Find an equation in standard form for the hyperbola with vertices at (0, ±3) and foci at (0, ±7)
Answers
The equation of a hyperbola is:
(x – h)^2 / a^2 - (y – k)^2 / b^2 = 1
So what we have to do is to look for the values of the variables:
For the given hyperbola : center (h, k) = (0, 0)
a = 3(distance from center to vertices)
a^2 = 9
c = 7 (distance from center to vertices; given from the foci)
c^2 = 49
By the hypotenuse formula:
c^2 = a^2 + b^2
b^2 = c^2 - a^2
b^2 = 49 – 9
b^2 = 40
Therefore the equation of the hyperbola is:
(x^2 / 9) – (y^2 / 40) = 1
Answer:
Hope this helps :)
Step-by-step explanation:
Related Questions
if 5(3x-7)=20 then what is 6x-8
Answers
15x-35=20
15x= 55
x= 55/15
x= 11/3
Plug this x value in.
6(11/3)-8
66/3 -8
22-8
14
Final answer: 14
una pizzeria hace pizzas de varios tamaños y las vende en cajas hexagonales de 39 cm de lado y 4.7 cm de alto ¿que cantidad de cartón se anestesia para cada caja teniendo en cuenta q la caja esta formado por dos partes compuestas de una base lateral ?
Answers
Final answer:
To calculate the amount of cardboard used for each box, we need to find the surface area of the hexagonal base and the lateral surface area. We can use the formula for the surface area of a hexagon to find the base area. Then, we multiply it by the height of the box and add the two areas together.
Explanation:
To find the amount of cardboard used for each box, we need to calculate the surface area of the hexagonal base and the lateral surface area. The surface area of a hexagon can be found using the formula:
Surface Area = 3 x √3 x s^2
where s is the length of the side of the hexagon. Given that the side length is 39 cm, we can substitute this into the formula to find the surface area of the hexagonal base. Once we have the surface area, we can calculate the lateral surface area by multiplying it by the height of the box, which is 4.7 cm. Adding the two areas together will give us the total amount of cardboard used for each box.
PLEASE HELP!!!!!!!dgbdgdbhdndcn
Answers
AC is only perpendicular to EF if angle ADE is 90 degrees
(angle ADE) + (angle DAE) + (angle AED) = 180
(angle ADE) + (44) + (48) = 180
(angle ADE) + 92 = 180
(angle ADE) + 92 - 92 = 180 - 92
angle ADE = 88
Since angle ADE is actually 88 degrees, we do NOT have a right angle so we do NOT have a right triangle
Triangle AED is acute (all 3 angles are less than 90 degrees)
So because angle ADE is NOT 90 degrees, this means AC is NOT perpendicular to EF
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Problem 2)
a) The center is (2,-3)
The center is (h,k) and we can see that h = 2 and k = -3. It might help to write (x-2)^2+(y+3)^2 = 9 into (x-2)^2+(y-(-3))^2 = 3^3 then compare it to (x-h)^2 + (y-k)^2 = r^2
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b) The radius is 3 and the diameter is 6
From part a), we have (x-2)^2+(y-(-3))^2 = 3^3 matching (x-h)^2 + (y-k)^2 = r^2
where
h = 2
k = -3
r = 3
so, radius = r = 3
diameter = d = 2*r = 2*3 = 6
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c) The graph is shown in the image attachment. It is a circle with center point C = (2,-3) and radius r = 3.
Some points on the circle are
A = (2, 0)
B = (5, -3)
D = (2, -6)
E = (-1, -3)
Note how the distance from the center C to some point on the circle, say point B, is 3 units. In other words segment BC = 3.
Which of the following statements is the converse of the statement "If each of two angles has a measure of 28 degrees, then the two angles are equal in measure"?
Answers
If the 2 angles are equal in measure the each of the 2 angles has a measure of 28 degrees.
AS you see in this example , the converse is not necessarily true.
Answer:
If two angles are equal in measure then each of the two angles has a measure of 28 degrees.
Step-by-step explanation:
The converse of a statement is found by switching the hypothesis and conclusion of a conditional statement.
The hypothesis is the part that comes after "if" and the conclusion is the part that comes after "then."
