Why is this equation: [tex]\frac{(x-2)^{2}}{24} + \frac{(y+5)^{2}}{29}=1[/tex] an ellipse and not a circle?
Usually, you can tell if it's an ellipse because the coefficients of x and y are different. Here, though, they're the same, yet every website is telling me it's an ellipse and not a circle. Why is that?
THANKS!
Answers
well, your observation is correct, for the form
Ax² + Bx + Cy² + Dy + E = 0if the coefficients are the of x² and y² are different and the same sign then we have an ellipse, hmmm I usually see a circle as an ellipse with equal major and minor axes, because is basically just that.
However, the rational form you have is that of an ellipse indeed, we can change it about to the form above and you'll see it so.
Just bear in mind that for the rational form for conics
if both fractions are positive and their denominator different, is an ellipse
if both fractions are positive and their denominator equal, is a circle
if one of the fractions is negative, then we have a hyperbola, and on a hyperbola the traverse axis is always the denominator with the positive fraction, so if the denominator is under the "x" fraction, then the traverse axis is horizontal, if under the "y" fraction, then vertical.
based on that fraction, is an ellipse with a center at (2 , -5).
now, the larger denominator is 29 and it's under the "y" variable, that means the major axis is in the direction of the y-axis, so is a vertical ellipse if you wish. Check the picture below.
![Why Is This Equation: [tex]\frac{(x-2)^{2}}{24} + \frac{(y+5)^{2}}{29}=1[/tex] An Ellipse And Not A Circle?Usually,](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/SmNAkZEYp1Lhg0OUhLjUwBcNSjO1b2ll.png)
Related Questions
NEED HELP ASAP 20POINTSS
Answers
Answer:
a) Low: 45 Q1=80 Q2=89 Q3=94 High=100 b) Look at attached image
Step-by-step explanation:
Organized numbers: 45,70,72|,80,|82,85,88|,89,|90,92,92|,94,|98,100,100
mark medians
Graph created in Desmos
Which is the best prediction of the test score for someone who completes 14 assignments? 20 70 50 100
Answers
A company claims that 9% of the items produced on a new machine are defective.
The factory will get rid of the machine if the data indicates that the proportion of defective items is more than 9%.
They take a random sample of 300 items and 50 are defective.
What null hypothesis is appropriate?
Answers
Considering the situation described, the appropriate null hypothesis is given by:
[tex]H_0: p = 0.09[/tex]
What are the hypothesis tested?At the null hypothesis, it is tested if the proportion is the expected one, that is, of 9%, hence:
[tex]H_0: p = 0.09[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the proportion is above 9%, hence:
[tex]H_1: p > 0.1[/tex].
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I NEED HELP PLEASE... HELPPPP MEEEE
Write a quadratic equation to represent each situation. Use your equation to answer each question. Be sure to define your variables and identify which is independent and which is dependent. Show all work. Round any decimals to the nearest hundredth.
1. A rocket is launched from a height of 10 meters with an upward velocity of 56 meters per second.
a. When will the rocket hit the ground?
b. What is the maximum height of the rocket?
c. After how many seconds does the rocket reach the maximum height?
2. A wooden deck of uniform width surrounds a rectangular pool as shown in the following image. The pool is 10 feet by 14 feet. What is the area of the wooden deck that surrounds the pool (not including the pool)?
a. If the deck is 3 feet wide, what is the area of the deck?
b. The area of the deck is 112 square feet. How wide is the deck?
3. A coffee shop sells 150 coffees a day at $3.50 apiece. They found for every $0.50 increase in price, they sell 10 fewer cups of coffee a day. The cups of coffee cost the shop $1.50 apiece.
a. How much should they charge to maximize their daily profits?
b. How many cups of coffee will they sell daily at that price?
c. What will their daily profits be?
Answers
Answer:
56. In the Vector Addition Lab, Anna starts at the classroom door and walks:
2.0 meters, West
12.0 meters, North,
31.0 meters, West,
8.0 meters, South
3.0 meters, East
Using either a scaled diagram or a calculator, determine the magnitude and direction of Anna's resulting displacement.
Answer: 30.3 meters, 172 degrees
To insure the most accurate solution, this problem is best solved using a calculator and trigonometric principles. The first step is to determine the sum of all the horizontal (east-west) displacements and the sum of all the vertical (north-south) displacements.
Horizontal: 2.0 meters, West + 31.0 meters, West + 3.0 meters, East = 30.0 meters, West
Vertical: 12.0 meters, North + 8.0 meters, South = 4.0 meters, North
The series of five displacements is equivalent to two displacements of 30 meters, West and 4 meters, North. The resultant of these two displacements can be found using the Pythagorean theorem (for the magnitude) and the tangent function (for the direction). A non-scaled sketch is useful for visualizing the situation.
Applying the Pythagorean theorem leads to the magnitude of the resultant (R).
R2 = (30.0 m)2 + (4.0 m)2 = 916 m2
R = Sqrt(916 m2)
R = 30.3 meters
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (4.0 m) / (30.0 m)
tangent(theta) = 0.1333
theta = invtan(0.1333)
theta = 7.59 degrees
This angle theta is the angle between west and the resultant. Directions of vectors are expressed as the counterclockwise angle of rotation relative to east. So the direction is 7.59 degrees short of 180 degrees. That is, the direction is ~172 degrees.
Useful Web Links
Vector Addition
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57. In a grocery store, a shopper walks 36.7 feet down an aisle. She then turns left and walks 17.0 feet straight ahead. Finally, she turns right and walks 8.2 feet to a final destination. (a) Determine the magnitude of the overall displacement. (b) Determine the direction of the displacement vector relative to the original line of motion.
Answer: (a) 48.0 feet; (b) 21 degrees from the original line of motion
This problem is best approached using a diagram of the physical situation. The three displacements are shown in the diagram below on the left. Since the three displacements could be done in any order without effecting the resulting displacement, these three legs of the trip are conveniently rearranged in the diagram below on the right.
Now it is obvious from the diagram on the right that the three displacement vectors are equivalent to two perpendicular displacement vectors of 44.9 feet and 17 feet. These two vectors can be added together and the resultant can be drawn from the starting location to the final location. A sketch is shown below.
Since these displacement vectors are at right angles to each other, the magnitude of the resultant can be determined using the Pythagorean theorem. The work is shown below.
R2 = (44.9 ft)2 + (17.0 ft)2 = 2305 ft2
R = Sqrt(2305 ft2)
R = 48.0 feet
The angle theta in the diagram above can be found using the tangent function.
tangent(theta) = opposite/adjacent = (17.0 ft) / (44.9 ft)
tangent(theta) = 0.3786
theta = invtan(0.3786)
theta = 20.7 degrees
This is the angle which the resultant makes with the original line of motion (the 36.7 ft displacement vector).
Useful Web Links
Vector Addition || Vector Components || Vector Resolution
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58. A hiker hikes 12.4 km, south. The hiker then makes a turn towards the southeast and finishes at the final destination. The overall displacement of the two-legged trip is 19.7 km at 309 degrees . Determine the magnitude and direction of the second leg of the trip.
Answer: 12.7 km, 347 degrees
Like the previous problem (and most other problems in physics), this problem is best approached using a diagram. The first displacement is due South and the resulting displacement (at 309 degrees) is somewhere in the fourth quadrant. (It is in the fourth quadrant because 309 degrees lies between 270 degrees or due South and 360 degrees or due East.) For communication sake, we will refer to the first displacement as A and the second displacement as B. Note that A + B = R. Since the magnitude and direction of the resultant is known, the x- and y-components can be determined using trigonometric functions. Since the angle of 309 degrees is expressed as a counterclockwise angle of rotation with due East, it can be used as the Theta in the equation.
Rx = R•cos(theta) = 19.7 km • cos(309 deg) = 12.398 km
Ry = R•sin(theta) = 19.7 km • sin(309 deg) = -15.310 km (the "-" means South)
Whatever the magnitude and direction of B is, it must add on to vector A in order to give a southward displacement of 15.310 km and a eastward displacement of 12.398 km. This could be expressed by mathematical equations as
The radius
of a sphere is 6 units.
Which expression represents the volume of the sphere,
in cubic units?
O ¾7(6)2
• 57(6)3
0 -(12)2
5a(12)3
Answers
Answer:
4/3 πr^3
= 4/3π (6)^3
therefore the answer is C
Difference of squares. Pls help algebra factoring polynomials 10 points
Answers
Answer:
4x(squared)-36
Step-by-step explanation:
=(2x+−6)(2x+6)
=(2x)(2x)+(2x)(6)+(−6)(2x)+(−6)(6)
=4x^2+12x−12x−36
=4x^2 −36
Below is a list of the steps used to construct a square inscribed in a circle.
Step M - Place the compass point at the endpoint of the diameter and the pencil at
the center of the circle to construct an arc.
Step N - Draw in two diameters using the points where the small arc intersects the
line segments and the center.
Step O - Construct a small arc by placing the compass point where the diameter
intersects the line segment and the pencil on the center of the circle.
Step P - Construct a line segment between the two points where the arc intersects the
circle.
Step Q - Draw line segments between the four points where the two constructed
diameters intersect the circle.
Which list shows these steps in the correct order?
M, N, O, P, Q
M, P, O, N, Q
O, P, M, Q, N
P, O, M, Q, N
Answers
Answer:
B: M,P,O,N,Q
Step-by-step explanation:
Sowy if i am wrong pls don't go hard on me.
Answer:
b
Step-by-step explanation:
took the test
Calculate the perimeter of the shape below. Show ur work!
Answers
Answer:
22 is the perimeter.
Step-by-step explanation:
You find the perimeter by adding up all of the sides of a shape. 9 + 9 = 18. 18 + 4 = 22.
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
Answers
Solving them, it is found that the equivalent equations are given as follows: 2 + x = 5, x + 1 = 4, -5 + x = -2.
What are equivalent equations?Equivalent equations are equations that have the same solution.
In this problem, the equations and their solutions are given as follows.
2 + x = 5 -> x = 3.x + 1 = 4 -> x = 3.9 + x = 6 -> x = -3.x - 4 = 7 -> x = 11.-5 + x = -2 -> x = 3.Hence the equivalent equations are: 2 + x = 5, x + 1 = 4, -5 + x = -2.
More can be learned about equivalent equations at https://brainly.com/question/2972832
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Divide. Give the quotient and remainder. 4374/5
Answers
Answer:
874
rem = 4.
Step-by-step explanation:
4374/ 5
= 874 remainder 4
Multiply and simplify the product. (3 – 5i)(–2 4i) select the product. 14 2i 14 22i 15 22i 26 2i
Answers
The product of the expressions (3 – 5i) and (–2 + 4i) is 14 + 2i. Then the correct option is A.
What is multiplication?It is also known as the product. If the object n is given to m times then we just simply multiply them.
The expressions are (3 – 5i) and (–2 + 4i).
Then the product of the expressions will be
(3 – 5i)(–2 + 4i)
–6 –10i + 12i –20i²
We know that i² = –1, then we have
–6 + 2i –20 (–1)
–6 + 2i + 20
14 + 2i
More about the multiplication link is given below.
https://brainly.com/question/19943359
Answer: B- 14+22i
Step-by-step explanation: edge 2023
Rewrite the rational expression with the given denominator.
Answers
Answer:
49t²r³
Step-by-step explanation:
Hello!
6r is multiplied by 7r³ to get to 42r^4. To keep a fraction proprtional, both numerator and denominator must be multiplied by the same amount.
We have to multiply 7t² by 7r³ to find the missing value.
Multiply:
7t² * 7r³49t²r³The missing value is 49t²r³
You buy 4 health bars and 3 health drinks for $10. Your friend buys 6 health bars and 2 health drinks for $10. Each health bar costs how much and each health drink costs how much
Answers
Using a system of equations, it is found that:
The cost of a health bar is of $1.The cost o a health drink is of $2.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Cost of a health bar.Variable y: Cost of a health drink.You buy 4 health bars and 3 health drinks for $10, hence:
4x + 3y = 10.
Your friend buys 6 health bars and 2 health drinks for $10, hence:
6x + 2y = 10
2y = 10 - 6x
y = 5 - 3x.
Replacing on the first equation:
4x + 3y = 10
4x + 3(5 - 3x) = 10
-5x = -5
5x = 5
x = 1
Then:
y = 5 - 3x = 5 - 3 = 2.
