HELP TIMER Write the equation of a hyperbola centered at the origin with x-intercept +/- 4 and foci of +/-2(squareroot 5)

HELP TIMER Write The Equation Of A Hyperbola Centered At The Origin With X-intercept +/- 4 And Foci Of

Answers

Answer 1

Given:

x-intercepts of the hyperbola are ±4.

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

Center of the hyperbola is at origin.

To find:

The equation of the hyperbola.

Solution:

The general equation of a hyperbola:

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

Where, (h,k) is the center of the hyperbola, ±a are x-intercepts, [tex](\pm c,0)[/tex] are foci.

Center of the hyperbola is at origin. So, h=0 and k=0.

x-intercepts of the hyperbola are ±4. So,

[tex]\pm a=\pm 4[/tex]

[tex]a=4[/tex]

The foci of hyperbola are [tex]\pm 2\sqrt{5}[/tex].

[tex]\pm c=\pm 2\sqrt{5}[/tex]

[tex]c=2\sqrt{5}[/tex]

We know that,

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

[tex](4)^2+b^2=(2\sqrt{5})^2[/tex]

[tex]16+b^2=20[/tex]

[tex]b^2=20-16[/tex]

[tex]b^2=4[/tex]

Taking square root on both sides, we get

[tex]b=\sqrt{4}[/tex]                    [b>0]

[tex]b=2[/tex]

Substituting [tex]h=0,k=0,a=4,b=2[/tex] in (i), we get

[tex]\dfrac{(x-0)^2}{4^2}-\dfrac{(y-0)^2}{2^2}=1[/tex]

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

Therefore, the correct option is (d).


Related Questions

SOMEONE HELP ME PLEASE

Answers

Answer:

The missing value is 5/2

Step-by-step explanation:

Find the surface area of each solid figure

Answers

Answer:

First find the SA of the triangular figure

4 x 3 = 12 cm^2 (the triangles on the sides)

2 x 3 = 6 cm^2 (the back square)

2 x 5 = 10 cm^2 (the slanted square)

*I'm not sure if this question includes the bottom of the triangle but here it is anyways

4 x 2 = 8 cm^2

Including the bottom the SA of the triangular figure is:

12 + 6 + 10 + 8 = 36 cm^2

Find the SA of the rectangular shape

4 x 2 = 8 cm^2 (the bottom square)

2 x 6 = 12 x 2 = 24 cm^2 (the sides)

4 x 6 = 24 x 2 = 48 cm^2 (the front and back)

Add them up

8 + 24 + 48 = 80 cm^2

If you wanted to find the SA of the whole figure it would be:

12 + 6 + 10 + 8 + 24 + 48 = 108 cm^2

Hope this helps!

Simplify:{x(6x - 1
A)
B)
2x-1
9
2x
x-
2x7.5
D

Answers

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {D. \:= 2 {x}^{2} - \frac{1}{3} x}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

[tex] \frac{1}{3} x \: ( \: 6x - 1 \: )\\[/tex]

[tex] = \frac{x \: ( \: 6x - 1 \: )}{3}\\[/tex]

[tex] = \frac{6 {x}^{2} - x}{3} \\[/tex]

[tex] = \frac{6 {x}^{2} }{3} - \frac{x}{3}\\ [/tex]

[tex] = 2 {x}^{2} - \frac{1}{3} x\\[/tex]

[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35♛}}}}}[/tex]

Sum of 5x^2+2x and 4-x^2

Answers

Answer:

4x^2 + 2x + 4

Step-by-step explanation:

5x^2 + 2x + 4 - x^2

4x^2 + 2x + 4

Answer:

2(2x^2 + x + 2)

Step-by-step explanation:

5x^2+2x + 4-x^2

Re arrange so like terms are next to each other

Keep the same symbol that is at the front of the term when moving it

5x^2 - x^2 + 2x + 4

We will just do the first part first

5x^2 - x^2

5x^2 - 1x^2 (is the same thing as above)

So because they are like terms (are both x^2)

We can just minus 1 from 5

5-1=4

So 4x^2

Now the equation is

4x^2 + 2x + 4

This is as small as it gets but you can also bring it to this

4, 2 and 4 all are divisible by 2 so

2(2x^2 + x + 2)

Steve Ballmer, the current CEO of Microsoft, used to be the manager of his college football team. Among his duties, he had to be sure the players were hydrated. When nearby construction forced a water shut off, Steve went to the Star Market to purchase bottles of water. He needed a total of 80 liters of water. Star Market sold water in two liter bottles and in half liter bottles. What possible combinations of the small and large bottles might he purchase in order to bring 80 liters to the football team?
a. Write an equation that models the possible combinations of half liter bottles and two liter bottles that would total 80 liters. (Be sure to define the variables.)
b. What is the x-intercept and what does it represent?
c. What is the y-intercept and what does it represent?

