed the catch on the kickoff and the Eagles recovered to deny Chicago a last ditch effort for a Hail Mary and an attempt to tie the game with a two-point conversion.

Jordan Howard scored a touchdown in his first game against his former team, finishing with 19 carries for 82 yards and a touchdown. Zach Ertz had his best game of the season as the Eagles tight end had nine catches for 103 yards and a touchdown, a 25-yard catch for his second score of 2019.

The Bears had just nine total yards in the first half, but rallied back in this game with two scoring drives in three possessions between the third and fourth quarter. Chicago's offense had no turnovers, but finished with just 164 yards of offense. Mitchell Trubisky went 10 of 21 for 125 yards with no touchdowns and a 66.6 passer rating. The Bears have lost their fourth consecutive game after a 3-1 start to the season, falling to 3-5 and remaining in last place in the NFC North.

Step-by-step explanation:

The number of points scored by the eagles is 19 points.

Suppose the points scored by the bears, eagles, and cowboys are x, x+2, x+4 respectively.

It is given the product of the points scored by the bears and cowboys was 37 more than the 8 times the sum of the points scored by the eagles and cowboys.

This means, x(x+4) =37+8(x+2+x+4)

x(x+4) =37+8(2x+6)

[tex]x^{2} +4x = 37+16x+48[/tex]

[tex]x^{2} -12x-85=0[/tex], which is a quadratic equation.

What is a quadratic equation?

Any equation in the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].

[tex]x^{2} -17x+5x-85=0[/tex]

[tex]x(x-17)+5(x-17)=0[/tex]

[tex](x-17)(x+5)=0[/tex]

[tex]x=17[/tex]

So, eagles scored x+2 = 17+2 =19 points.

Therefore, The number of points scored by the eagles is 19 points.

To get more about quadratic equations visit:

https://brainly.com/question/1214333

Graph this line using the slope and y-intercept:
y= 1/3x+9
(1/3 is fraction) i will give brainliest :)

Answers

Put a point at (0, 9)
And a point at (3, 10)

Explanation
Y-intercept is point in the y line
And slope is rise over run so if the fraction is 1/3 the. You go up one and to the right 3

Answer:

Two points, (0,9) & (3,10)

Step-by-step explanation:

First point, look at the +9 which should signal that it is 0,9 because that is the y-intercept

Next, use rise/run system to use the slope (1/3) and find your next point

Go up 1 from 9 to 10 (this is the rise part)

Go horizontally 3 to get your x-axis point (this is the run part)

Hope this helps and please award brainliest if possible!

Pls help. It is due in 20 mins

Answers

Rs1 40
100%-20%=80%
0.8(80/100)x200= 160
200-160=40

Please help me I need it please

Answers

the correct answer here is A, 22.4 hope this helped

Answer:

42.6%

Step-by-step explanation:

The percent increase is calculated as

percent increase = [tex]\frac{increase}{original}[/tex] × 100%

increase = $3.55 - $2.49 = $1.06

% increase = [tex]\frac{1.06}{2.49}[/tex] × 100% ≈ 42.6% (to the nearest tenth )

i need help on this ​

Answers

Answer:

The answer is B.

3x + 5y = 24

4x + 3y = 21

Step-by-step explanation:

x = cost of a chocolate chip cookie

y = cost of an oatmeal cookie

3x + 5y = 24

4x + 3y = 21

Lets solve:

-3(3x + 5y = 24) ==> -9x - 15y = -72

5(4x + 3y = 21) ==>   20x + 15y = 105

Let's add our new equations:

-9x - 15y = -72

20x + 15y = 105

11x = 33

/11    /11

x = $3.00 (the cost of each chocolate chip cookie)

Now lets find the cost of each oatmeal cookie using one of our original equations: 3x + 5y = 24

3(3) + 5y = 24

9 + 5y = 24

-9          -9

5y = 15

/5     /5

y = $3 (the cost of each oatmeal cookie)

Each type of cookie (chocolate chip and oatmeal), costs $3.00

Hope that helps!

Evaluate the expression 3. 14(a2 ab) when a = 4 and b = 2. (Input decimals only, such as 12. 71, as the answer. ) Answer for Blank 1:.

Answers

Answer:

1792

Step-by-step explanation:

14(a^2 ab)

a=4      b=2

=14(4^2*4*2)

=14(16*8)

=14*128

1792

Can someone help me and explain the answer to this problem: Jay's dog outgrew his rectangular pen that measured 10 feet by 14 feet. To make it larger, he increased each side length by the same amount, which increased the pen's area by 81 square feet. What is the greater side length of the larger pen in feet?