This means the hypothesis is "each of two angles has a measure of 28 degrees" and the conclusion is "the two angles are equal in measure."
This gives us the converse "If two angles are equal in measure then each of the two angles has a measure of 28 degrees."
A personal identification code consists of five digits (0 through 9). how many codes are possible?
a. 50
b. 252
c. 100,000
d. 30,240
Answers
on each place you have 10 possible digit,
so for 5 places it will be 10^5 = 100, 000
There are 30,240 codes that are possible which consist of five digits (0 through 9).
What is a permutation?A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.
There are 10 options for each of the 5 digits in the personal identification code (0 through 9). Since the order of the digits matters, we can use the formula for the number of permutations of n items taken r at a time, which is:
n!/(n-r)!
In this case, n is the number of options (10) and r is the number of items (5). Plugging these values into the formula gives us:
10!/(10-5)! = 10!/(5!) = 109876 = 30,240
Therefore, the correct answer is (d) 30,240.
Learn more about permutation here:
brainly.com/question/1216161
#SPJ5
An experiment consists of dealing 5 cards from a standard 52-card deck. what is the probability of being dealt aa 10, jack, queen, king, ace, all in the same suit
Answers
The probability of getting a royal flush is 1/649740 = 0.00000153907717
---------------------------------------------
Explanation:
There are 4 ways to get a royal flush. Those ways are
* You have a royal flush with nothing but hearts
* You have a royal flush with nothing but diamonds
* You have a royal flush with nothing but spades
* You have a royal flush with nothing but clubs
This is out of 52 C 5 = (52!)/(5!*(52-5)!) = 2,598,960 different five cards hands
So we have 4/2598960 = 1/649740 = 0.00000153907717
4xy - 9xy + -3xy Simplify the polynomial
Answers
The variable Z is inversely proportional to X. When X is 6, Z has the value 2. What is the value of z . When x = 13
Round to at least the thousandths place if needed.
Answers
Z= k/x
when x is 6, Z= 2
2=k/6
k=2*6
k=12
Z=12/X
when x = 13
Z=12/13
Z=0.923
If today is tuesday what day will it be in 100 days
Answers
How to determine the direction of a vector?
Answers
If 5+3+2=151012, 9+2+4=183662, 8+6+3=482466, 5+4+5= 202504 , then 7+2+5= ?
a.141035
b.143510
c.143542
d.143524
Answers
What is the equation of a circle with a center (-2, 3) and a radius r = 5?
Answers
(x - h)^2 + (y - k)^2 = r^2
(h, k) is the center.
So the equation would be:
(x + 2)^2 + (y - 3)^2 = 5^2
or
(x + 2)^2 + (y - 3)^2 = 25
The lifetime of a supertough aaa battery is normally distributed with mean of 28.5 hours and standard deviation of 5.3 hours. for a battery selected at random, what is the probability that the lifetime will be 25 hours or less?
Answers
z-score = (x - μ) / σ
where x is the data, μ is the mean, and σ is the standard deviation.
Substituting the known values,
z-score = (25 - 28.5)/5.3
z-score = -0.66
This translates to a percentage equal to 25.46%.
Therefore, from the supertough aaa batteries, approximately 25.46% has a lifetime that is only about 25 hours or less.
Which equation is not a quadratic equation?
y = 3x2 + 2
y = 5x - 2
y = -x2
y = 5x2 - 2x + 7
Answers
[tex]ax^{2} +bx +c[/tex]
where a, b and c are the coefficients of the expression and a ≠ 0.
If a = 0, the equation becomes a linear expression and is no longer quadratic.
Hence, in the above options; y = 5x -2 is the only one that is not a quadratic equation.
Which formula is used to find circular mil area?
Answers
For example, a wire has a diameter of 6×10⁻⁵ inches. To find its area:
A = πr² = π( 6×10⁻⁵ /2)² = 2.83×10⁻⁹ in²
Since 1 mil = 1/1000 (inch) or 0.001 inch
A = (2.83×10⁻⁹ in²)* (1 mil/ 0.001 inch)²
A = 0.00283 circular mils
if a 24-day single payment loan has a periodic interest rate of 8.4% what is the approximate APR of the loan?
