Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16

Answers

Answer 1

Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.

As per the given data the given equation is:

[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]

The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]

Your hyperbola opens left/right, because it is of form x - y.

Comparing terms, we find that

h = -4, k = 5, a = 3, y = 4

In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].

Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).

The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]

[tex]c^2=9+16=25$[/tex], so c = 5.

The coordinates of the foci are (-9, 5) and (-1, 5).

The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)

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Find The Vertices And Foci Of The Hyperbola With Equation Quantity X Plus 4 Squared Divided By 9 Minus

Related Questions

Question content area top Part 1 Without using paper and​ pencil, how would you find the sum of 8.8 and 5.5 and ​?

Answers

The sum of 8.8 and 5.5 is 14.3

What is addition?

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

To find the sum of 8.8 and 5.5 without using pen and pencil:

First, we break the term in simple manner.

8.8 = 8 + 0.3 + 0.5

And 5.5 = 5 + 0.5

And now adding the terms one by one,

0.5 + 0.5 = 1.0

0.3 = 0.3

8 + 5 = 13

Addition,

13 + 1 + 0.3 = 14.3

Therefore, the value is 14.3

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A line passes through 3,1 and 0,-3 whats the equation

Answers

Answer:

y=(this is a fraction) 4/3 times x-3

Step-by-step explanation:

Question 3
Determine if this statement is always, sometimes, or never true.
If a < 0, then |a| = -a

Answers

Answer:

the answer is neither

Step-by-step explanation:

An integer is a whole number that can be either greater than 0, called positive, or less than 0, called negative. Zero is neither positive nor negative. Two integers that are the same distance from the origin in opposite directions are called opposites.

GIVE THIS ANSWER FAST I WILL GIVE BRAINLIEST

Q IF 2X^3+AX^2-BX-15 HAS 2X+3 AS A FACTOR AND LEAVES A REMAINDER -5 WHEN DIVIDED BY(X-1),FIND THE VALUES OF A AND B

Answers

Answer:

could you just give the

Step-by-step explanation:

equation so I could try to solve it

help me pls !!!!!!!!!!

Answers

Answer:

c and d

Step-by-step explanation:

how many 1/4 are in 6

Answers

Answer:

24

Step-by-step explanation:

To answer this you simply need to divide 6 by 1/4

or

6÷1/4

which is also equivalent to 6*4

this will get you 24

HELP ME HELP ME PLEASEEEE I NEED QUICK

Answers

Answer:

<ABC and <CB both add up to 90 degrees and fit in the angle <ABD so they could be 45 degrees, or one could be 20 degrees while the other is 70, they just have to add up to 90 degrees

Step-by-step explanation:

8. Which of the following expressions is a factored form
expression 3x

2 − 10x − 8 ?

a. (3x-4)(x+2)
b. (3x-2)(x-4)
c. (3x-2)(x+4)
d. (3x+2)(x-4)
e. (3x+4)(x+2)

Answers

Answer:

D

Step-by-step explanation:

(3x+2)(x-4)

3x^2-12x+2x-8

3x^2-10x-8=0

pls help ASAP what do I put in the box (question is in screenchot)

Answers

Answer:

where is the question????

Answer:

where

Step-by-step explanation:

simplify (2√2+3√5) square 2​

Answers

Answer:

The answer is 22.4

What’s the equation to find angles in a parallelogram

Answers

S = (n - 2) x 180°

I’m pretty sure that’s what it is(?).

how to get the Y intercept when you don't have a 0 X coordinate?​

Answers

Answer: You plug in y as 0 into your equation.

Step-by-step explanation:

Do the above thing OK.

In a television survey, 4 out of 5 people liked comedy shows more than reality shows. If 6,000 people were surveyed, how many people preferred comedy shows?

Answers

Answer:

4,800

Step-by-step explanation:

6,000/5

1,200x4

4,800

103M) solve on the interval 0 ≤ x < 2pi
sin ( 4x ) = √3 / 2

Answers

solving sin ( 4x ) = √3 / 2 , the value of x is 15°

What is trigonometry?

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

For angle of 30° and 60°

sin 30° = 1/2

cos 60° = √3/2

tan60° = √3

for angle 60 °

sin60° = √3/2

cos 60° = 1/2

tan60° = 1/√3

since sin(4x) = √3/2

and sin 60° = √3/2

sin60° = sin(4x)

this means 60° = 4x

divide both sides 4

x = 60/4

x = 15°

therefore the value of x is 15°

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Can someone solve this rational equation and plz don’t link files

Answers

r=13/2

After I solved it it was kinda easy

Answer:

r=13/2

Step-by-step explanation:

Find the volume of a cone

Answers

Answer:

96π or 301.59 in³

Step-by-step explanation:

V(cone) = 1/3πr²h

= 1/3·π·6²·8

= 96π or 301.59

Answer:

301.58  

Step-by-step explanation:

The size of each exterior angle in a regular polygon is 15°. Work out how many sides the polygon has.

Answers

Sum of exterior angles = 360. 360/15=24. Answer is 24 sides.

For each graph, determine whether x and y are proportional.
If r and y are proportional, fill in the blank with a number in simplest form.
Graph 1
Graph 2
Graph 3
HELP PLEASE

Answers

the answer to this question is graph 3 :)) it is

What is the slope of the line?

Answers

Answer:

4

Step-by-step explanation:

slope, m = (y₂ - y₁)/(x₂ - x₁)

plug in the values, and we get m = (3 - (-1))/((3 - 2) = 4

As x increases by 1, y increases by 4.

-1

Step-by-step explanation:

The slope of a line characterizes the direction of a line. To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.

please help! i've tried to solve it but not getting the right answer

Answers

Answer:

Sorry I don't know this one, I got 5.32

Step-by-step explanation:

Write and solve an equation to find what fraction of the student f voted for fruit juice or water

Answers

If [tex]\frac{1}{4}[/tex] of fruit punch is pineapple juice. About [tex]\frac{1}{6}[/tex] of the fruit punch is orange juice, then fraction of punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The fraction of pineapple juice in fruit punch is = [tex]\frac{1}{4}[/tex] ;

the fraction of orange juice in fruit punch is = [tex]\frac{1}{6}[/tex] ;

the equation that can be used to find the fraction of fruit punch that is pineapple juice or orange juice is

⇒ [tex]Frcation Of (Pinapple Juice +Orange Juice)[/tex]

substituting the values ,

we get the equation as ;

⇒ [tex]\frac{1}{4} +\frac{1}{6}[/tex]

taking LCM as 4 and 6 as 12 and solving further  ,

we get ;

⇒ [tex]\frac{3}{12} +\frac{2}{12}[/tex] ; = [tex]\frac{5}{12}[/tex] .

Therefore , the fraction of fruit  punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The given question is incomplete , the complete question is

About 1/4 of fruit punch is pineapple juice. About 1/6 of the fruit punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice .

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2) The length of the road is 600 miles. If 1 inch represents 30 miles, what is the
length of the road?

Answers

Answer:

Are you asking for it from miles to inches?

If so it would be 20

Step-by-step explanation:

600/30=20

Hope this helps <3

Answer:I think it would be 20 inches that is if your supposed to do 600÷30

Step-by-step explanation:uhh I hope this is right good luck tho

A taste test asks people from Texas and California which pasta they prefer brand A or brand B. This table shows the results. Brand A Brand B Total 125 150 105 275 45 Texas California Total 80 90 170 60 A person is randomly selected from those tested. What is the probability that the person is from California, given that the person prefers brand A? Round your answer to two decimal places

Answers

Therefore , the solution of the given problem of probability comes out to be  thus brand A is more prefer by the person as probability of B IS 0.43.

Define probability.

A probability is a number that represents the likelihood that a certain event will occur. Probabilities may be expressed as percentages

range from 0% to 100% or from 0 to 1.

Here,

Given :

Which brand of pasta do Texas and California prefer

Because brand B is preferred by 45 persons in Texas, the answer would be A.

There are 105 persons that favor brand B overall.

=> 45/105

=> 15/ 35

=> 0.42857...

So ,

rounded it would be 0.43,

thus brand A is more prefer by the person

Therefore , the solution of the given problem of probability comes out to be thus brand A is more prefer by the person as probability of B IS 0.43.

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Jack split 25 jellybeans between his brother and himself so that his brother has one more than twice the number Jack has. How many jellybeans does each have?

Answers

Jack has 8
And his brother has 17

Answer:

Jack has 8 and his brother has 17

Step-by-step explanation:

j = # jack has

b = # brother has

j + b = 25

b = 1 + 2j  (brother has one more than twice the amount jack has)

j + 1 + 2j = 25

3j = 24

j = 8

b = 25-8 or 17

The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit.