The cost of a health bar is of $1.The cost o a health drink is of $2.More can be learned about a system of equations at https://brainly.com/question/24342899
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27
4 points
The ideal gas law, PV = nRT, is a well-known equation in science that describes the behavior of gases. P
is the pressure of the gas, Vis the volume of the gas, n is the amount of the gas, Ris the constant, and Tis
the temperature of the gas. Which of the following statements are equivalent to the equation written
above? Select all that apply.
P = nRt/V
T = PV-nR
V = nRT/P
n=PV/RT
R=nT/PV
Answers
Answer:
1,3,4
Step-by-step explanation:
ıf we rearrange formula we can obtain
p=nrt/v
t=pv/nr
v=nrt/p
r=pv/nt
Diameter = 50 cm
In terms of , what is the area of the circle?
Answers
Answer:
1,962.5
Step-by-step explanation:
r=d/2
50 / 2 = 25
25 = r
A= πr²
3.14 x 25²=1,962.5
[tex]Hope[/tex] [tex]this[/tex] [tex]helps![/tex]
Researchers studied the role that the age of workers has in determining the hours per month spent on personal tasks. A sample of 1,686 adults were observed for one month. The data are:
Answers
The 98 percent confidence interval for the mean hours spent on personal tasks for 25-44 years olds will be (3.97, 4.11).
How to calculate the confidence interval?From the complete information, it should be noted that the mean is 4.04, the standard deviation is 0.81 and the number is 708.
Since the sample size is large, so the z-critical will be used. In this case, the critical value is 2.33.
The 98% confidence interval will be:
= 4.04 + 2.33(0.81/✓768)
= 4.11
Also, 4.04 - 2.33(0.81/✓768)
= 3.97
Therefore, the 98% confidence interval is (3.97, 4.11).
Learn more about confidence interval on:
https://brainly.com/question/15712887
you are taking a trip at the same time as another family. your family traveled 1.900 miles in 2 days, their family traveled 2.700 miles in 3 days. who is traveling faste
Answers
Answer:
your family
Step-by-step explanation:
1,900/2 = 950
2,700/3 = 900
your family travels 950 miles every day whereas their family travels 900 miles every day :)
HELPP me please I beg
Answers
Answer: 78
Step-by-step explanation:
Area=b x h
13 x 6 =78
Answer:
78 m
Step-by-step explanation:
The formula to find the area of a rectangle or square = length * Height
A = L * H
In this scenario, the length is 6 and the height is 13
So the area (A) = 6 * 13 = 78
And don't forget your units ;)
Mark said, "in the data set,4, 5, 5, 8, the mean and mode the same. " Is he correct? Explain why or why not in your explanation make sure to state the value of the the means and the mode
Answers
Answer:
No
Step-by-step explanation:
the mean is 16 (add 4+5+5+8, then divide answer by 4) and the mode is 5 (occurs most in data)
enter the value of x such that blah blah blah look at the picture
Answers
Answer:
x=6
Step-by-step explanation:
Create equivalent expressions in the equation that all have equal bases, then solve for x.
A coin is tossed 20 times with the following results:
HHHTTTTHTTHHTTHTHHHH
What is the experimental probability of the coin landing on tails?
Answers
Using it's concept, it is found that there is a 0.45 = 45% experimental probability of the coin landing on tails.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For an experimental probability, these number of outcomes are taken from previous trials.
In this problem, 9 out of 20 trials resulted in tails, hence the experimental probability is given by:
p = 9/20 = 0.45 = 45%.
More can be learned about probabilities at https://brainly.com/question/14398287
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My sister need the anwser for this question: What is the area of a triangle with a base (b) of 12cm and a height (h) of 4cm?
Answers
Answer:
24 cm²
Step-by-step explanation:
You can show your sister how to use the formula for the area of a triangle.
The base dimension is substituted for the letter b, the height is substituted for the letter h, and then the arithmetic is carried out.
A = 1/2bh
A = (1/2)(12)(4) = (6)(4) = 24 . . . . square centimeters
What is the difference of the polynomials?
(8r6s3 - 9r5s4 + 3r4s5) - (2r4s5 - 5r3s6 - 4r5s4)
Answers
Answer:
see image.