A. 201.6%
B. 127.8%
C. 12.8%
D. 20.2%
Answers
Answer:
Option B, 127.8%
Step-by-step explanation:
If a 24-day single payment loan has a periodic interest rate of 8.4%.
First we divide 365 by 24 to make periods of 24 days in one year.
365 ÷ 24 = 15.21
periodic interest rate of 8.4%
then Annual Percentage Rate = 15.21 × 8.4 = 1 27.76 ≈ 127.8%
127.8% is the approximate APR of the loan.
A science experiment begins with a metal at −100° Celsius. The following function describes the temperature change per minute: f(x) = 89x − 100°. How will the graph of this function change if the metal is at 25° at the start of the experiment?
Answers
f ( x ) = 89 x - 100°.
This is the graph of a linear function in the slope-intercept form:
y = m x + b
Starting point is - 100°, so b = - 100°
If the metal is at the temperature of 25° at the start of experiment, then it would be: b = 35°
The new equation: g ( x ) = 89 x + 25°
g ( x ) || f ( x ) ( parallel functions ), 25° - ( -100° ) = 125°
Answer: The graph of the function will translate vertically 125° up.
Answer:
A
Step-by-step explanation:
Jacobysontop!
Two numbers, 3 and a, have a geometric mean of 9. Find the value of a.
Answers
So, if the geometric mean of 3 and a is 9 =>
9 = √(3a)
=> 9^2 = 3a
=> a = 9^2 / 3
a = 81 / 3
a = 27
Answer: the value of a is 27.
Examine the graph at right. Then in a sentence suggest why the graph rises at 11:00am and drops at 1:15pm
Answers
Suppose you draw a card from a well-shuffled pack of playing cards. What is the probability the card you draw will be an ace? A. 4/50 B. 1/13 C. 4/13 D. 1/52
Answers
Favorable outcome ={ 4 Aces}
P(drawing ONE Ace) = 4/52 = 1/13 = 0.0769 (answer B. 1/13)
Over what interval of time in minutes was the jogger heart rate changing at the constant rate
Answers
We have a graph of the heart rate vs time.
We want to find on what interval the heart rate increases with a constant rate.
That interval is 3min ≤ t ≤ 4 min
The general function that increases with a constant rate is the general linear function:
y = a*x + b
Where a is the slope and also defines the constant rate of change.
Then the interval where the jogger heart rate changes at a constant rate is the part where we have a linear function (not the horizontal line, there the heart rate does not change).
Then the interval where the heart rate changes with a constant rate is:
3min ≤ t ≤ 4 min
If you want to learn more, you can read:
https://brainly.com/question/21670190
If you had 5 green marbles and 8 red marbles, what's the probability that you'll pull out a marble that is green?
Answers
5+8 = 13 total marbles
5 are green
so you would have a 5/13 probability of picking a green one
What are the discontinuities of the function f(x) = the quantity x squared minus 16 over the quantity 4x plus 24
Answers
--------
4x + 24
when x = -6 the denominator 4x+24 = 0 so there is a discontinuity at x = -6
This is a vertical asymptote x = -6
There is also a sloping asymptote - you find this by getting the quotient
which is y = 0.25x - 1.5 This is the equation of this asymptote.
Answer:
x= -6 is the point of discontinuity.
Step-by-step explanation:
We have been given the expression
[tex]\frac{x^2-16}{4x+24}[/tex]
The first thing to find the discontinuity is to factorize the given rational function:
After factorization we get:
We will use [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]here, a=x\text{and}b=4[/tex] we will get:
[tex](x+4)(x-4)=x^2-4^2[/tex]
we will get:
[tex]\frac{(x+4)(x-4)}{4(x+6)}[/tex]
Discontinuity is the point where value of the function becomes not defined
Here, the point of discontinuity is -6 because when denominator becomes zero. function becomes not defined.
It has vertical asymptote but function is not defined.
Hence it is the point of discontinuity.
Which complex number has a distance of √17 from the origin on the complex plane?
A;2 + 15i
B:17 + i
C:20 – 3i
D:4 – i
Answers
Then by the pythagoras therem
17 = x^2 + y^2
D will satisfy this equation
4^2 + (-1)^2 = 17
answer is D 4 - i
Answer:
The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
D is correct
Step-by-step explanation:
We are given the absolute value of complex plane.
