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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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.
can someone help me please
Answer:
1)B 4 x 4 x 4 x 4
2)B 8292
Step-by-step explanation:
In the figure, what would be represented by c^2
A the sum of the lengths of legs a + b
B the area of the rectangle with diagonal
c the length of the hypotenuse of the triangle
D the area of a square constructed on the hypotenuse
Answer:
D
Step-by-step explanation:
We can go through each answer to see if it's right
A
In a right triangle, with c opposite the right angle, we know that
a²+b² = c²
The answer is stating that a+b = c². Unless both a and b are either 0 or 1, this is incorrect
B
The area of a rectangle is equal to length * width, or in this case, a* b. Compare this with our equation of
a²+b² = c² and this is incorrect
C
The hypotenuse, or the side opposite the right angle, is c. The answer is stating that c = c². This is incorrect unless c = 1 or c = 0
D
The square constructed on the hypotenuse would have a side length of c. The area of a square is length², or in this case, c². c² = c² so this is correct
What is the slope of y = 4 – 2x
?
Answer:
m = -2
Step-by-step explanation:
Use the slope intercept formula y = mx + b
You would switch the order to get y = -2x + 4 to get it in the correct format.
You can then see that -2 is the slope based off the slope intercept formula
(b = y intercept)
(m = slope)
Big Sam, an engineer of the Oval Express says: "We blew off a cylinder head an hour after leaving the station and had to continue the trip at three-fifths of the former speed, which brought us in two hours late. If the accident had occurred fifty miles father on, the train would have arrived forty minutes sooner". Based on Sam's description, how long was the run between the two train stations?
A. 150 miles
B. 200 miles
C. 250 miles
D. 300 miles
Answer:
Ig 200 miles
Step-by-step explanation:
I am guessing
Multiply.
[−3⋅914]⋅[(−0.1)⋅(−28)]
What is the product?
Answer:
x=5.3984
Step-by-step explanation:
A video is getting 150000 views every 3 days how long will it take to reach 400000 views?
Answer:
It will take 8 days.
Step-by-step explanation:
Find the unit rate;
150000/3 = 50000
4000000/50000=8
8 days.
Hope this helps.
(✿◡‿◡)
find the solution to the following system using substitution. y = - 4 + 9 y = 3x - 5
Answer:
1/2, 11/6
Step-by-step explanation:
y=-4+9y
9y-y=4
8y=4
y=1/2
3x-5=1/2
3x=5+1/2=11/2
x=11/6
please help :,)) an explained answer would be nice but if not that's ok :)
Answer:
3.75
Step-by-step explanation:
First we need to get the numbers into decimal form
3/4 can be written into 75
So the mittens weighed 2.75
So we subtract 6.5 and 2.75
Which is 3.75
So the mitten gained 3.75 pounds
Hope this helps!
Answer:
3.75
Step-by-step explanation:
Subtract to find the difference
2 3/4 is 2.75 as a decimal
6.5 - 2.75 = 3.75
Check the answer
2.75 + 3.75 = 6.5
So u can see Mittens gained 3.75 pounds between the time he was a kitten and his 6-month check up.
Can someone please help me on these? Please explain. Thank you.
Answer:
It might be 109 degrees
Step-by-step explanation:
Point J: 48 degrees
Point H: 23 degrees
Point F: 109 degrees
109 + 48 + 23 = 108 degrees
0.5 + (-1.5) - (-5.5) =
Answer:
4.5
Step-by-step explanation:
Answer:
4.5
Step-by-step explanation:
0.5 + ( -1.5 ) = -1
-1 - (-5.5) = 4.5
Hopefully this helped you. :)
plz help verbal expression
Answer:
3(9+r) = 27 + 3r
Sum = addition
Distributive property
Need help asap! Pls
Here is my solution, I hope it is helpful.
Answer:
x = 15
Step-by-step explanation:
Is the point (-2, 5) a solution to the equation 2x + 5y = 0?
Answer:
No
Step-by-step explanation:
substitute -2 for 'x' and 5 for 'y'
2(-2) + 5(5) = 0?
-4 + 25 = 21, not 0
can someone drop the awnser please
Answer:
b
Step-by-step explanation:
Answer: if you can choose multiple its c and d, otherwise i would just use c
Step-by-step explanation:
Maplewood Furniture Store is having a sale on dining room furniture. When a customer purchases a set of dining chairs, a one-time discount of $55 is applied to the total. During the sale, Rhianna buys a set of 6 chairs that match the table she inherited from her grandmother. Rhianna pays $455 in all. Which equation can you use to find the regular cost, c, of each chair? ( ANSWERS 6c - 55 = 455, 55(c - 6) = 455, 55c - 6 = 455, 6(c - 55) = 455,) What is the regular cost of the chair
The equation used to model the regular cost of each chair at Maplewood Furniture store is given by 6c - 55 = 455
A linear equation is in the form:
y = mx + b;
where y, x are variables, m is the rate of change and b is the y intercept.
Let c represent the regular cost for x chairs. Hence:
c = mx + b
Given that a discount of $55 is applied to the total, hence, b = -55.
