Write an equation in standard form of the hyperbola described.
Focus (4, 0); vertex (2, 0); center (0, 0)
Answers
Check the picture below, so the hyperbola looks more or less like so, so let's find the length of the conjugate axis, or namely let's find the "b" component.
[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=0\\ a=2\\ c=4 \end{cases}\implies \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{b^2} \\\\\\ c^2=a^2+b^2\implies 4^2=2^2+b^2\implies 16=4+b^2\implies \underline{12=b^2} \\\\\\ \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{12}\implies \boxed{\cfrac{x^2}{4}-\cfrac{y^2}{12}}[/tex]
Related Questions
A social security number contains nine digits, such as 224-10-7135. How many different social security numbers can be formed?
Answers
Answer:
420 million
Step-by-step explanation:
There are up to 420 million numbers that were assinged.
Can you solve for x please? this one has me by the balls.
Answers
Answer:
42.5
Step-by-step explanation:
(180-95)÷2=42.5
What is the area of this combined shape?
Answers
Answer:
the amount of space inside a shape composed of basic shapes put together.
Step-by-step explanation:
hope this helps.
(a) The area of a rectangular parking lot is 3657 m².
If the width of the parking lot is 53 m, what is its length?
Answers
Answer:
69 m
Step-by-step explanation:
[tex]\textcolor{steelblue}{\text{Area of rectangle= length ×width}}[/tex]
Given that the area is 3657 m² and the width is 53 m,
3657= length ×53
Divide both sides by 53:
length= 3657 ÷53
length= 69 m
i need help 100 points for a question
Answers
Answer:
34.28 ftStep-by-step explanation:
Find the length of semicircle
C = πd, circumference of circleC/2 = πd/2 = 3.14*4/2 = 6.28 ftFind the perimeter
P = 4 + 6.28 + 2*12 = 34.28 ftFor rectangle
L=12B=4Perimeter:-
2(L+B)2(12+4)2(16)32ftFor semicircle:-
radius=r=4/2=2ftPerimeter:-
πr2π6.28ftTotal:-
6.28+32-438.28-434.28ftI need the answer!! Please answer
Answers
Find the area of the right triangle
Answers
Answer:
Formula for area of a triangle;
A = BH x 1/2
B = The base
H = The height
1/2 = Half of the product of (base x height)
We first need to figure out the base of this triangle, so count the units across from the base of this triangle.
The base is 4 units.
Now we need to find out the height, so count the units above starting from the base of this triangle and to the end of this triangle.
The height is 7 units.
Now plug these values into our equation:-
A = BH x 1/2
A = 4(7) x 1/2
A = 28 x 1/2
A = 28/2
A = 14, the area of this right triangle is 14 square units.
How many minutes are in 3 hours?
There are 60 minutes in one hour.
Complete the table.
Answers
Answer:
180
Step-by-step explanation:
because there are 60 minutes in an hour and you need 3 you need to add 60 + 60 + 60 or your can do 60 x 3 which equals 180
Answer:
180 minutes
Step-by-step explanation:
1 hour - 60 minutes
2 hours - 120 minutes
3 hours - 180 minutes
Because there is 60 minutes in an hour, you can do 60 x 3 = 180. This will directly tell us how many minutes are in 3 hours. Or, you can add 60 minutes 3 times for 3 hours.
So, 60 x 3 = 180. There are 180 minutes in 3 hours.
22 mice were introduced to a new environment. Their population triples every year. Using m(t) as the function name and t for time, write this equation.
Answers
Answer:
when were they introduced?
Step-by-step explanation:
Find nth term of the sequence: 11, 15, 19, 23
Answers
The term
tn=a+(n−1)d
Where a= first term and d= common difference
hope it helps...!!!
Tim’s weight was 320 pounds in 2010 and is 180 pounds in 2020. What is the slope?
