state the vertices, foci, and asymptotes of the hyperbola with the equation
20x^2-25y^2=100
PLEASE SHOW YOUR WORK SO I CAN UDERSTAND!!!

Answers

Answer 1
To find the vertices, foci, and asymptotes of the hyperbola with equation 20x^2 - 25y^2 = 100, we need to first write the equation in standard form:

(x^2)/(5) - (y^2)/(4) = 1

From this equation, we can see that the hyperbola has a horizontal transverse axis, since the x^2 term is positive and is divided by a smaller number than the y^2 term. Therefore, the center of the hyperbola is (0,0).

Using the standard form of the hyperbola, we can find the values of a and b:

a^2 = 5, so a = sqrt(5)
b^2 = 4, so b = 2

Now we can find the vertices, foci, and asymptotes:

Vertices:
The vertices are located at (±a,0), so the vertices are at (-sqrt(5),0) and (sqrt(5),0).

Foci:
The foci are located at (±c,0), where c = sqrt(a^2 + b^2). Plugging in our values of a and b, we get:

c = sqrt(5+4) = sqrt(9) = 3

So the foci are at (-3,0) and (3,0).

Asymptotes:
The equations of the asymptotes are y = ±(b/a)x, so the equations of the asymptotes are:

y = ±(2/sqrt(5))x

Therefore, the vertices are (-sqrt(5),0) and (sqrt(5),0), the foci are (-3,0) and (3,0), and the equations of the asymptotes are y = ±(2/sqrt(5))x.

Related Questions

Find the area of the following figure:

Answers

Answer:

4.64m²

Step-by-step explanation:

Given,

H(known as height) = 3.2m

B(known as base) = 2.9m

In order to find the area we apply the formula

Area of a triangle = [tex]\frac{1}{2}bh[/tex]

                              = [tex]\frac{1}{2} X 2.9 X 3.2\\\frac{1}{2} X 9.28\\4.64m^{2}[/tex]

Answer:

4.64 meters squared

Show each step and all worl

Answers

Answer:

The correct answer is the one on the bottom. The other answers shown are all wrong. The correct answer is J

Step-by-step explanation:

First off, you have to figure out what's the unit rate, so we come across two points, in this case, I came up with the orgin and (10, 2). We did the rise over the run, which gave us a unit rate of 5 of y for every x. In this case, the correct answer would be H. Even though I can't see what H is, every single other one is correct, so we have to come to the conclusion that H is the correct choice for the one that's wrong.

F matches with the unit rate since 2/10 is also equaled to 0.2/1 since it's 0.2 per piece, so the piece is the x and the 0.2 is the y.

G matches with the unit rate because it's 6 workers per 30 children. 6/30 matches with 2/10.

H matches with the unit rate since it's 9 pages per 45 minutes, making the equation 9/45, which indeed, does match 2/10.

J doesn't match with the unit rate since 10 dollars per 2 hours implies that the equation is 10/2, which gives you the unit rate of 5/1 or 5, which is the reciprocal of 1/5.

Answer:

  J.  Richie earns $10 every 2 hours to pet sit for his neighbor

Step-by-step explanation:

You want to identify the situation with the different unit rate.

Unit rate

For proportional relations, such as the ones given in this problem, the unit rate is calculated by dividing a value for the dependent variable by the corresponding value for the independent variable. When the coordinates are expressed as an ordered pair (x, y), the unit rate is y/x.

Graph

The graph passes through a couple of grid intersections. One of them has coordinates (10, 2). The unit rate is 2/10 = 0.2.

F Gum

The unit rate is the rate for 1 unit: $0.20 for 1 piece. The numerical value of the unit rate is 0.20, same as the graph.

G Daycare

The given relation between children and workers is (children, workers) = (30, 6). The unit rate is 6/30 = 0.2, same as the graph.

H Reading

The relation between minutes and pages is (minutes, page) = (45, 9). The unit rate is 9/45 = 0.2, same as the graph.

J Earnings

The relation between hours and earnings is (hours, earnings) = (2, 10). The unit rate is 10/2 = 5, different from the graph.

The different unit rate is ...

 J.  Richie earns $10 every 2 hours to pet sit for his neighbor

__

Additional comment

Calculating the unit rate as y/x only works when the relation is a proportional one. All of the situations here have proportional relations.

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The table shows the snacks in Melissa's pantry.What is the probability that she chooses a fruit snack, puts it back, and then chooses a granola bar? This problem is based on Independent event problems.

Answers

Answer:

5/36

Step-by-step explanation:

The chance that Melissa chooses a fruit snack is 5/12. This is because there are 5 fruit snacks and 12 snacks in total. If she puts the fruit snack back, the chance of getting a granola bar is 4/12 or 1/3 because there are 4 granola bars and 12 snacks in total making it 4/12 and when simplified, 1/3. You must then multiply the fractions. After multiplying 5/12 by 1/3, you get 5/36.

2−
2
1

n=3n+162, minus, start fraction, 1, divided by, 2, end fraction, n, equals, 3, n, plus, 16

=
n=n, equals

Answers

To solve this equation, we can first simplify the left-hand side:

2^(3n+1) / (2^n - 1) = 3n + 16

We can then multiply both sides by 2^n - 1 to eliminate the denominator:

2^(3n+1) = (3n + 16)(2^n - 1)

Expanding the right-hand side:

2^(3n+1) = 6n*2^n + 16*2^n - 3n - 16

Simplifying:

2^(3n+1) = (6n - 3n)*2^n + (16 - 16)

2^(3n+1) = 3n*2^n

Dividing both sides by 2^n:

2^(n+1) = 3n

Taking the logarithm of both sides (with any base), we get:

n log(2) + log(2) = log(3n)

n = (log(3n) - log(2)) / log(2)

We can use a calculator to evaluate this expression, or simplify it further using logarithm rules:

n = log2(3n/2)

We can now use iterative methods or a graphing calculator to find a numerical solution for n. The solution is approximately 7.524.

The solution would be 7.524 I’m pretty sure

What is 0.3% written as a decimal

Answers

Answer:

0.003

Step-by-step explanation:

0.3 ÷ 100

= 0.003

Answer:

0.003

Step-by-step explanation:

0.3/100

I need help really bad please help!
.

Answers

I'm Just Guessing At The Possible Answers. Please post a picture of the drop-down answers...

1. Between 3 and 8

2. Well Distrubuted???

3. One Outlier (19.86)

A number is increased by 20%. Work out the original number of the increase is 600

Answers

Answer:

The answer would be 480

Step-by-step explanation:

The first step is to find out 20% of 600 and that would equal 120, the next step is to subtract 120 from 600 and the answer is 480.

Answer:

480

Step-by-step explanation:

If the number increased by 20% we can decrease it by 20% to get our number before it was increased.

20% of 600 is 120

600-120=480

Solve and show each step

Answers

Answer:

The correct answer is B.

Step-by-step explanation:

First off, if you don't already know what's the vertical line test, you're guaranteed to get this question wrong.

The vertical line test is a visual way to figure out if the function is a function. You just draw a line anywhere on the paper, and see if it intersects on one point or more than one point. If it intersects at only one point, it's a function because at the end of the day, you can have only one output for each input.

Think of this as an actual function. For example, if you go to a vending machine, and you put a dollar in for a single bag of chips, the next time you put a dollar in, you should get only one bag of chips, or else the machine is broken. It won't function.

In this case, it's a function since each input has its own output, or it passes the vertical line test, it's good to go. It's not a linear function since it's not straight, but hey, it at least is a function.

The correct answer is B!

What is the lcd of 5 1/2 + 2 1/3

Answers

Answer:

6

Step-by-step explanation:

because LCM(2, 3) = 6; Knowing the LCD, you can find equivalent fractions to yours 1/2 and 1/3 , with the denominator equal to found LCD: 1/2 = 3/6. 1/3 = 2/6.

Answer: The least common denominator is 6

Step-by-step explanation: I learned how to do this in school last year.

The volume of a cone with a height of 10 meters is 20π cubic meters. What is the diameter of the cone?

Please give an explanation. Will give brainliest.

Answers

Answer:

The diameter of the cone is 2[tex]\sqrt{6}[/tex] or [tex]\sqrt{24}[/tex]

Step-by-step explanation:

The volume of the cone formula is 1/3hπr².

We already are given the volume and the height, so we can plug those in.

Our formula to find the radius is this: 20π=1/3(10)πr².

Since we have π on both sides, cancel the π on both sides.

We are left with 20=1/3(10)r².

We move 1/3 to the other side, so then we get 60=10r².

We then divide 10 on both sides, so we get 6=r².

Square root both sides to find out the radius.

The result we get is [tex]\sqrt{6}[/tex]=r.

But, we're not done yet.

Diameter=double the radius.

Multiply this radius by 2, and we'll get 2[tex]\sqrt{6}[/tex], or [tex]\sqrt{24}[/tex].