Step-by-step explanation:
Since this is a subtraction problem remember to 'add the opposite' So change to addition between the two sets of parenthesis and change all the signs/operations in the second term.
Then combine like terms. This means the terms can only be added or subtracted if the have exactly the same variables and exponents. See image.
quick?
Graph the circle with center (−1, 2) that passes through (−6, 2). Find the area in terms of π and to the nearest tenth. Use 3.14 for π.
Answers
Answer:
The area is 78.5.
Step-by-step explanation:
The formula for the area of a circle is π r^2
In this case, r = 5.
How do you do this? I am really confused
Answers
Answer:
Step-by-step explanation:
ok, so this is an infinitly repeating function, so you can write it as:
sqrt(12-x)
Although, x is also equal to sqrt(12-x), so
x = sqrt(12-x), and
x^2 = 12-x
x^2-12+x = 0
now just apply the quadratic formula and you're good
hope i helped :D
Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they
worked on average 44. 2 hours per week. The standard
deviation of the sample was 2. 6. Estimate the mean of
the population with 90% confidence.
Answers
Overtime Hours Worked A random sample of 15 registered nurses in a large hospital showed that they worked on average 44. 2 hours per week. we can estimate with 90% confidence that the population mean of overtime hours worked by registered nurses in the hospital is between 42.5 and 45.9 hours per week.
What is t-distribution?The t-distribution is a probability distribution that is used to estimate the population mean of a normally distributed variable when the sample size is small or the population standard deviation is unknown.
To estimate the population mean with a 90% confidence interval, we can use a t-distribution with n-1 degrees of freedom, where n is the sample size.
First, we need to calculate the standard error of the mean, which measures the variability of sample means around the population mean. The formula for the standard error of the mean is:
SE = s / sqrt(n)
where s is the sample standard deviation and n is the sample size.
In this case, s = 2.6 and n = 15, so:
SE = 2.6 / sqrt(15) = 0.671
Next, we need to find the critical value of the t-distribution with 14 degrees of freedom and a 90% confidence level.
We can look this up in a t-table or use a calculator to find that the critical value is approximately 1.761.
Finally, we can calculate the confidence interval using the formula:
CI = X ± tα/2 * SE
where X is the sample mean, tα/2 is the critical value of the t-distribution, and SE is the standard error of the mean.
In this case, X = 44.2 and tα/2 = 1.761, so:
CI = 44.2 ± 1.761 * 0.671
CI = (42.5, 45.9)
Therefore, we can estimate with 90% confidence that the population mean of overtime hours worked by registered nurses in the hospital is between 42.5 and 45.9 hours per week.
For more details regarding t-distribution, visit:
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The math club is doing a car wash as a fundraiser. They charge $7 per car and $12 per minivan. The club wants to raise
$600
Which equation in standard form shows how many cars and minivans m they need to wash to meet their goal
Answers
Answer:
7x+12y ≤ 600
or7x+12y = 600
Step-by-step explanation:
Lets first call cars x and minivans y. Since they want to raise 600, you can do the sign ≤ and 600
≤ 600
Since it is $7 per car, we can do 7x.
Since it is $12 per minivan, we can do 12y.
Together, they have to add up to 600 or more.
7x+12y ≤ 600
If you provide some options, I might be able to give a better answer. Without options, I can't tell if they want an exact answer or not. So technically, the answer could also be:
7x+12y = 600
You and 3 friends go bowling. You bowl for 2.5 hours. You play 3 games and the total cost is $42.
Find the average rate of games per hour
Answers
Answer:
if you play 3 games and the total cost equals to 42
then just do 42 divided by 3 which is 14 so that should be your answer!
Step-by-step explanation:
im very sorry if i get it wrong im only trying to help
so i hope its correct
Which choice represents the expression below as a single exponential
expression?
4^5 • 42
• A. 410 . 410
O B. 410
O c. 43
O D. 47
Answers
Answer:
D
Step-by-step explanation:
When multiplying numbers with the same base but different exponents, add the exponents together.
show division using an array 1. 24÷4 Quotient= Remainder=
Answers
Answer:
Quotient: 6
Remainder: None
Step-by-step explanation:
24 divided by 4 is 6.