Answers
Answer:
-14
Step-by-step explanation:
We have two points
(2010, 320) and ( 2020, 180)
The slope is
m= ( y2-y1)/(x2-x1)
= ( 180-320)/(2020-2010)
= -140/10
= -14 lbs/ year
Men's Shoe Sizes The shoe sizes of eight different men were used to create the box plot above. Which of the sets of measurements below matches the given box plot? A. Shoe Size: 7, 8, 8, 9, 10, 11, 11, 12 B. Shoe Size: 7, 9, 9, 9, 10, 11, 11, 12 C. Shoe Size: 7, 8, 8, 8, 8, 11, 11, 12 D. Shoe Size: 7, 8, 8, 9, 10, 10, 10, 12
Answers
Answer:
The answer is
→ A. Shoe Size: 7, 8, 8, 9, 10, 11, 11, 12
Step-by-step explanation:
Hope this helped! :^)
⭐Brainliest will be appreciated!⭐
✉️Message me if you have any more questions!✉️
- ✨7272033Alt✨
Submitted on 4/16/2022 at 5:38 PM
(To avoid plagarism, by users whom decide to copy.)
I NEED HELP ON THIS QUESTION (I will give a Brainlist to the best one no links please.)
Answers
Answer:
1. 84.7
2. 24
3. 47.5
4. 57.5
Step-by-step explanation:
your welcome and mark as brainliest pls
20 points. A certain event may occur, but it is unlikely to occur.
Which statement about the probability of the event is true?
A. The probability is close to 0.
B. The probability is 0.
C. The probability is 1.
D. The probability is less than 0.
Answers
Answer:
A
Step-by-step explanation:
Close to 0 means there isn't a certain number, and there also isn't a certain answer for what the probability. While all of the others are alreaady stated, this is the only one that is not.
Question 8
1 pts
What is the best way to describe the central tendency of residential real estate prices in Westwood?
Hint: Westwood real estate is highly skewed. You are able to find houses that are $600,000 to
$69,000,000 with an average price of $1,020,000.
O Median
O Mean
Answers
The best way to describe the central tendency of residential real estate prices in Westwood is mean.
What are measures of central tendency?
A measure of central tendency attempts to describe a data set by determining the central value of the data set. Measures of central tendency are mean, median and mode
Mean is the average of a set of numbers.
Mean = sum of the numbers / total number
To learn more about mean, please check: https://brainly.com/question/25842202
Question 1 – A two-mass (pulley) system begins in the initial configuration shown in the figure. Once this system is allowed to
move, the cart will move to the right and the suspended mass will fall with the same (magnitude of) acceleration. Determine this
acceleration, A, of this system, and the force in the cable, F, accurate to 3 sig. dig.
Assume the pulley and cable has no mass.
Answers
Answer:
the suspended mass will fall with the same (magnitude of) acceleration. Determine this
accelerat
Step-by-step explanation:
36
36
is what percent less than 60
60
?
Answers
Answer:
thats only the answer <3
Jon mixed 3 cups of pineapple juice with 5 cups of
mango juice to make fruit punch.
Complete the equation below to represent the
relationship between the number of cups of
pineapple juice, p, and the number of cups of mango
juice, m.
p=
Answers
Answer:
p = 5/3m
Step-by-step explanation:
The Ratio of Pineapple juice to mango juice is 3:5. Since you can substitute the variable in, and they have already supplied part of the equation, you can set this equation up:
3p = 5m
divide both sides by 4
p = 5/3m
This tells us that for every cup of Pineapple juice, there is 5/3 cup of mango juice.
Hope this helps!
Brainiest always helps me out :)
Perform the indicated operation: (x3 – 3x + 1) – (x3 + 7 – 12x).
Answers
Answer:
[tex]\left( x^{3}-3x+1\right) -\left( x^{3}+7-12x\right)=9x - 6[/tex]
Step-by-step explanation:
[tex]\left( x^{3}-3x+1\right) -\left( x^{3}+7-12x\right) = x^{3}-3x+1-x^{3}-7+12x[/tex]
[tex]= -3x+1-7+12x[/tex]
[tex]=9x - 6[/tex]
The points (4,7) and (r. – 5) lie on a line with slope – 3. Find the missing coordinate r
Answers
Answer:
[tex]r=\frac{14}{3}[/tex]
Step-by-step explanation:
Set up an equation and solve for r using the formula for slope:
[tex]\frac{5-7}{r-4}=-3\\ \\-2=-3(r-4)\\\\-2=-3r+12\\\\-14=-3r\\\\\frac{14}{3}=r[/tex]
14,15,3,15,14,14,18,15,8 mean ,mode,median determine which measure of center best represenrs the data
Answers
Answer:
Mean: 12.9
Mode: 14,15
Median: 14
Step-by-step explanation:
f(x) = - 0.05(x ^ 2 - 26x - 120)
What do the zeros of this function represent? Remember the zeros are where f(x) =0.