If complex number is a+ib then absolute value [tex]\sqrt{a^2+b^2}[/tex]
We have to check the absolute value of each option and check which is equal to [tex]\sqrt{17}[/tex]
Option A: 2+15i
[tex]d=\sqrt{2^2+15^2}=\sqrt{4+225}=\sqrt{229}\neq \sqrt{17}[/tex]
Option B: 17+i
[tex]d=\sqrt{17^2+1^2}=\sqrt{289+1}=\sqrt{290}\neq \sqrt{17}[/tex]
Option C: 20-3i
[tex]d=\sqrt{20^2+3^2}=\sqrt{400+9}=\sqrt{409}\neq \sqrt{17}[/tex]
Option D: 4-i
[tex]d=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}= \sqrt{17}[/tex]
Hence, The complex number 4-i has distance [tex]\sqrt{17}[/tex] from origin.
There are 10 people in a room. if each person shakes hands with exactly 3 other people, what is the total number of handshakes?
Answers
10x3=30
What does b belong with?
Answers
b-5
C-6
D- 2
Explanation: To match the equations properly I just used the process is substitution and elimination.
please vote my answer brainliest. thanks!
Two spheres of the same density have a ratio of 4 to 9 in surface area. If the small sphere weighs 10 kg, what does the large sphere weigh?
Answers
Sphere Surface Area = 4 • π • r²
radius^2 = Surface Area / 4* PI
Let's say area of smaller sphere is 4 PI
radius^2 = 1
radius = 1
9/4 = 2.25
Area of the larger sphere = 4 * PI * 2.25
radius^2 = 2.25
radius = 1.5
Volume of a sphere = 4/3 • π • r³
Volume of larger sphere = 4/3 • π • 1.5^3
Volume of larger sphere = 3.375 times volume of smaller sphere
Mass of larger sphere = 3.375 * 10 kg
The larger sphere weighs 33.75 kg
Your teacher is giving you a test worth 100 points containing 40 questions. there are two-point and four-point questions on the test. let the number of two-point questions be x and the number of four-point questions be y. how many of each type of question are on the test?
Answers
2x + 4y = 100
2(40 - y) + 4y = 100
80 - 2y + 4y = 100
-2y + 4y = 100 - 80
2y = 20
y = 20/2
y = 10 <=== there are 10 four-point q's
x + y = 40
x + 10 = 40
x = 40 - 10
x = 30 <=== there are 30 two-point q's
Answer:
t=30 f=10
Step-by-step explanation:
t= 100*1 - 40*4 = 30
2*1 - 1*4
f= 2*40 - 1*100 = 10
2*1 - 1*4
t=30 f=10
Ship A receives a distress signal from the northeast and ship B receives a distress signal from the same vessel from the west. At what location is the vessel in distress located? Describe how you arrived at your conclusion using complete sentences.
Answers
Second based on the two directions from the points you know that up is north, Right is east, West is left, and down is south on the graph.
Draw a line from the two points in the direction that it says the ship received the call from.
so the ship is at Ordered pair 3,3 :)
Coordinate geometry is the use of a 2D plane to represent the location of points. The position or location of the distress is in the first quadrant.
The coordinates of ship A and B are not given. So, I will give a general explanation.
On the four cardinal points,
North is upwardsEast is at the rightWest is at the leftSouth is downwardSo, if ship A receives a distress from the northeast, then it means that the distress is coming from a location at the top right of A. i.e. the first quadrant.
Also, ship B receives distress from the west. This means that ship B is at the right-hand side of the distress.
So, we can conclude that the position or location of the distress is at the first quadrant.
It is impossible to determine the actual coordinates of the distress because the coordinates are not given (see attachment possible illustration)
Read more about coordinate geometry at:
https://brainly.com/question/18269861
Maggie’s brother is 12 years younger that three times her age . The sun of their ages is 44 . How old is Maggie
Answers
Maggie's brother's age = b
Maggie's age = m
b = 12 - 3m
44 = 12-3m
12-3m = 44
-12 -12
-3m = 32
÷ 3 ÷3
m = 10.67
So this would be Maggie's age
I hope this helped :)