Given:
Hyperbola with directrices at y = ±2 and foci at (0, 6) and (0, −6).
To find:
The equation of hyperbola.
Solution:
We have, directrices at y = ±2 so this hyparabola is along the y-axis.
The standard form of hyperbola is
[tex]\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1[/tex] ...(i)
where, (h,k) is center, foci are [tex](h,k\pm c)[/tex] and directrix are [tex]y=k\pm \dfrac{a^2}{c}[/tex].
On comparing foci, we get
[tex](h,k\pm c)=(0,\pm 6)[/tex]
[tex]h=0,k=0,c=6[/tex]
On comparing directrix we get
[tex]k\pm \dfrac{a^2}{c}=\pm 2[/tex]
[tex]\dfrac{a^2}{c}=2[/tex]
[tex]\dfrac{a^2}{6}=2[/tex]
[tex]a^2=12[/tex]
Now,
[tex]a^2+b^2=c^2[/tex]
[tex]12+b^2=(6)^2[/tex]
[tex]b^2=36-12[/tex]
[tex]b^2=24[/tex]
Putting [tex]h=0,k=0,a^2=12,b^2=24[/tex], we get
[tex]\dfrac{(y-0)^2}{12}-\dfrac{(x-0)^2}{24}=1[/tex]
[tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex]
Therefore, the equation of hyperbola is [tex]\dfrac{y^2}{12}-\dfrac{x^2}{24}=1[/tex].
Answer:
the person above has the right answer. I took the test.
Step-by-step explanation:
The person above is correct.
Your princpal has decided to provide a treat to everyone in your grade before thanksgiving break-ice cream bars! One box contains 48 bars. There are 338 students in your grade. How many boxes does he need to purchase?
Answer:
8 boxes approx
Step-by-step explanation:
Step one:
given data
One box contains 48 bars
Required
The number of boxes needed for a total of 338 students if each person is to get at least one bar.
Step two:
this can be gotten by dividing 338 by the number of the bar in a box
= 338/48
=7.04
=8 boxes approx
He needs to purchase at least 8 box
could somebody help me please
Answer:
Integers; -10
Step-by-step explanation:
Numbers that include zero, counting numbers and negative counting numbers are integers.
Whenever someone owes money to another, this is represented by adding a negative sign.
The angle between the generator and the central axis of a double-napped cone is 50°. Which conic section is formed
when a plane intersects the central axis at 50°?
circle
ellipse
parabola
hyperbola
SIMPLE CORDINATE PLOTTING! BRAINLIEST, 5 STAR, AND A LIKE ON UR ANSWER. SHOW SOME WORK.
Answer:
A
Step-by-step explanation:
( 2, -5 )
( -2, -5)
Hope this helps dude
Answer:
A is your answer :)
Step-by-step explanation:
Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains
Answer:
3/5
Step-by-step explanation:
We want to find the fraction of the original branch that remains, so we will assume a length of the branch in order to make our calculation easier.
Since Kim marks it off in thirds and fifths, let's find the least common multiple of 3 & 5.
Least common multiple of 3 & 5 is 15.
Thus,let's make the length of the branch to be 15-meter long.
Now, if the branch is 15 m long, considering the markings of thirds and fifths, the branch would be cut at:
3, 5, 6, 9, 10, 12 meters.
We are told that She then breaks the branch along all the markings and removes one piece of every distinct length. Thus;
Distinct lengths are;
3 metres
5 - 3 = 2 metres
10 - 9 = 1 meter
Total she removes = 3 + 2 + 1 = 6 meters.
Total remaining is;
15 - 6 = 9 meters
Expressing this as a fraction of the original branch gives:
9/15
Divide both numerator and denominator by 3 to get; 3/5
Due soon please help me
Answer:
D. (10*5)a^5+^6b^3+^2
Step-by-step explanation:
When you are multiplying two exponents with the same base, you keep the base and add the powers together. Hope this helps.
0 = 4(3.14)/5 ;r = 9 cm
Answer:
i don't think i know the answer to your question
Step-by-step explanation:
What is the equation of the line that has a slope of Y and contains the point (0, 3)?
Answer:
B
Step-by-step explanation:
if you take your anwser and multilpy it by the factor you get B
Answer:
equation of line in y
Step-by-step explanation:
slope Y and given point (0,3)
y=3
or y-3=0
On a certain day, a bakery produced a batch of rolls at a total production cost of $300. On that day, 4 5 of the rolls in the batch were sold, each at a price that was 50 percent greater than the average (arithmetic mean) production cost per roll. The remaining rolls in the batch were sold the next day, each at a price that was 20 percent less than the price of the day before. What was the bakery's profit on this batch of rolls
Answer:
$108
Step-by-step explanation:
Let number of rolls produced = [tex]x[/tex]
Total production cost = $300
Average production cost can be found by dividing the total production cost with the number of rolls produced.
