Explain the step by step process of finding a function for a hyperbola given the center (1,4), vertices (-7,4) and (9,4), and a point on the hyperbola at (-11, -6). Make sure to include the location of the foci.
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Answers
Answer:
(x -1)²/64 -(y -4)²/80 = 1foci (-11, 4) and (13, 4)Step-by-step explanation:
The standard form of a hyperbola whose transverse axis is horizontal is ...
(x -h)²/a² -(y -k)²/b² = 1 . . . . center (h, k); transverse axis 2a; conjugate axis 2b
The distance between the two vertices is given as (9 -(-7)) = 16 = 2a, so the value of a is 8 and we have the partial equation ...
(x -1)²/8² -(y -4)²/b² = 1
Filling in the given point value gives us an equation for b².
(-11 -1)²/8² -(-6 -4)²/b² = 1
9/4 -100/b² = 1
5/4 = 100/b²
b² = 80
So, the equation is ...
(x -1)²/64 +(y -4)²/80 = 1
__
The distance between the foci is 2c, where c² = a² +b².
c² = 64 +80 = 144 = 12²
c = 12, so the foci are at ...
(x, y) = (1 ±12, 4) . . . . . . . 12 units either side of the center
The foci are (-11, 4) and (13, 4).
_____
Additional comment
The steps are ...
use the given information to fill in as much of the equation as you can.use any given points or additional information to find the unknown values in the equationdetermine any additional information asked for (foci, asymptotes, ...)The relevant relations are ...
2a = length of transverse axis (distance between vertices)
2b = length of conjugate axis (distance between co-vertices)
±b/a = slope of asymptotes, which are lines through the center
2c = distance between foci, where c² = a² +b²
The equation is (x -h)²/a² -(y -k)²/b² = 1 for a hyperbola that opens horizontally with center (h, k). Swapping variables x and y will give a hyperbola that opens vertically. If the figure opens vertically, the asymptotes will have slope ±a/b.
The distances from a point to the foci have a constant difference of 2a.
Related Questions
Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard form, given that the point- slope form is y + 1= 2/3 (x -8)
Answers
Answer:
2x - 3y = 19
Step-by-step explanation:
y=(-5--1)/(2-8)*(x -8)+-1
y=-4/-6(x-8)-1
3y=2x-16-3
3y=2x-19
2x-3y=19
2x - 3V = 19
Step-by-step explanation:
y=(-5--1)/(2-8)*(x-8)+-1
y=-4/-6(x-8)-1
3y=2x-16-3
3y=2x-19
2x-3y=19
what are the values? f(3)
Answers
Answer:
it's simply what we follow and respect like we value our culture
Step-by-step explanation:
hope this will help
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental
fee to use a kayak for 4 days. She also paid $18 for a guided waterfall tour. Tara
paid $94 in all. What was the rental cost of each day Tara used the kayak?
Answers
Answer:
she will pay $19 for each day
Step-by-step explanation:
94-18=76
76÷4=19
The rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
Let x be the rental cost of each day Tara used the kayak.
4x + 18 = 94
4x = 94 - 18
4x = 76
x = 76/4
x = $19
Thus, the rental cost of each day Tara used the kayak is $19 if Tara stayed at the Merry Mountain campgrounds last weekend. She paid a rental fee to use a kayak for 4 days.
Learn more about the linear equation here:
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#SPJ2
Solve the following inequality 17 less than or equal to negative 3X +2 less than or equal to 26.. what is the answer
Answers
Answer:
-5 less than or equal to x less than or equal to -8
Step-by-step explanation:
You have to isolate x.
Start with removing +2.
Take 2 away from both sides
15 less than or equal to -3x less than or equal to 24
Then, the only thing you have to isolate after that is -3, you have to remove it from x.
Since -3x is multiplying, you have to divide by -3 on the other sides.
15 divided by -3 is -5
24 divided by -3 is -8
Therefore,
The answer is...
-5 less than or equal to x less than or equal to -8
Question is in image
Which best explains if qudrillateral WXYZ can be a parallelogram?
Answers
Answer:
A
Step-by-step explanation:
If the figure is to be a parallelogram, opposite sides must be the same length. This requires ...