Answers
We are given function for the path coming out of the cannon.
We also given x is the horizontal distance from the cannon.
We need to explain, what f(x) represents there.
f(x) represents y-axis.
And y-axis also represents height.
Height represents a vertical distance.
Therefore, we could say f(x) represents vertical distance (height) from the cannon for x horizontal distance from the cannon.
Allowing 20% discount on the marked price if a watch, the value of the watch will be Rs. 2376. If the VAT of 10% is added, find its marked price.
Ans: Rs. 2700
Answers
original price be x
x-0.2x=23760.8x=2376x=2970VAT 10%
So new price is 10% less
2970-0.10(2970)2970-297Rs 2673≈2700If x²+ y²= 80 and xy = 12, find the value of (x - y)².
Answers
[tex](x-y)^2\\\\=x^2+y^2 -2xy\\\\=80-2(12)\\\\=80-24\\\\=56[/tex]
We know the identity (a−b)2 =a2 −2ab+b2
Thus we have (x−y)2 =x2 −2xy+y2
Help picture below problem 13
Answers
Answer:
it's obtuse angle...
mark me brainliest
= Obtuse triangle
Explanation:(a triangle in which one of the interior angles measures more than 90° degrees.)
which has a greater magnitude 17 ft above sea level or 11 ft
Answers
Answer:
1 - 52= 52 33= 33 52 > 33, so -52 dollars has the greater magnitude. 1 - 141 = 14 [23] = 23 14 < 23, so 23 feet has the greater magnitude.
Step-by-step explanation:
Hope This Helps
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 44 ft/s. The ball's height h (in feet) after seconds is given by the following.
h = 3+44t-16t^2
Find all values of t which the balls height is 23 feet.
Answers
Answer:
See below ↓↓
Step-by-step explanation:
Given function
h = 3 + 44t - 16t²We need to calculate the possible values of t at h = 23 feet.
Subsituting h = 23,
23 = 3 + 44t - 16t²16t² - 44t + 20 = 0Divide throughout by 4 as it is a common factor4t² - 11t + 5 = 0Solving for 't' using quadratic formula
t = 11 ± √121 - 4(4)(5) / 8t = 11 ± √41 / 8Solutions
t = 11 + 6.4 / 8 = 17.4/8 = 2.175 secondst = 11 - 6.4 / 8 = 4.6/8 = 0.575 secondsAnswer:
t = 2.175 s (3 dp)
t = 0.575 s (3 dp)
Step-by-step explanation:
Given equation: [tex]h=3+44t-16t^2[/tex]
To find all values of t for which the ball's height is 23 ft, substitute h = 20 into the equation and solve for t:
[tex]\implies h=23[/tex]
[tex]\implies 3+44t-16t^2=23[/tex]
[tex]\implies 16t^2-44t-3+23=0[/tex]
[tex]\implies 16t^2-44t+20=0[/tex]
Factor out common term 4:
[tex]\implies 4(4t^2-11t+5)=0[/tex]
Divide both sides by 4:
[tex]\implies 4t^2-11t+5=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Use the quadratic formula to solve for t:
[tex]\implies t=\dfrac{-(-11) \pm \sqrt{(-11)^2-4(4)(5)} }{2(4)}[/tex]
[tex]\implies t=\dfrac{11 \pm \sqrt{41}}{8}[/tex]
Therefore,
t = 2.175 s (3 dp)t = 0.575 s (3 dp)How many solutions does the equation (20 - 12x) = 5 - 3x have?
Answers
Answer:
x=5/3
Step-by-step explanation:
there is only 1
Giving brainliest! need this question rlly soon thank you so much :)
Answers
Write an equation of the line in slope-intercept form.
y=
Answers
Answer:
The equation of the line in slope intercept form is y=1/3x+2
Step-by-step explanation: