What is the equation of a hyperbola with a = 1 and c = 9? Assume that the transverse axis is horizontal.

What Is The Equation Of A Hyperbola With A = 1 And C = 9? Assume That The Transverse Axis Is Horizontal.
What Is The Equation Of A Hyperbola With A = 1 And C = 9? Assume That The Transverse Axis Is Horizontal.
What Is The Equation Of A Hyperbola With A = 1 And C = 9? Assume That The Transverse Axis Is Horizontal.
What Is The Equation Of A Hyperbola With A = 1 And C = 9? Assume That The Transverse Axis Is Horizontal.

Answers

Answer 1

Answer:

Step-by-step explanation:

The general formula for a horizontal hyperbola :

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

Given: a = 1 we know a² = 1 ,and that c = 9 so we know c² = 9² = 81

We also know that the relation between a, b, c for a hyperbola is c²= a²+b²

c²= a²+b², substitute what we know

81 = 1 +b², subtract 1 from both sides of the equation

80 = b²

The equation of our hyperbola is:

[tex]\frac{x^{2} }{1 } -\frac{y^{2} }{80 } =1[/tex]  or  [tex]x^{2} -\frac{y^{2} }{80} =1[/tex]


Related Questions

9
Emily drives 186 miles in 3 hours.
(a) What is her average speed?

Answers

Answer:

Her average speed would be 62 mph.

Step-by-step explanation:

Step 1. Do 186 divided by 3
Step 2. The answer you would get is 62
Step 3. Label to get 62 miles per hour (mph)
I hope that this helps! :)

Step-by-step explanation:

Displacement = 186 miles

Time taken = 3hours

Average speed = ?

Now,

[tex]average \: speed = \frac{total \: distnce}{total \: time \: } \\ = \frac{186}{3} \\ [/tex]

= 62 miles per hour

How do I find the difference in the simplest form?

Answers

Answer:

2

Step-by-step explanation:

[tex] \frac{8x}{4x - 7} - \frac{14}{4x - 7} \\ \\ = \frac{8x - 14}{4x - 7} \\ \\ = \frac{2 \cancel{(4x - 7)}}{\cancel{(4x - 7)}} \\ \\ = 2[/tex]

Solve: 101x-99y=103
-99x+101y=-97

Answers

Answer:

[tex]x=2; y=1[/tex]

Step-by-step explanation:

Let's remember that if we replace one equation in a system with a linear combination of the equations (ie adding or subtracting them together, after multiplying them with some nice numbers) we are left with an equivalent system. So let's add and subtract them together, and use the new equations to work with.

[tex]I+II: 2x+2y=6\\I-II:200x-200y=200[/tex]

Better, now let's simplify the expression and let's use the new system

[tex]x+y=3\\x-y=1[/tex]

Done. At this point you can use whatever method you like to solve the system to get to the final solution. Adding and subtracting works great, and you get [tex]x=2, y=1[/tex] which, if you check by replacing in the original, is indeed a valid solution.

After plotting the data where x=the side of a polygon, and f(x) = the area of the polygon, Jack used technology and
determined the appropriate model to approximate the area of the polygon, F(x) = x^2 + 3x + 2. Use the model Jack
created to predict the area of a polygon that has a side length of 3.

10
18
19
020

Answers

Answer: 19

Step-by-step explanation:

As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1

Therefore, f(3) = 19

Problem 1: Verify whether these two functions are inverses: (x + 5) f(x) = (2x + 1) and g(x) = (5 - x) (2x - 1) What is g(x))? Use your keyboard and the keypad to enter your answer. Then click Done

Answers

g(f(x)) = x

What is inverse function?

An inverse function is defined as a function, which can reverse into another function.