Please help with part b and if u can tell me if I did part 1 correctly I’d appreciate it

Answers

Answer: No but close

Step-by-step explanation:

In order to do this, we have to get the equation. You got the have to do x+x+2(2x-5). Since there are two sides that are x, and two sides that are five less than twice of x. We get 2x+4x-10. The answer is 6x-10. I think

May somebody help with this please!

Answers

Answer:

5 ft

Step-by-step explanation:

In order to find the missing side length, we need to take a look at what has been given to us.

From what I see, this shape looks like two rectangles connect at their ends.

What do we know about rectangles?

-Rectangles have 2 sets of sides that are equal length, totaling 4 sides.

So, let's say we know the length of the longest side of the tallest rectangle.

-That side length is 15ft.

Now, we know that the opposite side of that imaginary rectangle has to be of equal length of 15ft. But, only 10 ft are show...

Since we know that there are more than 10 ft we must subtract 10 ft from the 15 ft to get the side length marked as "?", or what should have been left at that side.

15ft - 10ft = 5ft

Below is a single die and a spinner with the numbers from 1 to 8.


(A) if the die is tossed and the pointer is spun what is the problability of getting a 5 on the die and a 7 on the spinner?


(B) What is the problability of getting a number less than 3 on the die and a number greater than 5 on the spinner?

Answers

Answer:

(A) P(5 on die) = 1/6, P(7 on spinner) = 1/8

(1/6)(1/8) = 1/48

(B) P(less than 3 on die) = 2/6 = 1/3

P(greater than 5 on spinner) = 3/8

(1/3)(3/8) = 1/8

can someone help (answer only) :P

Answers

Answer:

29.7

Step-by-step explanation:

Answer: 29.7

Step-by-step explanation:

PLSS HELP!!! LOOK AT PICTURE

Answers

Answer: 1/5

Step-by-step explanation:

there is one 4 in the group of 5, 1/5

I believe the answer is 1/5 but you can divide 1 by 5 and then move the decimal point to the right two times to get the percentage

what value of x makes this equation true -(x+3)=2(x-3)

A. 0
B. 1
C. 2
D. 3

Answers

Answer:

To solve the equation -(x + 3) = 2(x - 3) for x, we can follow these steps:

Step 1: Distribute the negative sign on the left side of the equation:

-(x + 3) = 2(x - 3)

=> -x - 3 = 2(x - 3) (using the distributive property)

Step 2: Expand the right side of the equation:

-x - 3 = 2x - 6

Step 3: Add x to both sides of the equation to isolate the x term on one side:

-x + x - 3 = 2x + x - 6

=> -3 = 3x - 6

Step 4: Add 6 to both sides of the equation:

-3 + 6 = 3x - 6 + 6

=> 3 = 3x

Step 5: Divide both sides of the equation by 3 to solve for x:

3/3 = 3x/3

=> 1 = x

So, the correct value of x that makes the equation true is B. 1.

PLEASE MARK BRAILYISTT :D

Answer:

B, one

Step-by-step explanation:

In order to solve this, you can solve the equation. First, you can use the distributive property to get -x-3=2x-6. If you make the variables on one side and the constants on the other, you will get -3x-3=-6. This can further simplify to -3x=-6. Divide both sides by -3 to get that x=1. Then, the correct answer is B.

What is 24d + 0.2 = 29.6

Answers

Answer:

d=1.225

Step-by-step explanation:

24d+0.2=29.6

24d=29.6−0.2

24d=29.4

d= 29.4/24

d=294/240

d=49/40

d=1.225

To solve the equation, you just need to isolate the variable d. Here's the equation:

24d + 0.2 = 29.6First, subtract 0.2 from both sides:24d = 29.4Now, divide both sides by 24 to solve for d:d = 29.4 / 24d ≈ 1.225

Please help I'm struggling with this I have so much homework to do ​

Answers

Answer:

Look at Explaination

Step-by-step explanation:

Im very busy rn so i cant provide an answer, but I can easily explain mean median and mode. Mean is all the numbers added up divided by the amount of numbers there are.

Ex: 1,2,3,4,5 is the number list so you add 1,2,3,4, and 5. Then you divide that sum by 5 because there is 5 numbers there.

Median is simply just the middle of the list, for ex 1,2,3,4,5 3 is the median, but if it is 1,2,3,4,5,6 then you would make it 3.5.

Mode is the most repeated number in the list

Ex: 1,1,2,3,4,5,5,5,6,7

The Mode in the list is 5, since it is repeated 5 times. If none repeated then it is N/A if it is tied then put both numbers.