Answers

Answer:

ok so first lets find the original area which is just lenth*width

10*14=140

so they increace it by 81 so

140+81=221

then we just need to find what they increases the side by we know its the same so lets just say that x so

(10+x)(14+x)=221

x=3

so the longest time is 17 since 14+3=17

Hope This Helps!!!

help please! i will give brainliest

Answers

Answer:

x=6

Step-by-step explanation:

[tex]4(x+5)=9x+4x-34[/tex]

Step 1 :[tex]4x+20=9x+4x -34[/tex]

At step one, you have distributive property.

Step 2:[tex]4x+20=13x-34[/tex]

Step two you have to combine like terms.

Step 3:[tex]4x-4x+20=13x-4x-34[/tex]

Now is subtraction property

Step 4:[tex]20+34=9x-34+34[/tex]

additon

Step 5:[tex]\frac{54}{9}=\frac{9x}{9}[/tex]

division

x=6

simplify the expression by combining like terms

Answers

-1/4d+f
Hope this helps

What is the volume of a right circular cylinder with a base diameter of 6 m and a height of 5 m? Enter your answer in the box. Express your answer using π. M³ $\text{Basic}$.

Answers

The volume of the cylinder depends on its radius and height. The volume of the cylinder is 141.3 m3.

What is the volume of the cylinder?

The volume of the cylinder is defined as the density of the cylinder which measures the amount of material contained by the cylinder.

Given that the height h of the cylinder is 5m and the diameter d of the base of the cylinder is 6m.

The radius of the cylinder is given below.

[tex]r = \dfrac {d}{2}[/tex]

[tex]r= \dfrac {6}{2}[/tex]

[tex]r = 3\;\rm m[/tex]

The volume of the cylinder is calculated as given below.

[tex]V = \pi r^2 h[/tex]

[tex]V = 3.14 \times 3^2 \times 5[/tex]

[tex]V = 141.3 \;\rm m^3[/tex]

Hence we can conclude that the volume of the cylinder is 141.3 m3.

To know more about the volume of the cylinder, follow the link given below.

brainly.com/question/12748872.

The following table shows the working populations, average salaries, and income tax rates of France and Germany. Country Workforce Average Salary (€) Income Tax Rate France 31,491,232 29,766 69. 3% Germany 38,844,017 32,104 45. 2% Based on the information in the table, how do the annual tax revenues of Germany and France compare to one another? a. The French government gathers €85,930,190,677 more than the German government. B. The French government gathers €543,141,128,984 more than the German government. C. The German government gathers €309,680,310,056 more than the French government. D. The German government gathers €223,750,119,378 more than the French government.

Answers

Percentage is a way to describe a part of a whole. French government gathers €85,930,190,677 more than the German government.

What is Percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

We know that the number of people who are working in France is 31,491,232 and their average salary is €29,766 while the amount of tax they pay from their salary is 69.3%. therefore, the total amount of tax that France will gather,

[tex]Tax_{France} = 31,491,232 \times 29,766 \times 69. 3\%[/tex]

               [tex]= 31,491,232 \times 29,766 \times \dfrac{69. 3}{100}\\\\= 31,491,232 \times 29,766 \times 0.693\\\\=6.49596\times 10^{11}[/tex]

Now, the population that is working in Germany is 38,844,017 while the average earning of the population is €32,104 and they pay 45.2% of their salary as tax. therefore,

[tex]Tax_{Germany} = 38,844,017 \times 32,104 \times 45.2\%[/tex]

                   [tex]= 38,844,017 \times 32,104 \times 45.2\%\\\\= 38,844,017 \times 32,104 \times \dfrac{45.2}{100}\\\\= 38,844,017 \times 32,104 \times 0.452\\\\=5.63666 \times 10^{11}[/tex]

Further, the difference between the tax of the two countries can be written as,

[tex]\text{Differene in the tax}= Tax_{France} - Tax_{Germany} = 85,930,190,677[/tex]

hence, the French government gathers €85,930,190,677 more than the German government.

Learn more about Percentage:

https://brainly.com/question/6972121

Answer:

Based on the information in the table, how do the annual tax revenues of Germany and France compare to one another?

a. }  The French government gathers €85,930,190,677 more than the German government.

b. }   The French government gathers €543,141,128,984 more than the German government.

c. }   The German government gathers €309,680,310,056 more than the French government.

d.}   The German government gathers €223,750,119,378 more than the French government.

Step-by-step explanation:

Correct on Edge 2022

Rewrite the equation 3x – 5y=30 in slope-intercept form.
a. y= -3/5x +30

b. y= -5/3x -6

C. x= 5/3y -6

d. y = 3/5x - 6

Answers

Answer: D) y = 3/5x - 6

The correct answer is D. The equation in slope-intercept form is y = 3/5x - 6.

Step-by-step explanation:

Hope this helps =)

the students at lincoln middle school are being split into 5 equal teams for dodgeball. each team has 20 people on it. how many total students are there?

Answers

Answer:

100

Step-by-step explanation:

5 x 20 is equal too one hundred

REALLY EASY POINTS
-
What are the values of a positive attitude?