What are the slope and y-intercept of the line that models this situation? I

Answers

The slope and the y-intercept of the given data table will be option A) Slope= -0.0018, y-intercept = 212

The y-intercept of any linear equation is the point at which the line or the curve intersects the vertical i.e the Y- axis.

To find this intercept, the value of x is taken to be 0 in the model, since on the Y-axis, the value of x is 0.

Here from the given table, we need to check the boiling point or the value of Y for which the value of the altitude or the x value is 0

Hence we get the y-intercept as 212° F.

Now, the formula for slope

= change in y/ change in x

here we will take any two data rows and divide the difference in boiling points by the difference in altitudes.

Taking the first 2 rows gives us

Slope = -0.9/500

= -0.0018

Hence we choose option A) Slope = -0.0018, y-intercept = 212

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Complete Question

The table shows the linear relationship between x, the altitude in feet, and y, the boiling point of water in degrees Fahrenheit. What are the slope and y-intercept of the line that models this situation?

A. Slope= -0.0018, y-intercept = 212

B. Slope= 0.0018, y-intercept =-212

C. Slope =212, y- intercept= 0.0018

D. Slope=-212, y-intercept = 0.0018

Need help ASAP! due soon

Answers

Answer:

y= 2x

Step-by-step explanation:

no y cause the y-intercept is 0, so just y=2x

and i got 2 from dividing 24/12 and 48/24 giving me the x.

Answer:

Step-by-step explanation:

Two points on this line are (36, 72) and (0, 0).  These are 'nice' points in that they are exactly at the intersection of grid lines.

The slope can be found immediately from (36, 72) if the other point is (0, 0):

m = rise / run = 72/36 = 2

Adapting the slope-intercept formula y = mx + b, and using the point (0, 0), we get 0 = 2(0) + b, which tells us that b = 0.  Then the equation of the line in this graph is y = 2x.

which function is equal to -1/2?​

Answers

A is equal to -1/2

B is equal to .866

C is equal to 1/2

D is equal to -.866

Therefore your correct answer is c

Sara put her dog on a diet and kept track of his weight. At the end of 4 weeks,
she recorded her dog's weight change as -3 1/2 pounds. She noticed her dog lost
the same amount of weight each week. What is the dog's weight change each
week of the diet?

Answers

Answer:

Weight change per week = -0.875 or -7/8

Step-by-step explanation:

Sara recorded her dog's weight change as -3.5 pounds after 4 weeks of dieting. We know the weight loss is consistent each week, so we need to find out how much the dog loses in one week.

To find out the weight change per week, we can use the formula:

Weight change per week = Total weight change / Total number of weeks

Plugging in the known values:

Weight change per week = -3.5 / 4

Weight change per week = -0.875

The dog loses 0.875 pounds each week.

or -0.875 pounds is the weekly weight change of the dog during the dieting period.

What is another name for angle 1?




∠JNL

∠N

∠MNK

∠NLJ

Answers

Answer: JNL

Step-by-step explanation: We can give angle 1 another name by using 3 letters which include the letter of the vertex point in the middle, and two other letters of the two rays that meet at the vertex point.

f(x) and g(x) below, find the value of (fog)(-8).
f(x) = 3x²-3x - 8
g(x) = -x - 7

Answers

Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

Function: A Definition

A function is a relationship between a collection of sources or one product for each input. Simply described, a function is a group of equations linked to a single, distinct output. A declaration, rule, or law that specifies the relationship between two variables is known as a function in mathematics (the dependent variable). When a rules of this kind is employed, there is just one output. by photographer Alex Federspiel. This sentence provides a y=x2 example. Any input for x has only one output for y. Since x is indeed the input value, y is, by definition, a function of x.

Here,

Given :

f(x) = 3x²-3x - 8

g(x) = -x - 7

To find : fog)(-8)= ?

Thus,

We find

=> F(g(x)) => 3g(x)² -3g(x) - 8

=> f(-x-7) =3⋅(-x-7)²-3⋅(-x-7)-8

At x =-8

=> 3(-8-7)² - 3(-8-7)-8

=> 3(225)-3(15) -8

=> 675 - 45 -8

=> 622

Therefore , the solution of the given problem of function comes out to be fog(-8)= 622.

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