The mean for ou is 59 mean for opponents is 13.5

ANSWER QUICK PLS
look at the trapezium below, work out the size of angle
angle tuv
angle vwt
give your answer in degrees

Answers

Answer:

Step-by-step explanation:

107 is the answerrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr

Angle TUV is 73 degrees and angle VWT is 122 degrees

Please answer question #35

Answers

Answer:

X × (100-25)

Step-by-step explanation:

Lets take X and then multiply it by its discount, 25% which is (100-25). Your final product will be what you bought divided by 25%.

Hope that helped. Try it with your teacher, might be wrong...

After a number of months, a bank balance was –$46.83. Each month, the bank charges a $5.95 fee for having a negative balance. Write an inequality to determine at most how many months the fee was charged. Let x be how many months the fee was charged.

Can someone pls explain this to me and the answer also.

Answers


Answer: 7 months and 87 days

.
After a number of months, a bank balance was –$46.83
Charges applied/ month = $ 5.95
So, no of months charges applied = Bank balance/Charges applied
x = \frac{46.83}{5.95} x= 5.95
46.83
x = 7.87x=7.87
So no. of months charges is 7 months and 87 days.

Answer: Your answer is 7 months, 87 days

Hope it helped :D

Someone pls help a s a p will give brainlist thingy

Answers

i think it’s 120°, x=10° because 4x+20+3x=90
- 20 from both sides
and 7x=70
divided by 7, x= 10
I did the math on paper and got 101? See if that helps :)

IM SORRY BUT PLS HELPPP!!!

Answers

Answer:

Step-by-step explanation:

it is 1,3,5,15,2369,115,345

it’s 1/3
there is three cards and there is only one factor of 5 so it’s 1/3

Find the solution for each equation.

Answers

Answer:

5x(x - 4) = 10   X = 6

18 + x = 20      X = 2

18= x X 10 - 22  X = 4

Step-by-step explanation.

Answer:

1. X= 6

2. X= 4

3. X= 2

Step-by-step explanation:

3) If a person walks 1/4 mile in 1/5 hour, compute the unit rate as a complex fraction, ____ miles per hour which is equivalent to ____ miles per hour.​

Answers

Answer:

1 1/4 miles per hour which is equivalent to 5/(1/4) miles per hour.​

Explanation:

I am not sure but I think this is the right answer

Answer: 818.1 miles 9000 mps

Step-by-step explanation:

due to the equipment bill that was already

I WILL GIVE BRAINLIST An office manager needs to wrap a box with paper for shipping. A figure of the rectangular prism is shown.

A rectangular prism with base dimensions of 4 and one-fourth inches by 3 and one-half inches. The height is 4 inches.

How much paper does the manager need to wrap the entire box?

forty-five and one-fourth in2
fifty-seven and three-fourths in2
sixty-three and three-fourths in2
ninety-one and three-fourths in2

Answers

Answer: sixty-three and three fourths in2

Step-by-step explanation:

We have to find the surface area. We can use the formula, and plug in the numbers.

Use the graph to answer the question.

Graph of polygon ABCDE with vertices at negative 3 comma 3, negative 3 comma 6, 1 comma 6, 1 comma 3, negative 1 comma 1. A second polygon A prime B prime C prime D prime E prime with vertices at 11 comma 3, 11 comma 6, 7 comma 6, 7 comma 3, 9 comma 1.

Determine the line of reflection.

Reflection across x = 4
Reflection across y = 4
Reflection across the x-axis
Reflection across the y-axis

Answers

The line of reflection is x = 4, since the line x = 4 divides the original polygon and its image into congruent halves.

Answer:

Reflection across x = 4

Step-by-step explanation:

I took the test so you don't have to! Trust me.

In a game of chance, players spin the pointer of a spinner with six equal-sized sections.
The outcomes of the game are shown in the table below.
Which outcome has a frequency closest to its expected frequency?
A)1
B)2
C)3
D)4

Answers

Answer:

D)4 i think because it is the one landed on the most.

D)4 is the closest expected frequency to 1

What is the distance from (5, −18) to (5, 24)?
A. −42 units B. −6 units C. 6 units D. 42 units

Answers

D. 42 units

counting from -18 to 24 is 42

Answer:

Step-by-step explanation:

b

HELPP PLS PLSSSSSS, LOOK AT IMAGE!!!!!!!!!!!

Answers

Answer: 1/2

Step-by-step explanation:

1,2,7 out of 6   3/6=1/2

Answer:

2/6

Step-by-step explanation:

1 and 2 are factors of 14 while the rest are not so that is 2 and there are 6 total sides so it would be 2/6

Other Questions
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