[tex]f(x)= \frac{(x + 5)}{(2x + 1)}[/tex]

[tex]g(x)= \frac{(5 - x)}{(2x - 1)}[/tex]

 [tex]g(f(x))=g( \frac{(x+5)}{(2x +1)})[/tex]

Substitute the value of f(x),

[tex]g(f(x))= \frac{(5 - \frac{(x + 5)}{(2x + 1)})}{(2 \frac{(x + 5)}{(2x + 1)} - 1)}[/tex]

[tex]g(f(x))= \frac{\frac{10x+5-x-5}{2x+1} }{ \frac{2x+10-2x-1}{2x+1}}[/tex]

[tex]g(f(x)) = \frac{9x}{9}[/tex]

g(f(x)) = x

Hence, g(f(x)) = x

Learn more about inverse function

https://brainly.com/question/2541698

#SPJ2

Solve by completing the square:
x2 + 2x-8= 0
-8
a.
x = -4 or 2
b. X= 4 or 2
-
=
c.
x= -4 or - 2
d. X= 4 or - 2
x

Answers

The answer is 4 trust me bro

Find MQ in parallelogram LMNQ .

Answers

Answer:

MQ = 16.4

By the Parallelogram Diagonals Theorem , MP = PQ

So MQ = 2 · MP

Step-by-step explanation:

Parallelogram Diagonals Theorem

The diagonals of a parallelogram bisect each other, i.e. they divide each other into two equal parts.

P is the point of intersection of the diagonals.

Therefore, MP = PQ and LP = PN

If MP = 8.2, then PQ = 8.2

⇒ MQ = 8.2 + 8.2 = 16.4

Need help with math probelm if do 5 stars and brainly points

Answers

Set up:-

Find volume of closet storageFind volume of each cubeDivide and get no of cubes

Solution:-

Here it's a cuboid

Length=L=6.5ftBreadth=B=4ftHeight=H=12.5ft

Volume:-

[tex]\\ \rm\rightarrowtail V=LBH[/tex]

[tex]\\ \rm\rightarrowtail V=6.5(4)(12.5)[/tex]

[tex]\\ \rm\rightarrowtail V=325ft^3[/tex]

For cubes

sides=0.25ft

Volume:-

[tex]\\ \rm\rightarrowtail V=side^3[/tex]

[tex]\\ \rm\rightarrowtail V=(0.25)^3[/tex]

[tex]\\ \rm\rightarrowtail V=0.015625ft^3[/tex]

Now

Total cubes:-

[tex]\\ \rm\rightarrowtail \dfrac{325}{0.015625}[/tex]

[tex]\\ \rm\rightarrowtail 20800cubes[/tex]

hey guys can you please help me with these questions​ please explained them

Answers

B for question 12

B for question 13

Step-by-step explanation:

U = Union

n= intercestion

B'= not b

A"= not a

so AnB'

should be B

if 2.50 = 1

2.50x8=

20

1×8 =

8

should be $8

The accompanying diagram show a cross-section of a rectangular pyramid. The cross sectional area is 36in and is 3 inches from the vertex of the pyramid. If the height of the pyramid is 5 inches, what is the area of the rectangular base?

Answers

The area of the rectangular base is the amount of space on the rectangular base

The area of the rectangular base is 60 square inches

How to determine the area of the rectangular base?

The question is incomplete; as the diagram is not given.

So, I will apply the concept of similar shapes to determine the area of the rectangular base

To determine the area of the rectangular base, we make use of the following equivalent ratio:

Ratio = Height : Area

This gives

3 : 36 = 5 : Area

Express as fraction

36/3 = Area/5

Evaluate the quotient

12 = Area/5

Multiply both sides by 5

Area = 60

Hence, the area of the rectangular base is 60 square inches

Read more about areas at:

https://brainly.com/question/24487155

Martina is ordering an ice cream dessert. She must order a size and a flavor of ice cream. There are 4 sizes and 2 flavors to choose from. How many different
cream desserts could she order?

Answers

Answer: 8.

Step-by-step explanation: There are 4 sizes, so let's say that the sizes are small, medium, large, and extra large.  There are 2 flavors, so let's say that the flavors are chocolate and vanilla.  The possible combinations are below:

Small chocolateMedium chocolateLarge chocolateExtra large chocolateSmall vanillaMedium vanillaLarge vanillaExtra large vanilla

As you can see, there are 8 possible combinations that she can choose from as far as 4 sizes and 2 flavors go.

Have a great day! :)

2. Find the length of AD if the length of AB is 14 units, the length of BC is 5 units, and the length of CD is 8 units,​

Answers

Answer: sqrt(285)

Step-by-step explanation:

Peter is buying a circular rug for his bedroom. The rug has an area of 40 square feet. What is the approximate diameter of the rug? Show your work or explain your answer.

Answers

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

What is area?

Area is the amount of space occupied by a two dimensional shape or object.

The area of a circle is given by:

Area = π * diameter²/4

The rug has an area of 40 square feet. Hence:

40 = π * diameter²/4

Diameter = 7.14 feet

The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.

Find out more on area at: https://brainly.com/question/25292087


A minibus drives with a constant speed
of 32 km/h. How long will it take to travel
a distance of 80 kilometers?

Answers

Given Information :-

A minibus drives with a constant speed of 32 km/hr

To Find :-

Time taken to travel a distance of 80 kilometers

Formula Used :-

[tex] \qquad \star \: \red{ \underline{ \boxed{ \sf Time = \dfrac {Distance} {Speed} }}} \: \star[/tex]

Solution :-

Putting the values in the formula, we get,

[tex] \sf \longrightarrow Time = \dfrac{80 }{32} \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \cancel{\frac{80}{32} } \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = \dfrac{10}{4} \: \: \: \: \: \: \: \\ \\ \\ \sf \longrightarrow Time = 2.5 \: hrs \\ \\ [/tex]

Thus, the time taken to travel 80 km with that speed is 2.5 hours.

[tex] \underline{ \rule{227pt}{2pt}}[/tex]

Find the domain of
[tex]y = \frac{1}{(1 - \sin(x) } [/tex]

Answers

Let's see

Denominator must not be equal to zero or the function becomes undefined

[tex]\\ \rm\rightarrowtail 1-sinx\neq 0[/tex]

[tex]\\ \rm\rightarrowtail sinx\neq 1[/tex]

[tex]\\ \rm\rightarrowtail x\neq \dfrac{n\pi}{2}[/tex]

So

[tex]\\ \rm\rightarrowtail Domain\in R-\left\{\dfrac{n\pi}{2}\right\}[/tex]

A rectangular room measures 18 ft by 37 ft. How many
square feet of tile are needed to cover the floor?

Answers

Step-by-step explanation:

the area of a rectangle is length × width.

in our case

37 × 18 = 666 ft²

so, we need 666 ft² of tiles.

Answer:

666 square feet

Step-by-step explanation:

To find the number of square feet of tile, we need to find the area:

A = L × W

A = 18 × 37

A = 666 ft²

Martin is an artist who molds plaster into unique shapes.
How much plaster can Martin fit into the mold shown?

Answers

Step-by-step explanation:

the volume of this object is the sum of the volume of the 2 blocks.

the large block is a cube of 4×4×4 = 64 ft³

the small block is 1×1×2 = 2 ft³

so, in total, he can fit 64+2 = 66 ft³ of plaster into the mold.

When 3(2x^2+4x+7)−(x^2−8x+11) is simplified, what is the coefficient of the x term?

Answers

Answer:

Step-by-step explanation:

when  3(2x^2+4x+7)−(x^2−8x+11) is solved you get

5x^2 + 20x + 10.

the x term is

2

+

2

,

0

)

,

(

2

2

,

0

)

[tex]3(2x^2+4x+7)-(x^2-8x+11)\\\\=6x^2 +12x + 21 -x^2+8x -11\\\\=5x^2+20x +10\\\\\text{The coefficient of the x term is 20}[/tex]

find x correct to 2 decimal places

Answers

Answer:

Step-by-step explanation:

The value of x in the triangle is 205.24 calculated by using tan function.

By using tan function we find the value of x.

Let us divide x to two parts which includes two right triangles.

We know than tan function is a ratio of opposite side and adjacent side.

tan 55 = 106/adj

adj= 106/1.428

adj=74.22

Now let us find the adjacent side length of larger triangle similarly.

tan 39  = 106/ adj

0.809 = 106/adj

adj=106/0.809

adj=131.025

So the value of x is 74.22+131.025

=205.245

Hence, the value of x in the triangle is 205.24.

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ3

11. Maria's age is 3 years more than twice George's age. Which expression represents George's age in terms of Maria's?

Answers

Answer:

C

Step-by-step explanation:

Okay, the catch of this question is that they do a very good job of explaining Maria's age in terms of George's age, but they leave George's age in terms of Maria's all up to you.

First start off by doing an expression of what they explicitly give you. Maria's age in terms of George's age.

Let's use variables g, representing George's age and m representing Maria's age

m = 2g + 3

Okay, this is all dandy and all, but they ask us for George's age in terms of Maria's, so we need to isolate for g.

subtract the 3 from both sides, like so:

m - 3 = 2g

then divide 2 from both sides: (remember we're dividing the whole thing)

(m-3)/2 = g

Now we have an expression for George's age in terms of Maria's.

g = (m-3)/2 or [tex]g = \frac{m-3}{2}[/tex]

The answer that gives us this, is C.

If tanθ= 2/5 find cosθ using identities. This is in quad. 1.

Answers

Answer: 5/2

Step-by-step explanation:

What is the value of X?
Sin 55° = cos X.
Enter your answer in the box.

Answers

Answer:

x = 35°

Step-by-step explanation:

sin x = cos (90° - x)

sin 55° = cos (90° - 55°)

sin 55° = cos 35°

x = 35°

50 POINTS!
Exploiting for points will be reported.


Sophie deposited money into an account in which interest is compounded semiannually at a rate of 3.7%. She made no other deposits or withdrawals and the total amount in her account after 15 years was $12,158.10. How much did she deposit?

SHOW WORK FOR BRAINLIST

Answers

$7,015.11

total money accrued : $12,158.10years :  15 years rate of interest : 3.7%deposited : A

Depth meanings:

P is deposited moneysemiannually : 2 times in a yearA is received or acquired moneyt is time in yearsr is rate in percentage

[tex]\sf P = \dfrac{A} { (1 + \dfrac{r}{n})^{nt}}[/tex]

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{3.7\%}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = \dfrac{12,158.10} { (1 + \dfrac{0.037}{2})^{(2)(15)}}[/tex]

[tex]\rightarrow \sf P = 7015.113646[/tex]

Put the expressions in order from least to greatest.

Answers

Answer:

[tex]\frac{11^{4} }{11^{11} } ,\frac{1}{11^{-4} }, 11^{5}*11^{2}, (11^{-3})^{-3}[/tex]

Step-by-step explanation:

For this, you need to know the rules of exponents:

If the coefficient is the same, you can do things to it (which I will get into)

In this case, all the coefficients are 11, so we don't have to worry about the coefficients being different.

For the first one, you can subtract the denominator exponent by the numerator exponent like so:

[tex]11^{4} * 11^{-11} = 11^{-7}\\[/tex]

(When you multiply, you add the exponents)

Also, the rule is: [tex]x^{-y} = \frac{1}{x^{y} }[/tex] or [tex]\frac{1}{x^{-y} } = x^{y}[/tex]

For the second one, you can use the rule mentioned before:

[tex]\frac{1}{11^{-4} } = 11^{4}[/tex]

For the third one, you want to multiply the exponents (in these kinds of cases, you can multiply the exponent by the exponent)

So:

[tex](11^{-3} )^{-3} = 11^{9}[/tex]

Finally, the fourth one, you can simply just add the exponents:

[tex]11^{5} * 11^{2} = 11^{7}[/tex]

Then, just order them from least to greatest by their exponents value :)

In the diagram, the length of Line segment Y Z is twice the length of Line segment A Z.

Triangle X Y Z is shown. Angle X Y Z is a right angle. An altitude is drawn from point Y to point A on size Z X to form a right angle.

Line segment Y A is an altitude of ΔXYZ. What is the length of Line segment Y A?

5 StartRoot 3 EndRoot units
10 StartRoot 3 EndRoot units
15 units
20 units

Answers

Answer:

5 startrood 3 endroot units .

The length of YA from the figure is 10√3 units

Pythagoras theorem

According to the pythagoras theorem;

YZ² = AZ² + YA²

Given that YZ = 2AZ, hence;

20²  = 10² + YA²

YA²  = 400 - 100
YA²  = 300

YA = √300

YA = 10√3 units

Hence the length of YA from the figure is 10√3 units

learn more on Pythagoras theorem here:

https://brainly.com/question/343682

#SPJ9

what is the volume of a rectangular prism with height of 12 inches and a base with an area of 2 square inches.

Answers

Answer:

24 cubic inches

Step-by-step explanation:

Volume is side x side x side. You already have done side x side so it is just side x area.

How do I solve for X?

