The equation of the hyperbola that has a center at ( 6 , 9 ) , a focus at ( 11 , 9 ) , and a vertex at ( 9 , 9 ) (x−C)^2/A^2−(y−D)^2/B^2=1

Answers

Answer 1

Answer:

[tex]A=-3[/tex]

[tex]C=6[/tex]

[tex]B=4[/tex]

[tex]D=9[/tex]

Step-by-step explanation:

From the question we are told that:

Center of hyperbola at ( 6 , 9 )

Focus of hyperbola at ( 11 , 9 )

Vertex of hyperbola at ( 9 , 9)

Equation of hyperbola [tex]\frac{(x-C)^2}{A^2} -\frac{(y-D)^2}{B^2}=1[/tex]

Generally the C and D of the hyperbola equation is mathematically given by

[tex]Centers (6,9)[/tex]

[tex]C=6[/tex]

[tex]D=9[/tex]

Generally the A and B a of the hyperbola equation is mathematically given by

 [tex]A=x_c-x_v[/tex]

 [tex]A=6-9[/tex]

 [tex]A=-3[/tex]

 [tex]C'=x_c-x_f[/tex]

 [tex]C'=6-11[/tex]

 [tex]C'=-5[/tex]

Therefore with Center,Focus ,Vertex on the same line

 [tex]B^2=C'^2-A^2[/tex]

 [tex]B^2=(-5^2)-(-3^2)^2[/tex]

 [tex]B^2=(25)-(9)[/tex]

 [tex]B^2=16[/tex]

 [tex]B=4[/tex]


Related Questions

Nathan cut an isosceles triangle from felt to
make a spirit banner. Two sides of his banne
had the following measures: 15 inches and
7 inches. Which could be the measure of the
third side of Nathan's banner?
A 20 inches
B 15 inches
C 10 inches
7 inches

Answers

Answer:

B) 15

Step-by-step explanation:

only options are 15 or 7 inches because the problem mentioned the triangle is isosceles (they have two equal sides)

we can eliminate 7 because of the triangle inequality theorem

if two sides of a triangle are 7 then their sum is only 14 and it would need to be greater than the third side of 15

A because it can’t be B and it Can’t be C so my answer is A

A rhombus has sides 11cm long the shorter diagonal of the rhombus is 8cm long find the size of the smaller angles of the rhombus correct to the nearest degree

Answers

Answer:

42.64°

Step-by-step explanation:

Note: A rhombus has all its sides equal, its opposite angle are equal, its  has bigger and smaller diagonal, diagonal bisect the angles and diagonal bisect each other.

From the diagram attached,

sinθ = opposite/adjacent

sinθ  = 4/11

θ = sin⁻¹(4/11)

θ = 21.32

Therefore, from the diagram,

The smaller angle of the rhombus = 2θ

The smaller angle of the rhombus = (2×21.32)

The smaller angle of the rhombus = 42.64°

Solve the equation for all values of x by completing the square,
x^2 + 2x = 35

Answers

Answer:

x = 5

Because, if you substitute 5 for x you will get 35.

5^2 + 2*5= 25+10, or 35

Step-by-step explanation:

anyone know the answer? its algrebra
Does the equation represent an exponential function?

y = 4 • 5x

Yes
No

Answers

Answer:

yes is rhe anwers that was that i put

Please help I don’t understand this

Answers

9514 1404 393

Answer:

  WV = 6

Step-by-step explanation:

The hash marks indicate the corresponding lines are the same length. That is, W is the midpoint of YZ, because YW ≅ WZ. Similarly, V is the midpoint of XY, because XV ≅ VY.

Using this information, it can be shown that ∆YWV ~ ∆YZX. This means corresponding sides have the same ratio.

Because YW is half of YZ, WV is half of ZX.