Answers

Answer:

3 values of postivity is Optimistim, Kindness, and an open mind/Growth mind set.

Step-by-step explanation:

If f(x) = 9/4x, what is the value of f(-10)

Answers

Step-by-step explanation:

Substitute f(-10) into the function:

[tex]f(-10)=\frac{9}{4(-10)}[/tex]

Multiply:

[tex]f(-10)=\frac{9}{(-40)}[/tex]

Simplify:

[tex]f(-10)=-0.225[/tex]


Write an equation in slope-intercept form for the line with slope - 3/5 and y-intercept -1. Then graph the line.

Answers

Answer: equation: y= -3/5x - 1

See the attached image

heeeeelppppp please heeelpppp omg 25 points

Answers

Answer:

The fraction, or the one on the right is larger by just a few decimals.

Step-by-step explanation:

Have an amazing day :D

What is the solution to the proportion? (1 point)

Answers

Answer:

Your answer would be 25.

Evaluate the function

Answers

Answer:

[tex]f(10) \: is \: \: - 183[/tex]

Step-by-step explanation:

[tex]f(x) = { - 2x}^{2} + 17[/tex]

Question :

Find f(10) ?

Solution :

[tex]f(x) = { - 2x}^{2} + 17[/tex]

Substitute x = 10

[tex]f(10) = - 2 {(10)}^{2} + 17[/tex]

[tex] f(10) = - 2(100) + 17[/tex]

[tex]f(10) = - 200 + 17[/tex]

[tex] \boxed{f(10) = - 183}[/tex]

What is the volume of this figure

Answers

Answer :

22 Cubic Units Enjoy.

◊ YusuCr ◊

How many lines of symmetry does a scalene triangle have.

Answers

Answer:

Your answer would be 0.

Hope this helps :D

can someone pls help me on this question i’ve literally been stuck on it all day

Answers

Let me know if you have questions

Solve Tangent (x minus pi) minus cosine (x minus StartFraction 3 pi Over 2 EndFraction) = 0, x is an element of left-brace 0, 2 pi).

Answers

Answer:

  x ∈ {0, π, 2π}

Step-by-step explanation:

The expression can be simplified, which facilitates an answer.

  tan(x -π) -cos(x -3π/2) = 0

The tangent function has a period of π, so tan(x-π) = tan(x). The cosine function shifted right by 3π/2 is equivalent to the opposite of the sine function.

  tan(x) +sin(x) = 0 . . . . substitute simpler equivalents

  sin(x)/cos(x) +sin(x) = 0 . . . . use equivalent for tan(x)

  sin(x)(1/cos(x) +1) = 0 . . . . factor out sin(x)

  sin(x)(cos(x)+1)/cos(x) . . . . . combine terms to a single fraction

This has solutions where sin(x) = 0 and where cos(x) = -1. Those solutions are integer multiples of π.

  x ∈ {0, π, 2π}

Answer:

B

Step-by-step explanation:

-1 < x < 4
x is an integer.
Write down the possible values of x.

Answers

Answer:

0, 1, 2, 3

Step-by-step explanation:

-1 < x < 4 means that x has to be an integer (whole number aka no fractions)  between -1 and 4. Note that the < and > means that x cannot be -1 or 4 since it has to be greater than -1, or smaller than 4.

I'm very confused, can someone explain this to me?

Answers

Answer: 118 degrees

Step-by-step explanation:

By the exterior angle theorem.

3x + 12 + 2x + 16 = 6x + 10

5x + 28 = 6x + 10

x = 18

So measure of angle 3 = 6(18) + 10 = 118 degrees

Math question from my quizziz, I don't know if it's 1/a^9 or a^9

Answers

Answer:

red or 1/a9

Step-by-step explanation:

with that it is

a^ (3-12)

a^ (-9)

and then you can't have -9 in the top so you put it on the bottom

1/ a^9

Answer:

[tex]\frac{1}{a^9}[/tex]

Step-by-step explanation:

Cancel the common factor of [tex]a^3[/tex] and [tex]a^1^2[/tex]

[tex]a^3^-^1^2=a^-9[/tex]

Same things as 3-12 = -9

Hence, [Red] or [tex]\frac{1}{a^9}[/tex] is the correct Answer.

[RevyBreeze]

Please help! It's homework!

Answers

Answer:

Can’t see clearly

** if u can answer this quickly it will be very appreciated!**
Fill in each blank with a number so that every row, column, and diagonal so that it adds up to the same total.

Answers

Answer:

9 -5 -4 6

-2 4 3 1

2 0 -1 5

-3 7 8 -6

the scale of a map is 1cm : 17km. find the actual distance corresponding to the map distance. the distance on the map is 2.5cm

Answers

Step-by-step explanation:

1cm:17km so

2.5cm=17*2.5=42.5

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