Average production cost per roll = $[tex]\frac{300}{x}[/tex]
[tex]\frac{4}{5}[/tex] of the rolls were sold at a price 50% higher than the average production cost per roll.
i.e.
Money earned by selling [tex]\frac{4}{5}[/tex] of the rolls:
[tex]\dfrac{4}{5}x \times \dfrac{300}{x}\times \dfrac{150}{100}\\\Rightarrow \$360[/tex]
Money earned by selling the remaining the remaining rolls:
[tex]\dfrac{1}{5}x\times \dfrac{300}{x}\times \dfrac{80}{100}\\\Rightarrow \$48[/tex]
Total money earned by selling all the rolls = $360 + $48 = $408
Total profit can be calculated by subtracting the total production cost from the total money earned.
Total profit = $408 - $300 = $108
which one is greater 1.72 or 1.720
Answer:
there equal.
Step-by-step explanation:
Answer:
They are equal.
Step-by-step explanation:
If there is a 0, it doesn't necessarily mean they are different numbers.
6(2a + b) + b A. 12a + 12b B. 12a + 7b C. 8a + 8b D. 8a – 8b
Answer:
Step-by-step explanation:
6(2a + b ) +b
12a + 6b +b
12a + 7b
so answer B looks good
Answer: B) 12a+7b
Step-by-step explanation:
6(2a+b) +b
12a+6b+b
Combine like terms
12a+7b
Therefor B is correct
hey it is pretty late i hope u get your work done and get good sleep and have some points
Answer:
Thanks for the points. ❤❤Solve the following equations
3x-6y=14
y=x+4
Answer:
y=2
Step-by-step explanation:
\©°©°©°¥=¥=€=€°`°€°€°%=
What does this expression represents -3+3x^3. Is asking how many polynomial terms and what is the constant term and what the leading term is and what is the coefficien? Help me please
Answer:
constant term is -3, the leading term is 3x^3, the coefficient is 3.
Step-by-step explanation:
Please help me, thanksssss❤️
Answer:
N = 8
Step-by-step explanation:
Hope this helps. Pls give brainliest.
Gabby spent 44.10 for 14 gallons of gas. What was the unit cost, or price per gallon
how to graph x<4. (((((((((((((((((((((((((((
k/3.8 + 57.6 = 28.3
The value of k is =
Answer:
k = -111.34
Step-by-step explanation:
In this question, you will solve for k.
Solve:
k/3.8 + 57.6 = 28.3
Subtract 57.6 from both sides.
k/3.8 = -29.3
To get "k" by itself, multiply both sides by 3.8 to eliminate the fraction.
k = -111.34
-111.34 is the value of "k".
When a figure is rotated, does every point move the same distance? Explain. *
No. The angle of rotation is different for each point, and each point and its image are, therefore, different distances from the center of rotation, so the distance each point moves varies.
Yes. Since the angle of rotation is the same, the distance that each point moves is the same.
No. Although each point is rotated through the same angle, points that are different distances from the center of rotation move different distances.
Yes. When rotating a figure, the rotation indicates that each point moves the same distance, such that the angle of rotation may vary from point to point.
Answer:
Yes. Since the angle of rotation is the same, the distance that each point moves is the same.
Step-by-step explanation:
Answer Yes. Since the angle of rotation is the same, the distance that each point moves is the same i think
Step-by-step explanation:
3. 'a' and 'b' are the intercepts made
by a straight-line with the co-
ordinate axes. If 3a = b and the line
pass through the point (1, 3), find
the equation of the line.
Given:
'a' and 'b' are the intercepts made by a straight-line with the co- ordinate axes.
3a = b and the line pass through the point (1, 3).
To find:
The equation of the line.
Solution:
The intercept form of a line is
[tex]\dfrac{x}{a}+\dfrac{y}{b}=1[/tex] ...(i)
where, a is x-intercept and b is y-intercept.
We have, 3a=b.
[tex]\dfrac{x}{a}+\dfrac{y}{3a}=1[/tex] ...(ii)
The line pass through the point (1, 3). So, putting x=1 and y=3, we get
[tex]\dfrac{1}{a}+\dfrac{3}{3a}=1[/tex]
[tex]\dfrac{1}{a}+\dfrac{1}{a}=1[/tex]
[tex]\dfrac{2}{a}=1[/tex]
Multiply both sides by a.