Answers

9514 1404 393

Answer:

  a.  x + 4y = 160

  b.  160

  c.  40

Step-by-step explanation:

a. We can define the variables as ...

  x = number of 1/2-liter bottles

  y = number of 2-liter bottles

For the total number of liters to be 80, we require

  1/2x + 2y = 80

We can multiply this by 2 to eliminate the fraction.

  x + 4y = 160

__

b. The x-intercept is 160. It is the number of 1/2-liter bottles required when no 2-liter bottles are used.

__

c. The y-intercept is 40. It is the number of 2-liter bottles required when no 1/2-liter bottles are used.

Margot surveyed a random sample of 180 people from the United States about their favorite sports to watch. Then she sent separate, similar, survey to a random sample of 180 people from the United Kingdom. Here are the results:

Favorite sport to watch United States United kingdom Total
Basketball 60 51 111
Football 67 14 81
Soccer 28 86 114
Tennis 25 29 54
Total 180 180 360

Margot wants to perform a x^2 test of homogeneity on these results. What is the expected count for the cell corresponding to people from the United Kingdom whose favorite sports to watch is tennis?

Answers

Answer:

27

Step-by-step explanation:

The expected count in a χ² test can be obtained thus :

Expected count for each each point in a two way table ::

(row total * column total) / total

Therefore, expected count for cell corresponding to people from United Kingdom whose favorite sport is tennis :

Row total = (51+14+86+29) = 180

Column total = (25 + 29) = 54

Total = 360

Hence,

Expected count = (180 * 54) / 360

Expected count = 27

solve the system of equations y=x-7 y=x^2-9x+18

Answers

9514 1404 393

Answer:

  (x, y) = (5, -2)

Step-by-step explanation:

Equating expressions for y, we have ...

  x^2 -9x +18 = x -7

  x^2 -10x +25 = 0 . . . . . add 7-x to both sides

  (x -5)^2 = 0 . . . . . . . . factor

The value of x that makes the factor(s) zero is x=5. The corresponding value of y is ...

  y = x -7 = 5 -7 = -2

The solution is (x, y) = (5, -2).

What is the area of the parallelogram shown?

Answers

Answer:

Area = 96 square m

Step-by-step explanation:

[tex]Area = base \times height = 12 \times 8 = 96 \ m^2[/tex]

Answer:

The area of parallelogram is 96 m ².

Step-by-step explanation:

According to the question , we have given a parallelogram with base 12 m and height is 8 m. We need to find the area of parallelogram.

Solution :-

Using Formula

Area of parallelogram = Base × Height

Substitute the values into this formula

Area of parallelogram = 12 m × 8 m

multiply, we get

Area of parallelogram = 96 m²

Therefore, The area of parallelogram is 96 m ².

Solve for X in the triangle. Round your answer to the nearest tenth

Answers

Answer:

[tex]\displaystyle x \approx 9.9[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Trigonometry

[Right Triangles Only] SOHCAHTOA[Right Triangles Only] sinθ = opposite over hypotenuse

Step-by-step explanation:

Step 1: Define

Identify variables

Angle θ = 64°

Opposite Leg = x

Hypotenuse = 11

Step 2: Solve for x

Substitute in variables [sine]:                                                                           [tex]\displaystyle sin(64^\circ) = \frac{x}{11}[/tex][Multiplication Property of Equality] Multiply 11 on both sides:                      [tex]\displaystyle 11sin(64^\circ) = x[/tex]Rewrite:                                                                                                             [tex]\displaystyle x = 11sin(64^\circ)[/tex]Evaluate:                                                                                                           [tex]\displaystyle x = 9.88673[/tex]Round:                                                                                                               [tex]\displaystyle x \approx 9.9[/tex]

Pls help ASAP!!!!!!!!!!! I NEED HELP IMMEDIATELY!!!
Jaime had ten posters, but only five could fit on his closet door. How many different ways can he arrange the five posters out of the ten on his closet door?



A. 252
B. 648
C. 6,048
D. 30,240

Answers

Answer:

its c

Step-by-step explanation:

The answer to the question is 6,048

Please help me with this question

Answers

9514 1404 393

Answer:

  D(1, 2)

Step-by-step explanation:

The ordered pair is always (x-coordinate, y-coordinate).

The x-coordinate is the distance to the right of the y-axis. (It is negative for points left of the y-axis.) Here, point D lies 1 unit right of the y-axis, so its x-coordinate is 1.

The y-coordinate is the distance above the x-axis. (It is negative for points below the x-axis). Here, point D lies 2 units above the x-axis, so its y-coordinate is 2.

The ordered pair describing the location of D is ...

  (x-coordinate, y-coordinate) = (1, 2)

In △CDE, DE=14, CE=9, and m∠E=71∘. What is the length of CD⎯⎯⎯⎯⎯⎯? Enter your answer, rounded to the nearest hundredth, in the box.

Answers

Answer:

13.96units

Step-by-step explanation:

To get the length of CD, we will use the cosine rule as shown:

CD² = DE²+CE²-2(DE)(CE)cos m<E

Substitute the given values

CD² = 14²+9²-2(14)(9)cos71

CD² = 196 + 81 - 252cos71

CD² =277 - 252cos71

CD² = 277 - 82.0431

CD² = 194.95682

CD = √194.95682

CD = 13.96 units

Hence the length of CD of 13.96units

Bill can hit a bucket of 323 golf balls in 17 hours.
How many golf balls can Bill hit in 23 hours?

Answers

Bill can hit 437 golf balls in 23 hours.

Explanation:

Bill’s unit rate of golf balls per hour is:
323 ÷ 17 = 19

19 golf balls per hour

To find how many golf balls Bill can hit in 23 hours, multiply:
19 • 23 = 437

Therefore, Bill can hit 437 golf balls in 23 hours.

Please, say if my answer is right
If its, glad to help!

-SpaceMarsh

I was wondering if someone could answer this :)

Answers

Answer:

17

Step-by-step explanation:

2a+30 = 4a-4

+4 +4

2a+34 = 4a

-2a -2a

34 = 2a

÷2 ÷2

a=17

Hope this helps! :)

Answer:

A = 17

Step-by-step explanation:

Opposite angles are congruent in a parallelogram

Hence 2a + 30 = 4a - 4

( Note that we've just created an equation that we can use to solve for a)

We now solve for a

2a + 30 = 4a - 4

Add 4 to both sides

2a + 34 = 4a

Subtract 2a from both sides

34 = 2a

Divide both sides by 2

a = 17

I need big help on this one

Answers

It’s a black screen so the answer would be black

What is the value of z in the equation 3z+9=z?

Answers

In the exact form, Z equals -9/2

It take 6 Pounds of flour to make 36 cakes. How much flour is needed to make 9 cakes?

Answers

Answer:

54 pounds

Step-by-step explanation:

To find out how much flour is needed to make 9 cakes, we first need to find out how much much flour is needed to make 1 cake. For that, we need to divide 6 by 36. That will give you 6. Now that we know how much flour is needed to make 1 cake, we will just have to multiply 6 by 9 to find out how much flour is needed to make 9 cakes. That will give you 54 pounds, which is your final answer.

Use the graph to answer the question.
What is [tex]\frac{AD}{AB}[/tex] in simplest form?
A. [tex]\frac{10}{3}[/tex]
B. [tex]\frac{1}{3}[/tex]
C. [tex]\frac{17}{5}[/tex]
D. 3

Answers

Answer:

D. 3

Step-by-step explanation:

Distance between A and D = AD = 9 units

Distance between A and B = AB = 3 units

[tex] \frac{AD}{AB} = \frac{9}{3} [/tex]

Simplify by dividing

[tex] \frac{AD}{AB} = \frac{3}{1} [/tex]

[tex] \frac{AD}{AB} = 3 [/tex]

The answer is 3

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. y2(y2 − 4) = x2(x2 − 5) (0, −2) (devil's curve)

Answers

Answer:

Step-by-step explanation:

Given that:

[tex]y^2 (y^2-4) = x^2(x^2 -5)[/tex]

at point (0, -2)

[tex]\implies y^4 -4y^2 = x^4 -5x^2[/tex]

Taking the differential from the equation above with respect to x;

[tex]4y^3 \dfrac{dy}{dx}-8y \dfrac{dy}{dx}= 4x^3 -10x[/tex]

Collect like terms

[tex](4y^3 -8y)\dfrac{dy}{dx}= 4x^3 -10x[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

Hence, the slope of the tangent line m can be said to be:

[tex]\dfrac{dy}{dx}= \dfrac{4x^3 -10x}{4y^3-8y}[/tex]

At point (0,-2)

[tex]\dfrac{dy}{dx}= \dfrac{4(0)^3 -10(0)}{4(-2)^3-8-(2)}[/tex]

[tex]\dfrac{dy}{dx}= \dfrac{0 -0}{4(-8)+16}[/tex]

[tex]\dfrac{dy}{dx}= 0[/tex]

m = 0

So, we now have the equation of the tangent line with slope m = 0 moving through the point (x, y) = (0, -2) to be:

(y - y₁ = m(x - x₁))

y + 2 = 0(x - 0)

y + 2 = 0

y = -2

62x+2.63x = 1
Solve
EN

Answers

Step-by-step explanation:

answer is in photo above

Answer:

-2/5

Step-by-step explanation:

Find all real zeros of the function y = -7x + 8

Answers

9514 1404 393

Answer:

  x = 8/7

Step-by-step explanation:

The only real zero of this linear function is the value of x that makes y=0:

  0 = -7x +8

  7x = 8 . . . . . . add 7x

  x = 8/7 . . . . . .divide by 7

Find z such that 97.5% of the standard normal curve lies to the left of z. (Enter a number. Round your answer to two decimal places.)

Answers

Answer:

z=1.96

Step-by-step explanation:

Using normal distribution table or technology, 97.5% corresponds to z=1.959964, generally denoted z=1.96, or 1.96 standard deviations above the mean.

(above value obtained from R)

X Y
-10 2
-15 3
-25 5

Determine whether y varies directly with x. If so, find the constant of variation and write the equation

Answers

Answer:

x = -5y

Step-by-step explanation:

x = ay

-10 = 2a

a = -5

x = ay

-15 = 3a

a = -5

x = ay

-25 = 5a

a = -5

find the value of x. what is the relationship of these 2 angles? set up and solve an equation

Answers

As it is right angled, thus it will be equal to 90.

= 2x + 5 + x + 25 = 90

= 3x + 30 = 90

= 3x = 60

= x = 60/3

= x = 20

Answer:

x = 20°

Step-by-step explanation:

[tex]2x + 5 + x + 25 = 90 \\ 3x + 30 = 90 \\ 3x = 90 - 30 \\ 3x = 60 \\ x = \frac{60}{3} \\ x = 20 \\ [/tex]

factorize for me



y + 3y + 2-sin2x=0​

Answers

Answer:

−(−4y−2+sin2(x))=0

Step-by-step explanation:

All the edges of the object in the diagram are equal in length. The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges. What
is the shape of the cross-section resulting from the cut?
СА.
an equilateral triangle
B.
a square
C.
a rhombus
D.
a regular hexagon

Answers

Answer:

The shape from the cross-section resulting from the cut would be a Rhombus

Step-by-step explanation:

Edmentum Plato users!

The shape of the cross-section resulting from the cut is C. Rhombus.

What is a rhombus?

A rhombus simply means a shape that has opposite sides to be parallel and the sides are equal.

Here, the information states that the edges of the object in the diagram are equal in length and that the object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.

Therefore, the shape of the cross-section resulting from the cut is a rhombus.

Learn more about rhombus on:

https://brainly.com/question/20627264

3. Find the measure of the exterior angle in the diagram below.​

Answers

Answer:

the value of x is 29° which is b

Help with this Geometry question please

Answers

Answer:

Angle A = [tex]77^{o}[/tex]

Step-by-step explanation:

cos A = adjacent / hypotenuse

cos A = 18/82

cos A = 0.22

A = [tex]cos ^{-1}[/tex]0.22

A = [tex]77^{o}[/tex]

Find the value of X

Answers

Answer:

100°

Step-by-step explanation:

the lower right angle is 180-149 = 31°

the sum of all three angles in a triangle is 180°.

so the solution is 180-31-49

PLEASE HELP ME I HAVE TO PASS THIS TEST

30 POINTS

Answers

Answer:

Hi, there the answer is

These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Hope This Helps :)

Step-by-step explanation:

First degree equations

A first degree equation has the form

ax + b = 0

There are some special cases where the equation can have one, infinitely many or no solution

If , the equation has exactly one solution

If a=0 and b=0 the equation has infinitely many solutions, because it doesn't matter the value of x, it will always be true that 0=0

If a=0 and  the equation has no solution, because it will be equivalent to b=0 and we are saying it's not true. No matter what x is, it's a false statement.

We have been given some equations, we only need to put them in standard form

-5x + 12 = –12x – 12

Rearranging

7x + 24 = 0

It has exactly one solution because a is not zero

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

-5x + 12 = 5x + 12

Rearranging

-10x + 0 = 0

It has exactly one solution because a is not zero

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

-5x + 12 = 5x – 5

Rearranging

-10x + 17 = 0

It has exactly one solution because a is not zero

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

-5x + 12 = -5x – 12

Rearranging

0x + 24 = 0

It has no solution, no matter what the value of x is, it's impossible that 24=0

Answer: These are the equations with exactly one solution

-5x + 12 = –12x – 12

-5x + 12 = 5x + 12

-5x + 12 = 5x – 5

Hi the answer is -5x+12=-12x-12
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