Answers

The value of x in the special right triangle is 39.60 ft.

Right angle triangle

Right angle triangle has one of its angles as 90 degrees. The side and angles can be found using trigonometric ratios.

Therefore, let's find the base of the triangle with 30 degrees.

sin 30° = opposite / hypotenuse

1 / 2 = 7 / b

b = 14 ft

Let's use the value(14 ft) to find the height of the biggest triangle.

sin 30 = opposite / hypotenuse

sin 30 = 14 / h

0.5h = 14

h = 14 / 0.5

h = 28 ft

Therefore, let's find the value of x .

sin 45° = 28 / x

x = 28 / 0.70710678118

x = 39.5979797464

x = 39.60 ft

learn more on right triangle here: https://brainly.com/question/10412877

What happens to the coordinates of a shape when the shape reflects about the x-axis? What happens to the
coordinates when the shape reflects about the y-axls? Explain.

Answers

Hey there!

Here's what happens to the coordinates of a point when it's reflected around the x-axis:

(x, y) --> (x, -y) or (x, -y) --> (x, y)

So the point's x-coordinate hasn't changed.

Here's what happens to the coordinates of a point when it's reflected around the y-axis:

(x, y)--> (-x, y) or (-x, y) --> (x, y)

So the point's y-coordinate hasn't changed.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power!

Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C

Answers

B)
It is the only logical answer. As it does not add an extra zero like C, and it doesn’t multiply the wrong number like A. Hope it helped!

Answer:

B

Step-by-step explanation:

62x4=248

4x2=8

6x4=24 and carry the 0 and get 240

240+8=248 and you get B

Determine the value of y, if x is -1

equation: y= | x |-4

Answers

Answer:

y = -3

Step-by-step explanation:

y = | x | - 4

y = | -1 | - 4

y = 1 - 4

y = -3

Comment any questions!

Other Questions
i need help please its due today Help Im so bad at math What is the trigonometric ratio for cosn? enter your answer, as a simplified fraction, in the boxes. $$ triangle l m n with right angle m. l m equals 15. l n equals 39. m n equals 36. In an experiment using a calorimeter, the following data was obtained:Mass of calorimeter + water .............150gMass of calorimeter ...100gFinal temperature of water 55oCInitial temperature of water . 25oCWhat is the total number of Joules absorbed by the water? As a team lead, Emilio has convened a group of five team members to solve an issue with the marketing campaign. This is an example of a(n) Classify each polynomial expression by number of terms and by degree. Identify the leading coefficient.Polynomial ExpressionTerm NameDegree NameLeading Coefficient3+ 4+122monomial2+5binomialtrinomial answer please i need help with this How do the roots and stem take part in the transport of water in a plant? please make a good explanation and make long answer pls! thanks :D The electric potential, which is a scalar field, may be represented graphically by equipotential curves. The lines of electric field may be obtained from those equipotentials. Four rectangles have been placed on the graph below. Assess the region of the graph where the magnitude of the electric field is greatest. Drag the label Emax to the rectangle in that region. Assess the region of the graph where the magnitude of the electric field is smallest. Drag the label Emin to the rectangle in that region. Are there exceptions to the rule that a defendant has a right to counsel at a lineup what is the definition of an average? P1 = (1,5). P2 = (x,2) .p1p2=5 Choose the correct connective. There may be two or more variants.1. We're studying now ... there's an interesting film on TV.2. I'd like to talk to you... I know you're busy. 3. ... her efforts, she failed the exam.4. ... we were having difficulties, we felt optimistic.5. We didn't win the game... all our hard work. 6. ... it rained a lot, we enjoyed our holiday.7. ... the traffic, they arrived in time.8. ... I was really tired, I couldn't sleep. Why can't the fire protection problems in a community be solved solely by building more fire stations and hiring more emergency response personnel? ) Which expression represents the SUM of n and 12? How does the climate of Chicago compare with that of Toronto? My son explained that the healthy vegetable side of his stomach felt full, but that the dessert side was very empty. the primary purpose of this sentence is to a entertain b persuade c inform Pls help me with this what is anemia, why do people with sickle cell anemia have anemia? If the volume of a cuboid is 120 cm' and it has a length of 10cm, a height of 4cm, the width of the cuboid is ? cm,