15 = x +8 ⇒ x = 7 . . . . long sides equal length
and ...
x +2 = 2x -5 . . . . . short sides equal length
7 = x . . . . . . . . . . add 5-x
The value x=7 will make opposite long sides have lengths 15 mm and opposite short sides have lengths 9 mm.
Figure WXYZ can be a parallelogram with one pair of sides measuring 15 mm and the other pair measuring 9 mm.
What is the prime factorization of 24?
1. 2x2x2x3
2. 2x2x3
3. 8x3
4. 6x4
Answers
Answer:
1. 2x2x2x3
Step-by-step explanation:
Let's do process of elimination.
2. 2x2x3
2x2=4 4x3=12
2 is false.
3. 8x3
8x3=24
3 is true, but 8 is not a prime number.
4. 6x4
6x4=24
4 is true, but 6 is not a prime number.
This leaves 1. 2x2x2x3.
1. 2x2x2x3
2x2=4 2x3=6 6x4=24
1 is true, and 2 and 3 are prime numbers. So, the answer is 1.
-hope it helps
Answer:
1. 2x2x2x3
Step-by-step explanation:
Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.
[tex]24\:\mathrm{divides\:by}\:2\\\\\quad \:24=12\cdot \:2[/tex]
[tex]12\:\mathrm{divides\:by}\:2\\\\\quad \:12=6\cdot \:2[/tex]
[tex]6\:\mathrm{divides\:by}\:2\quad\\\\ \:6=3\cdot \:2[/tex]
[tex]2, 6\:\mathrm{divides\:by}\:2\quad \\\\\:6=3\cdot \:2[/tex]
Poppy is the manager of a unisex hair salon.
The salon uses a mixture of three products for hair colouring
This table shows the number of millilitres (ml) of each product used for the mixture
Product
Amount
Colour
30ml
Developer
60ml
Conditioner
60ml
Poppy has the following amount of each product in stock
3.5 litres of Colour
0.5 litres of Developer
2.2 litres of Conditioner
The salon has about so appointments for hair colouring per month
Poppy can only order products in whole litres.
For next month, she thinks she has enough colour and conditioner in stock but she needs to
order 4 litres of developer
24 Is Poppy correct?
Explain your answers
Show your working
Examiner
use only
(5 marks)
Answers
The content of the mixture, which are the colour, developer, and
conditioner, are in a fixed proportion to each other.
Poppy is incorrect, she should order 3 liters of developer and 1 liter of conditioner.Reasons:
The table of the amount of each product used in the mixture are;
[tex]\begin{tabular}{|c|c|c|c|}Product&Colour&Developer&Conditioner\\Amount&30 ml&60 ml&60 ml\end{array}\right][/tex]
The number of appointment per month = 50
The quantities used per month have a proportional relationship
Quantity used a month are;
Colour = 30 ml × 50 = 1,500 ml
Developer = 60 ml = × 50 = 3,000 ml
Conditioner = 60 ml × 50 = 3,000 ml
Quantity available are;
Colour = 3.5 liters
Developer = 0.5 liters
Conditioner = 2.2 liters
The quantity needed = Quantity used - Quantity available
Therefore;
Quantity needed are;
Colour = 1,500 ml - 3,500 ml = -2,000 ml
Developer = 3,000 ml - 500 ml = 2,500 ml
Conditioner = 3,000 ml = 2,200 ml = 800 ml
Therefore, Poppy has enough colour but she needs 2,500 ml of developer and 800 ml conditioner
Therefore, she should order;
3,000 ml = 3 liters of developer
1,000 ml = 1 liter of conditioner
Therefore;
Poppy is incorrect, she should order 3 liters of developer and 1 liter of conditioner.
Learn more about proportional relationships here:
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Please solve i need help :,) tyy
Answers
Answer:
6. 47
7. –25
8. 15
9. –33
10. –9
Step-by-step explanation:
Substitute.
6. x=-7
y = -8x - 9
= -8(-7)-9
= 56-9
y=47
7. x=2
y= -8x-9
= -8(2)-9
= -16-9
y= -25
8. x=-3
y= -8x-9
= -8(-3)-9
=24-9
y= 15
9. x=3
y= -8x-9
= -8(3)-9
= -24-9
y= -33
10. x=0
y= -8x-9
= -8(0)-9
= 0-9
y= -9
PLEASE HELP !!!
x^2-34=16x
Answers
Answer:
Complete the SquareSolve for x over the real numbers:(x - 8)^2 - 100 = 0
Add 100 to both sides:(x - 8)^2 = 100
Take the square root of both sides:x - 8 = 10 or x - 8 = -10
Add 8 to both sides:x = 18 or x - 8 = -10
Add 8 to both sides:Answer: x = 18 or x = -2
Step-by-step explanation: DONT TRUST THIS THOUGH
Which relation is a function mastery test
Answers
Answer:
The relation which is a function is the one in which none of the first coordinates repeated.
Step-by-step explanation:
The dot product of u ∙ u = 45 what is the length of u?
Answers
Answer:
67 hah why you solve this
[tex]\textbf{u} \cdot \textbf{u} = 45\\\\\implies |\textbf{u}|^2 =45\\\\\implies |\textbf{u}| = 3\sqrt{5}[/tex]
How much pure alcohol must a pharmacist add to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution? ASAP
Answers
20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.
Let x represent the volume of pure alcohol (100%) in cm³ needed to be added. Hence:
x * 100% + 10 cm³ * 10% = 70% * (x + 10 cm³)
x * 1 + 10 * 0.1 = 0.7 * (x + 10)
x + 1 = 0.7x + 7
x - 0.7x = 7 - 1
0.3x = 6
x = 20 cm³
Therefore 20 cm³ of pure alcohol is added to 10 cm of a 10% alcohol solution to strengthen it to a 70% solution.
Find out more on equation at: https://brainly.com/question/13763238
Answer:
20 cm³
Step-by-step explanation:
Casey borrowed $4500 at a 5% interest rate for 4 years.
What was the total interest?
Enter your answer in the box.
Hint: Use the formula I=P*R*T where
I= Interest Earned/Owed
P= Principal
R= Rate
T= Time
PLEASE HURRYYYY!
Answers
I = $4500 x 5% x 4
5% = .5
4500 x .5 x 4 = 9,000
I think this should be correct .
what is the slope of -y=-x+6
Answers
Answer:
m = 1b = -6Step-by-step explanation:
We know that:
-y = -x + 6y = mx + bFirst, we need to change the 'y' sign.
=> -y = -x + 6=> y = x - 6Now, let's compare both of the equations to find slope.
=> (y = x - 6) = (y = mx + b)We can see that the slope is 1 and the y-intercept is -6.
Conclusion:
Therefore:
m = 1b = -6Hoped this helped.
x² – 2xy + y², x² + 2xy + y², 4x² – xy + y², x² – y²
Answers
Answer:
[tex]\left(4x^2-xy+y^2\right)\cdot \left(x+y\right)^2\cdot \left(x-y\right)^2\\[/tex]
Step-by-step explanation:
need help with math probelm
Answers
[tex]28+24=4(7)+4(6)=4(7+6)[=4(13)=52][/tex]
The answer: 4(7+6)
ok done. Thank to me :>
Line f has a slope of -9/7. Line g is perpemdicular to f. What is thr slope of line g
Answers
How many different five-letter
arrangements can be made from the
letters in the word "PLUTO"?
5
25
60
120
Answers
Answer:
my guess would probably be 5 but it could also be 25. (id like to say the answer but i cant cause this should be something for you to decide the answer not me.
Step-by-step explanation:
I hope this helps you!
Each of the following is a tip for saving EXCEPT:
A.
shop smart
B.
use credit cards
C.
pay yourself first
D.
focus on reaching a goal
Answers
A (good way to save money): If you shop smart, you can pick up amazing deals like BOGO's, 50% Off, 60 or even 70% off and yet you can still get so many brand that people enjoy
B (good way to save money): If you have a good credit card company, you can earn free rewards or even cheaper rewards for things that can cost large amounts
C (helps save lots of money): This is almost like paying another bill every month, where you set aside a certain amount every month for in the future like vacations or when you hit retirement. This could also be considered the answer because that could also bring to the lack of able to pay all bills needed
D (this is where I think the answer could be possible): Some people make "goals" of spending hundreds of dollars on shopping mall trips or goals of purchasing tons of things that want and can cost thousands of dollars, which is considered a waste of money
How could I write this out?
Answers
Answer:
1.6 divided by 8 is 0.2
Step-by-step explanation:
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answers
Answer:
[tex]\displaystyle m = \frac{-1}{3}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Step-by-step explanation:
Step 1: Define
Identify points from given graph.
Point (0, -1)
Point (-3, 0)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m.
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{0 - -1}{-3 - 0}[/tex][Order of Operations] Evaluate: [tex]\displaystyle m = \frac{1}{-3}[/tex]please help i only have a few minutes left!!
Answers
Answer:
VI
Step-by-step explanation:
The letter "A" is a vowel and a capital letter, so this should be categorized in group VI, where the vowel circle and the capital letter circle overlap.
Answer:
F
Step-by-step explanation:
It is a capital letter and a vowel
Divide (x^3+2x-6x-9) by (x+3)
Answers
Answer:
x² - 3x + 5 - [24÷(x+3)]
Step-by-step explanation:
1. Expand (x³ + 2x - 6x - 9)
= x³ - 4x - 9
2. Divide [x³ - 4x - 9 by x+3]
= x² + [(-3x^2-4x-9) ÷ (x+3)]
3. Divide [(-3x^2-4x-9) by (x+3)]
= -3x + [(5x-9) ÷ (x+3)]
x² - 3x + [(5x-9) ÷ (x+3)]
4. Divide [(5x-9) ÷ (x+3)]
= 5 + [(-24) ÷ (x+3)]
x² - 3x + 5 + [(-24) ÷ (x+3)]
= x² - 3x + 5 - [24 ÷ (x+3)]
Solve for g. Make sure to use scrap paper to show your work.
( 144 + 6 x 8 ) ÷ 3 = g
192
64
48
Answers
the answer is 64 multiplication can be done with calculator or normal
6(x 2) 3(x 3) help me help me help me help me help me HELP MEEEEE PLZ its from usatestprep
Answers
Answer:
i dont now
Step-by-step explanation:
9. A box of cereal weighs 600 grams. How much is this weight in pounds?
Explain or show your reasoning. (Note: 1 kilogram = 2.2 pounds)
Answers
Answer:
1.323 pounds I think I'm not too sure thi sorry
Answer:
1.32 pounds
Step-by-step explanation:
convert 1kg to 1000g
[tex]1000g = 2.2pounds[/tex]
Find out how many pounds per 100g
[tex]100g = 0.22 \: pounds[/tex]
multiply by 6 to get 600g and multiply right hand side of the equation as well
[tex]600g = 0.22 \times 6[/tex]
[tex]600g = 1.32 \: pounds[/tex]
Help help help help help help help math math
Answers
Answer:
Step-by-step explanation:
5x + 10 + 10x + 5 = 180
15x + 15 = 180
15x = 165
x = 11
Please help! photo is attached with the problem.
Answers
The football team has a total of 350 jerseys. There are 154 medium-sized jerseys. What percent of the jerseys are medium-sized jerseys?
Pls help me
Answers
Answer:
Step-by-step explanation:
Given : The total number of jerseys = 350
The number of medium-sized jerseys = 154
Then, the percent of the jerseys are medium-sized jerseys will be :-
\begin{gathered}\dfrac{\text{Number of medium-sized jerseys }}{\text{Total jerseys}}\times100\\\\=\dfrac{154}{350}\times100\\\\=0.44\times100=44\%\end{gathered}
Total jerseys
Number of medium-sized jerseys
×100
=
350
154
×100
=0.44×100=44%
Therefore , the percent of the jerseys are medium-sized jerseys = 44%
Freddy’s savings account went from $520 to $321 after he purchased a new bike. What was the percent decrease? *
Answers
If my calculations are correct, the percentage decrease faced here is roughly 38.2%. Based on the calculations, the bicycle costs 199$ and when the cost is subtracted from 520, you would create the percentage of 38.2%.