  YW/YZ = 1/2 = WV/ZX = WV/12

Multiplying by 12 gives the value of WV:

  WV = 12(1/2)

  WV = 6

_____

This is a long way to say that the midsegment (WV) is half the length of the base (ZX) of a triangle.

you do not have to exsplain

Answers

Answer:

V=87.92

Step-by-step explanation:

v=bh,V=3.14*2*2*7

Solve the system.
6x - y = -15
x+2y = 17
Enter your answer as a coordinate pair in the blank.

Answers

The coordinate pair of the given system is (-1,9)

What are coordinate pairs?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

Define Equation.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Multiply the first equation by 2 and add the equation 2(6x - y) = 2(-15)

Add the new equation 12x - 2y = -30 to the second equation

12x - 2y = -30, x+2y = 17, add the two equations to eliminate y

13x = -13

x = -1

Substitute -1 back into the equation x+2y = 17.

-1 + 2y = 17

2y = 18

y = 9

So the solution of the system is x = -1, y = 9

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A granola recipe calls for 3 cups of oats, 1 cup of almends. 1 cup of pecans, and 1 cup of dried fruit. What is the ratio of fruit to eats? Yolanda says that for every 2 cups of nuts, there are 2 cups of fruit. Explain why her answer is incorrect and give the correct ratio of nuts to fruit. Explain your answer.​

Answers

The ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that a granola recipe calls for 3 cups of oats, 1 cup of almonds. 1 cup of pecans, and 1 cup of dried fruit

The ratio of nuts to fruits is -

r = (3 oat cups + 1 almond cup + 1 pecan cup)/(1 dried fruit cup)

r = 5/1

5 : 1

For every 5 cups of nuts, there is 1 cup of dried fruit cup.

Therefore, the ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

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Can y’all help me and tell me the answer?

Answers

100!

100 is your answer because there is exactly 100 percentages in the number 100. So 65% of that would be equal to 65.

PLEASE HELP!! i’ll mark you brainliest please !

Answers

it’s c i think because if you do the math

Triangle ABC is similar to triangle DFE. What scale factor is required to dilate triangle DFE so that its image, D′F′E′, is congruent to triangle ABC?

Answers

Answer:

1/4

Step-by-step explanation:

I need your help! I'm struggling and need help solving. If you can include an explanation that would be great!

Answers

Answer:

Answer choice A

Step-by-step explanation:

It's nice to know which way the equation is going, so graphing it helps (if you can, use Desmos!)

Since the equation is facing up (BOTH SIDES UP) as x approaches infinity & negative infinity, f(x) is always going to be increasing so it is always going towards infinity.

Solve for the value of x.

Answers

Answer:

x = 3

Step-by-step explanation:

x + x + x could also be written as 3x, and count the number of "1's" given on both sides:

3x + 4 = 13

=> subtract 4 on both sides of "="

3x = 9

=> Divide by 3 on both sides of "="

x = 3

Hope this helps!

Answer:

x=3

Step-by-step explanation:

I believe the answer would be x is equal to 3.

If you first create the equation you get 3x*4= 13

There are 3 green 'x' so that is 3x. The four orange boxes can be represented as 4, and the 13 orange boxes can be represented as 13.

Then, you solve the equation.

3x * 4 =13

Subtract 4 from both sides.

3x= 9

And simplify.

x=3.

I hope this helps! (:

Describe the likehood of the event given its probability . you make a free throw 70 percent of the time

Answers

Answer:

Yes. 70% is a good percentile, most people understand the workings of a free throw (where you stand on the line, how to place your feet, how to shoot) and standing still gives you an advantage. For the people who don’t understand the workings, they are apart of that 30%.

When 10 is substacted from the square of a number the result is 3 times the number find the positive solution

Answers

Answer: So the positive solution is:

ANSWER:    X = 5

(x = 5 ),  (x = - 2 )

Step-by-step explanation:

when 10 is subtracted from the square of a number the result is 3 times the number.

Find the positive solution.

Let:   x = number

Let x^2 = square of a number.

x^2 - 10x = 3x transpose

x^2  -  3x - 10 = 0

Apply Factoring: Fractions of  10  are   5  and 2

( - 5)(2)  =   - 10

- 5  + 2  =  - 3

( x - 5 )(x + 2) = 0

x - 5 = 0      x + 2 = 0

x = 5             x   =  - 2

So the positive solution is:

ANSWER:    X = 5

I hope that helps!!!!

what is 5 2/3 x 3/4 equal?

Answers

Answer: 4 1/4

Step-by-step explanation: Decimal= 4.25

Answer:

Exact form: 17/4

Decimal Form: 4.25

Mixed number form: 4 1/4

Write answer in scientific notation

Answers

Answer:

5 x 10^7

Step-by-step explanation:

(5 x 10^4)·(1 x 10³) = 5 x 10^7 = 50 million

HELPPPPPPPPPPPPPPPPP

Answers

Answer:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

5/6 roughly equals to 0.8

The answer is C

Which of the following best estmates the sum: 1/2 + 1/3

Answer: C) 0.8

The casino game of chuck-a-luck seems quite simple and that it would be a pretty good bet. In this game, three dice are rolled (usually inside a wire cage). You can bet a set amount, let's say $5, on a specific number 1-6. You win the amount of your bet for each appearance of your number on the dice. If the number does not appear, you lose your bet. For example, let's say you bet $5 on the number 3. If it appears on exactly one die, you win $5 (and keep your bet) with probability 75/216. If it appears on exactly two dice, you win $10 (and keep your bet) with probability 15/216. If it appears on all three dice, you win $15 (and keep your bet) with probability 1/216. If it appears on none of the dice, you lose your original $5 bet. Construct the probability distribution for chuck-a-luck and determine your expected winnings on a $5 bet.

Answers

The expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

What is the probability distribution?

A probability distribution is a mathematical function that describes the probability of different possible values of a variable.

The probability of winning on a $5 bet on a specific number in chuck-a-luck is determined by the number of ways that the number can appear on the three dice and the total number of possible outcomes.

If the number appears on exactly one die, there are 3 ways that this can happen out of a total of 6^3 = 216 possible outcomes, giving a probability of 3/216 or 1/72.

If the number appears on exactly two dice, there are 3 ways to choose the two dice on which it appears, and 3 ways to choose the third die, giving a total of 33 = 9 ways out of 216 possible outcomes, giving a probability of 9/216 or 1/24.

If the number appears on all three dice, there is only 1 way this can happen out of 216 possible outcomes, giving a probability of 1/216.

If it appears on none of the dice, there are (543) ways this can happen, giving a probability of (54*3)/216 = 20/216.

We can use this information to construct the probability distribution for chuck-a-luck:

x P(x)

-5 (losing the bet) 20/216

5 (winning the bet for one appearance) 1/72

10 (winning the bet for two appearances) 1/24

15 (winning the bet for three appearances) 1/216

To find the expected winnings on a $5 bet, we can multiply the value of each outcome by its corresponding probability, and sum the results:

E(X) = (-5)(20/216) + (5)(1/72) + (10)(1/24) + (15)(1/216)

E(X) = -5/43.2 + 5/72 + 5/12 + 15/216

E(X) = -0.1157

Hence, the expected winnings on a $5 bet are -0.1157 dollars. This means that on average, you will lose about 11.57 cents for each $5 bet you make.

Therefore, the game is not a good bet, as you are expected to lose money in the long run.

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if 0°<0<90° and sin0=12/13, find cos0 using trigonometric identities.