[tex]2=a[/tex]
The value of a is 2. So, x-intercept is 2.
Putting a=2 in [tex]b=3a[/tex], we get
[tex]b=3(2)[/tex]
[tex]b=6[/tex]
The value of b is 6. So, y-intercept is 6.
Putting a=2 and b=6 in (i), we get
[tex]\dfrac{x}{2}+\dfrac{y}{6}=1[/tex]
Therefore, the equation of the required line in intercept form is [tex]\dfrac{x}{2}+\dfrac{y}{6}=1[/tex].
1,615 / 10 the the power of 2
If x) = 4x^2 + 1 and g(x) = x^2 - 5, find (f + g)(x).
Answer:
C. 5x² - 4
General Formulas and Concepts:
Algebra I
Composite FunctionsCombining Like TermsStep-by-step explanation:
Step 1: Define
f(x) = 4x² + 1
g(x) = x² - 5
(f + g)(x) is f(x) + g(x)
Step 2: Find (f + g)(x)
Substitute: (f + g)(x) = 4x² + 1 + x² - 5Combine like terms: (f + g)(x) = 5x² - 4Please Help me!! It's for testing!
Jude is going from his house to the library. He walks as a rate of 100 yards per minute and bikes as a rate of 300 yards per minute. On his way to the library, Jude walks for 12 minutes and then rides his bike the rest of the way. The library is 6000 yards from his house.
How many minutes did it take Jude to go from his house to the library?
22 Minutes
28 Minutes
30 Minutes
48 Minutes
Answer:
28 minutes
Step-by-step explanation:
100 yards times the 12 minutes he walked = 1200 yards. 6000-1200=4800
4800÷300=16
16 + 12 = 28
Answer:
28 Minutes
Step-by-step explanation:
The library is 6000 yd from the house.
He walks at a rate of 100 yd per minute for 12 minutes, which is 1200 yd of progress.
He bikes the rest of the 4800 yd on his bike at a rate of 300 yd per minute.
4800/300=16 minutes.
16+12=28 minutes.
is it bad if you over think to much (ik its not question but i really dont no one to talk to rn so ....)
if you get the right answer, no. if you get the wrong answer yes
it all depends on what the question is and such
Answer: No not unless it affects you and your mental health
Step-by-step explanation:
Im a huge over thinker and i blame myself for a lot of things that arent even my fault. Over thinking things isnt always the best way to go you should always have someone to talk to. If your feeling worthless or down just know you are enough! You are perfect and dont try to change it for anyone. Its not bad to overthink unless it affect you so greatly that it hurts to smile. I know times are tough right now but you will get through it just stay strong. I hope this helped :)
2(x + 7) + 3 x = 12
what is the first step In solving this equation for x?
Answer:
The first step would be to distribute that 2 into the numbers in the parenthesis.
Step-by-step explanation:
Answer:
Step-by-step explanation:
I feel like there are many ways to begin this problem, but I'd distribute the 2(x+7) so that you are left with 2x+14. This way you can add 2x and 3x and subtract 14 to the other side.
1. Choose the correct common fraction.
0.13
0.3
none of these
1/3
What is the value of x?
Answer:
the value of x is one of those answers i can tell you son
Step-by-step explanation:
and it is NOT 3/4 thast FOR SURE
In triangle ABC, m_A = 55°, m B = 30°, and a = 8. Which equation should you
solve to find b?
Answer:
B) sin55/8 = sin30/b
Step-by-step explanation:
Just did it on AP3X :)
Five members of the Varsity Math team are running late for a big
competition and hurrying toward the arena - but they forgot that they would
have to cross the stream that cuts through campus. When they reach the
stream, there's a small boat tied up on their side that they can "borrow" to get
to the other side.
The boat will hold one, two or three of the students, but not more.
Fortunately, two of the team members are also on the crew team, and when
the boat contains only one or both of them, they can make it across the stream
in one minute. Unfortunately, the other three teammates are very
inexperienced with boats, and when any of them is aboard, there is so much
awkwardness and flailing that the crossing will take four minutes, regardless
of whether one of the crew teammates is on board.
The team members adopt the fastest strategy for rowing back and forth
across the stream to get everyone to the other side for the competition. How
many minutes does it take all five team members to get across?
Answer:
8 min
Step-by-step explanation:
Crew C =2
loser L =3
min 1 2C goes
min 1 1C comes
min 4 3L goes
min 1 1C comes
min 1 2C goes
total min 8
PLS HELP I NEED AN ANSWER ASAP
Answer:
4/sin (35)
Step-by-step explanation:
sin(35)=4/AB