Rhianna buys a set of 6 chairs and pays 455, hence:
6c - 55 = 455
6c = 510
c = 85
The equation is given by 6c - 55 = 455 and the regular cost of each chair is $85
Find out more at: https://brainly.com/question/25737132
sir 柴米米米米 Read: Marley is buying ribbon to make bows. She buys 123 inches of green ribbon She buys 97 inches of plaid ribbon. She buys 237 inches of polka-dot ribbon. Lastly, sh buys 104.5 inches of red ribbon. How many inches of ribbon does Marley buy?
Answer:
561.5 inches
Step-by-step explanation:
You just add all the four numbers together
123+97+237+104.5=561.5
Carl sold 32 sodas for $114 Medium sodas cost $300 and large sodas
cost $4.00 How many sodas of each size were sold?
Answer:
14 - medium sodas and 18 - large sodas
Step-by-step explanation:
x+y = 32 (the amount of medium and large sodas add up to 32)
3.00x + 4.00y = 114 (the cost of each soda = the amount of money made)
x = 32-y (isolate x and subsitiue it into the following equation)
3x+4y=114 --> 3(32-y) + 4y = 114
96 - 3y + 4y = 114
y=18
plug in 18 in to this equation x = 32-18, x=14
PLEASE HELP RELATIONSHIPS IN TRIANGLES
Answer
TN=22
Step-by-step explanation:
You know that MT+TP+TN using the Orthocenter thereom.
Write 110% as a mixed number in simplest form
Answer:
1 1/10
Step-by-step explanation:
110% = 110/100 = 11/10 = 1 1/10
Simplify Exponents and Roots
A linear function that represents the number of video games purchased at an electronics store is compared to a different linear function that represents the amount of money the store made that day. Describe the key features of the functions that are needed to determine if these lines intersect.
Answer:
See there y-intersept and if slope is negative or positive to see if they intersect
In a game, 2 players each flip a coin. I fboth land on heads, player A gets 2 points and player Bioses 1 points. Ifboth land on tails, player B gets 2 points and player A loses 1 point. Find the expected value of the game for each player.
Building a probability distribution, it is found that the expected value for both players is of 0.25 points.
The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.In this problem, the four possible outcomes, considering Player A - Player B, are:
H - H
T - H
H - T
T - T
That is, considering a success as the number of heads, the distribution is:
[tex]P(X = 0) = 0.25[/tex]
[tex]P(X = 1) = 0.5[/tex]
[tex]P(X = 2) = 0.25[/tex]
For Player A, the earnings of each outcome are: -1, 0 and 2
Hence, the expected value is:
[tex]E_A(x) = -1(0.25) + 0(0.5) + 2(0.25) = 0.25[/tex]
For Player B, the earning of each outcome are: 2, 0 and -1.
Hence:
[tex]E_B(x) = 2(0.25) + 0(0.5) - 1(0.25) = 0.25[/tex]
The expected value for both players is of 0.25 points.
You can learn about expected value at https://brainly.com/question/24855677
39. Which ordered pair is a solution to the
equation y=-6x? (MAFS.912.A-
REI.4.10)
a. (12,-2)
b.(3,-9)
C. (-10, 60)
d. (18,-3)
Answer:
Its letter A. (12, -2)
Step-by-step explanation:
Two increased by five times a number is twenty two
What is the equation
Answer:
2 + 5 x a = 22
Step-by-step explanation:
Emily borrows £580 from a bank at an interest rate of 896 per year.
She will give the money back after 4 years.
How much money will Emily have to pay back?
Answer: £4,164
Step-by-step explanation: multiply 896 by 4 to get £3,584 next add 580 to 3,584 to get £4,164
Answer: 4,164
Step-by-step explanation: I am confused if the 896 is a percent or the money she owes every year, now here is the explanation.
Emily took the £580 and after the 4 years she owes 896*4 = £3,584 plus the original £580 which is £4,164
If it it without the original £580 then the answer is 896*4 = £3,584
If that is not correct then i am sorry
pretty sure this is a joke question about south park my teacher put on my test but i dont watch south park
the question is
TRUE or FALSE
if you ever come across a physican named dr. doctor RUN!
Answer: true you should run
tom measured his frisbee from the center to the outside and found it to be 6 inches what is the approximate circumference of tom frisbee
Answer: 37.68 inches
A frisbee is round so its a circle. And the formula of circumference of a circle is 2πr (r = 6 inches and π = 3.14)
So, 2πr = 2 * 3.14 * 6
2πr = 37.68 inches
Identify If the gas pressure in a ball is low,
how will it affect the physical properties of
the ball?
HELP PLS!!
Answer: i hope it was helpful
Step-by-step explanation:
The ball will appear normal or fully blown up with air. It will bounce like a normal ball that is inflated well. The ball will appear deformed and deflated.
Consider the equation of a circle x^2-2x+y^2-4y-4=0. If the line 2x-y+a=0 is its diameter. Then find the value of a.
Answer:
a=0
Step-by-step explanation:
x²-2x+y²-4y-4=0
(x²-2x+1)+(y²-4y+4)-9=0
(x-1)² + (y-2)² = 3²
Center: (1,2) radius: 3
(1,2) on line 2x-y+a=0
2*1 - 2 + a = 0
a = 0