• 12/5
• 5/12
• 12/13
• 5/13

Answers

here's the solution,

we know :

[tex] \sin( \theta) = \dfrac{perpendicular}{hypotenuse} [/tex]

So,

[tex] \dfrac{p}{h} = \dfrac{12}{13} [/tex]

so.. let the perpendicular be 12x and hypotenuse be 13x

now,

by applying pythagoras theorem,

[tex]b {}^{2} = h {}^{2} - p {}^{2} [/tex]

where,

b = base h = hypotenuse p = perpendicular

So,

[tex]b {}^{2} = ({13x})^{2} - ({12x})^{2} [/tex][tex] b {}^{2} = 169x {}^{2} - 144x {}^{2} [/tex][tex] {b}^{2} = 25x {}^{2} [/tex][tex]b = 5x[/tex]

so,

[tex] \cos( \theta) = \dfrac{b}{h} [/tex]

[tex] \cos( \theta) = \dfrac{5x}{13x} [/tex]

[tex] \cos( \theta) = \dfrac{5}{13} [/tex]

hope it helps !!

i need help with number seven with a full explanation please

Answers

The value of x would be 32.

What are a congruent quadrilaterals?

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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By analyzing the figure, The value of x would be 32.

What are a congruent quadrilaterals?

In geometry, two figures are congruent if they have the same size and shape. Congruent figures can be moved or oriented in different ways, but they will always match up exactly. In the case of quadrilaterals, they are congruent when they have the same side lengths and corresponding angles.

In the given figure PQRS ~ WXYZ

x = YZ

x = 32.

Hence, the value of x would be 32.

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Aliyah had $28 to spend on six pencils.After buying them she had $10. How much did each pencil cost?

Answers

Answer:

$3

Step-by-step explanation:

28-10=18

18/6=3

Each pencil cost $3.

First you subtract 28 - 10 which equals 18. This is because you already know Aliyah didn’t spend those $10 on pencils. So it says she bought 6 pencils with $18. To find out how much each pencil cost you divide. 18 divided by 6 equals 3. So each pencil costs $3. I hope this helps!

Help me please and thank you!

Answers

Answer:

-4/3

Step-by-step explanation:

-2 - 1 is -3

6-2 is 4

what is the volume of cylinder when the radius is 3 and height is 13.33

Answers

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]

Is the relationship a function?
{(1,4), (4,1), (1,5),(5,1)]

Answers

Answer:

no

Step-by-step explanation:

hdjdjdnbdbdjddhhdhfhr r rjfnfn

Answer:

It is a function

Step-by-step explanation:

A linear function

[tex]x = y - 3[/tex]

and

[tex]x = y - 4[/tex]

Find the value of c in the triangle shown below.
9
8
Choose 1 answer:

Answers

a^2 = c^2 - b^2

9^2 - 8^2

81-64 = 17

Square root of 17 = 4.12311

So x = 4

a) What is the size of angle ABC? b) Use your answer to part a) to work out the size of reflex angle CBD. Give your answers to the nearest degree. ​

Answers

Answer:

a) 110

b) 250

Step-by-step explanation:

Read the top row of numbers for a.  We are starting at zero and going to 110

Reflex is when two angles add up to 360

360 - 110 = 250

Hexagon PQRSTU is shown on the coordinate grid. Hexagon PQRSTU is dilated with the origin

as the center of the dilation using the rule (x, y) → ( 3 x, 3 y) to create hexagon P'Q'R'S'T'U'.
2 2

Which statement is true?

A) Hexagon P'Q'R'S'T'U' is smaller than hexagon PQRSTU because the scale factor is a fraction.

B) Hexagon P'Q'R'S'T'U' is smaller than hexagon PQRSTU because the scale factor is greater than one.

C) Hexagon P'Q'R'S'T'U' is larger than hexagon PQRSTU because the scale factor is greater than one.

D) Hexagon P'Q'R'S'T'U' is larger than hexagon PQRSTU because the scale factor is less than one.

Answers

B is the best answer to go with

Can someone please answer this! I am very confused.

Answers

There is nothing to answer, the screen is blank. Sorry!

The area of the base of the cone is 9π^2 in and a height of 6 in. What is the volume of the cone, in terms of π? Need answer ASAP!

Answers

Answer: 18pi^2

Step-by-step explanation:

Volume of cone formula = 1/3 x base area x height

so 1/3 x 9pi^2 x 6

= 18pi^2

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