Give the coordinates of the center, foci, vertices, and covertices of the ellipse with equation 41x^(2)+16y^(2)+246x-192y+289=0. Sketch the graph, and include these points.
Answers
The equation of an ellipse centered at (h,k) with major axis length 2a and minor axis length 2b is (x−h)2a2+(y−k)2b2=1. To solve this equation, write it in standard form and divide by the coefficient of x^(2). This gives a perfect square for the x terms and a perfect square for the y terms. The ellipse's coordinates are: center = (h, k), vertices = (-3±a, 6) (-3+23, 6), (-3-23, 6) (-20, 6), (-26, 6) (-3, 6±b), (-3, 6-37) (-3, 43), and (-3, -31) (-3±c, 6).
The equation of an ellipse centered at (h,k) with the major axis length 2a and the minor axis length 2b is shown by the given equation: (x−h)2a2+(y−k)2b2=1.The given equation is \(41x^(2)+16y^(2)+246x-192y+289=0\)Here, we have x and y in the form of squares, but we have x and y values, which are in linear terms.
Thus, we have to use the completing square method as follows:
First, we write the given equation in the standard form as follows: \(41(x^(2) + 6x)+16(y^(2)- 12y)+289=0\)
.Then, we will take the coefficient of x^(2) term and divide the equation by it. This will give us a perfect square for the x terms and a perfect square for the y terms as well.The new equation is \(41(x + 3)^(2)/529 + 16(y-6)^(2)/1369 = 1\).Here, the standard equation is (x−h)2a2+(y−k)2b2=1, which we will compare with the above equation. By comparing we get, h = -3, k = 6, a = √529 = 23, b = √1369 = 37.
Therefore, the coordinates of the center, foci, vertices, and co-vertices of the ellipse are:Center = (h, k) = (-3, 6)Vertices = (-3±a, 6) = (-3+23, 6), (-3-23, 6) = (20, 6), (-26, 6)Co-vertices = (-3, 6±b) = (-3, 6+37), (-3, 6-37) = (-3, 43), (-3, -31) Foci = (-3±c, 6), where c = √(a^2-b^2) = √(529-1369) = 24 (-3+24, 6), (-3-24, 6) = (21, 6), (-27, 6)
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Related Questions
How do you write 1.3 × 105 in standard form?
Answers
Given:
The scientific notation of a number is \(1.3\times 10^5\).
To find:
The standard form of the given number.
Solution:
Standard form: The normal way of writing a number is called standard form. For example: 200, 25600, 1025000 etc.
We have,
\(1.3\times 10^5\)
It can be written as
\(1.3\times 10^5=1.3\times 100,000\)
\(1.3\times 10^5=130,000\)
Therefore, the standard form of the given number is 130,000.
Mini Blenders Inc. has come up with a unit selling price of $15.00. Their Fixed costs are $30,000 for the year, during which 15,000 units are expected to be sold. A 25% profit margin on sales is included in the selling price. What is MBI's % profit on cost? 33.33% 0.30% O 50% O22% 25%
Answers
MBI's % profit on cost is 33.33%.
To calculate the % profit on cost, we need to determine the profit and divide it by the cost.
The selling price of each unit is $15.00, and 25% of this price is the profit margin, which is $15.00 * 25% = $3.75.
The cost per unit is the selling price minus the profit margin, which is $15.00 - $3.75 = $11.25.
The total cost for producing 15,000 units is $11.25 * 15,000 = $168,750.
The profit is the difference between the total revenue and the total cost, which is $15.00 * 15,000 - $168,750 = $81,250.
The % profit on cost is the profit divided by the cost, multiplied by 100: ($81,250 / $168,750) * 100 ≈ 48.15%.
Therefore, the correct answer is not provided in the given options. The closest option to the calculated result is 50%, but the actual % profit on cost is approximately 48.15%.
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one hundred forty one millon six hundred twenty thousand written in standard form
Answers
Answer:
141,620,000
Step-by-step explanation:
I hope that's what you meant ^^
Answer:
141,620,000
Step-by-step explanation:
................
Resolution and solutions the researchers want to find out if a new treatment for depression is effective. the depression was assessed by the beck depression inventory, which results in scores that range from 0 to 63. which method is an appropriate hypothesis test to determine whether scores of depression are different pre- and post-treatment?
Answers
An appropriate hypothesis test to determine whether scores of depression are different pre- and post-treatment would be the paired t-test.
The paired t-test is suitable in this scenario because it compares the mean scores of depression before and after the treatment within the same group of participants.
This test takes into account the paired nature of the data, where each participant is measured twice (pre- and post-treatment).
By conducting a paired t-test, the researchers can assess whether there is a statistically significant difference in depression scores before and after the treatment. This will help determine the effectiveness of the new treatment for depression.
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Question 12(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Answers
Thus, we may estimate that there were 557 principals present at the meeting.
Explain about the Proportion:A mathematical comparison of two numbers is called a percentage. These figures frequently serve as a comparison between various objects or individuals. Take the scenario where you entered a crowded room as an example.
We can forecast how many principals will attend the conference according to the data supplied.In a room with 70 individuals in total and 52 principals, the ratio of principals to attendees would be as follows:52/70 = 0.743 or 74.3%
Applying this ratio to the total number of attendees, we can extrapolate the proportion of principals at the conference, assuming that it is reflective of the conference as a whole:
Total principals at conference = Proportion of principals x Total number of attendees
Total principals at conference = 0.743 x 750
Total principals at conference ≈ 557
As a result, we may estimate that there were 557 principals present at the meeting.
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use the limit process to find the slope of the graph of the function at the specified point
Answers
The slope is the ratio of the vertical change between two points the rise to the horizontal change between the same two points.The slope of a line is respresented with (\(x_{1}\),\(y_{1}\)) represents the first point whereas (\(x_{2}\),\(y_{2}\)) represents the second point.
we find the slope of the graph of the function at the specified point firstly we pick two points on the given line and determine the cordinates.find out the difference in y coordinates of two points and also find out the difference in x coordinates of two points ,than divided the difference in y coordinates by the difference in x coordinates.
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A concert venue offers tickets in 3 zones: orchestra, grand tier, and balcony. Tickets in the orchestra zone are most expensive, and tickets in the balcony zone are least expensive. Managers of the venue want to survey approximately 150 guests at an upcoming concert about their overall experience. They want to take a systematic random sample of the 3000 guests they expect to attend. Which of these strategies will accomplish their intended design?
A. Use a computer to randomly select 150 tickets and invite those guests to participate in the survey
B. Randomly select one of the first 20 guests to arrive and every 20th guest thereafter to take the survey
C. Invite the first 150 guests that arrive to participate in the survey
D. Randomly select 50 tickets from each zone and invite those guests to participate in the survey
Answers
The correct answer for the given question is option B. Randomly select one of the first 20 guests to arrive and every 20th guest thereafter to take the survey
.The strategy that will accomplish the intended design is to randomly select one of the first 20 guests to arrive and every 20th guests thereafter to take the survey.
This strategy ensures that guests are systematically selected and that the sample is randomly selected.
It also ensures that all three zones are represented in the survey.
A systematic random sample is a type of probability sampling in which the sample is selected according to a systematic process.
The sampling interval is determined by dividing the population size by the sample size.
For example, if there are 3000 guests and the desired sample size is 150, the sampling interval would be 20.
The first guest selected would be randomly chosen from the first 20 guests to arrive, and every 20th guest thereafter would be included in the sample.
The other options given in the question will not accomplish the intended design,:
A. Using a computer to randomly select 150 tickets and invite those guests to participate in the survey will not ensure that the sample is systematically selected.
B. Inviting the first 150 guests that arrive to participate in the survey will not ensure that the sample is randomly selected.
C. Randomly selecting 50 tickets from each zone and inviting those guests to participate in the survey will not ensure that the sample is systematically selected.
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37 of the 998 digital video recorders (dvrs) in an inventory are known to be defective. what is the probability that a randomly selected item is defective?
Answers
The probability that a randomly selection of 998 digital video recorders in a inventory one of them is defective is 3.71%
To solve this exercise the formula and the procedure that we have to use for probability is:
% probability= (achieving success / possible outcomes) * 100
Information about the problem:
Achieving success = 37Possible outcomes = 998Applying the formula to calculate the probability we get:
% probability= (achieving success / possible outcomes) * 100
% probability= (37/ 998) * 100
% probability= (0.0371) * 100
% probability= 3.71%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
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Is this function linear or nonlinear? Why?
X^4+x^2=y
Is this function linear or nonlinear? Why?
2x+3y-x-y=4
Is this function linear or nonlinear? Why?
X=y=45
Is this function linear or nonlinear? Why?
Y=5x-10
Is this function linear or nonlinear? Why?
Y=56
Is this function linear or nonlinear? Why?
X^2+y=45
Is this function linear or nonlinear? Why?
Y=3x^5+4x^3
Is this function linear or nonlinear? Why?
Y=3x^5+4x^3
Is this function linear or nonlinear? Why?
Y=\|~11x+3
Answers
Answer:
1: No, x is raised to a power
2: Yes, can be solved in the form of y = mx + b
3: If this is supposed to be x + y = 45, then yes because it can be solved in the form of y = mx + b
4: Yes, it is in the form of y = mx + b
5: Yes, it is in the form of y = mx +b, it has a slope of zero and will be a horizontal line, which will pass the vertical line test
6: No, x is raised to a power.
7: No, x is raised to a power.
8: No, x is raised to a power
9: Is that supposed to be pi? If so, yes, it is in the form of y = mx + b
Step-by-step explanation:
2. Tyrel estimates that he can average $6.20 per hour throughout the week on all the jobs he does. Last week he worked 18.75 hours. If his estimate was correct, how much did he earn last week?
Answers
Answer:
303.75
Step-by-step explanation:
the new minimum wage is 15 dollars this is unbelievable these lies
“Delaneys internet provider charges $14.95 per month plus $5.75 for each gigabyte of data she stores in the cloud. Write an equation to model the cost per month for this situation.”
Answers
Answer:
5
Step-by-step explanation:
14.95×5.75 dhdhfhfhfhrhththththtbththththtbthththtbtbtbtbthtbtbtbth
2. Suppose A is a n x n matrix. Write a matlab code to find: (a) sum of diagonal elements (b) product of diagonal elements (c) Execute the sum and product when A= ones (5)
Answers
it displays the computed sum and product of the diagonal elements.
Here's a MATLAB code to find the sum and product of the diagonal elements of a given matrix `A`, as well as an example execution for `A = ones(5)`:
```matlab
% Define the matrix A
A = ones(5);
% Get the size of the matrix
[n, ~] = size(A);
% Initialize variables for sum and product
diagonal_sum = 0;
diagonal_product = 1;
% Calculate the sum and product of diagonal elements
for i = 1:n
diagonal_sum = diagonal_sum + A(i, i);
diagonal_product = diagonal_product * A(i, i);
end
% Display the results
disp("Sum of diagonal elements: " + diagonal_sum);
disp("Product of diagonal elements: " + diagonal_product);
```
Example execution for `A = ones(5)`:
```
Sum of diagonal elements: 5
Product of diagonal elements: 1
```
In this example, `A = ones(5)` creates a 5x5 matrix filled with ones. The code then iterates over the diagonal elements (i.e., elements where the row index equals the column index) and accumulates the sum and product. Finally, it displays the computed sum and product of the diagonal elements.
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for breakfast bob has three options: cereal, eggs or fruit. he hasto choose exactly two items out of the three available.(a) describe the sample space of this experiment
Answers
According to the concept of probability, the sample space for the experiment is explained below.
The term probability in math is called as the occurrence of a random event and the sample space is defined as a collection or a set of possible outcomes of a random experiment.
Here we have know that the same space of this experiment is the possible outcomes of selecting two out of the three breakfast.
Here let us consider that the sample space is B
And the the sample space is written as.
=> {(cereal and egg), (cereal and fruit), (fruit and egg), (fruit and cereal), (egg and fruit), (egg and cereal)}
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I need help with this equationnnnn
Answers
Answer:
5x + 4y + 12
Step-by-step explanation:
x + 2 + 10 - y + 4x + 2y + 3y =
= 5x + 4y + 12
The length of a movie is 1 hour 45 minutes. Mary has already watched the first 55 minutes.
How many more minutes does the movie last? Which equation did you use to find the answer
Answers
Answer:
50 minutes left
Step-by-step explanation:
1 hour is 60 mins
60 mins+45mins=105 mins
105-55=50
50 mins left
Answer:
50 minutes remaining in the movie
Step-by-step explanation:
1 hour= 60 minutes
+45 minutes
----------------------
105 minutes in movie total
- 55 minutes watched
----------------------
50 minutes remaining in the movie
factor out the common factor: -48y - 6x
i get how to do it but i'm not sure whether to put the negative in the greatest common factor or in the binomial. so basically -6(8y+x) or 6(-8y-x).
Answers
Answer:
-6 (x + 8y)
Step-by-step explanation:
Factor -48y -6x
-6x-48y
Answer : -6 (x+8y)
Please help me for gods sake:(
Answers
Answer:
Step-by-step explanation:
y=3x-2, plug in each for x and y on the table and they work
Please help me guys I beg you I will give you lots of credit plz
Answers
Answer:
11m/min
Step-by-step explanation:
slope of the line = velocity of the turtle
slope = y/x
= 55/5
=11
Answer:
11
Step-by-step explanation:
55 meters by 5 minutes, so divide 55 by 5 to find one minute.
55/5 = 11
Prove algebraically that (image). Trigonometric Identities. Please help.
Answers
Answer:
Step-by-step explanation:
$1.29, $1.92, $3.19, $1.79, $3.99, $479, 55.19, $5.29, $5.49
4) Henry had 9 items in his shopping cart with different prices (shown). His mean cost of these items was $5.88. At the register, he added a gift card to his purchase for $40.00. Choose ALL
statements about how the gift card price will affect the mean and median of the items he purchased
A) Both the mean and median will increase.
B) Only the mean of the prices will increase
Only the median of the prices will increase
D) The mean will increase by more than the median
D) Neither the mean nor median of the prices will increase
Answers
The conclusion on the mean and median after the gift card is added is:
C: Only the median of the prices will increase
How to find the mean and median of the distribution?The mean (average) of a data set is gotten by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest.
The mean of the dataset is:
Mean = (1.29 + 1.92 + 3.19 + 1.79 + 3.99 + 479 + 55.19 + 5.29 + 5.49)/9
Mean = $61.91
If he added a $40 gift card, then:
New mean = (1.29 + 1.92 + 3.19 + 1.79 + 3.99 + 479 + 55.19 + 5.29 + 5.49 + 40)/10 = $59.715
Initial median:
1.29, 1.79, 1.92, 3.19, 3.99, 5.29, 5.49, 55.19, 479
Initial median = 3.99
Final median after the gift card of $40:
1.29, 1.79, 1.92, 3.19, 3.99, 5.29, 5.49, 40, 55.19, 479
Final median = (3.99 + 5.29)/2 = $4.64
Thus, only median will increase
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Write the equation in point-slope
form that passes through the point (1,3) and has a slope of 1/2.
Answers
Answer:
\(\huge\boxed{y-3=\dfrac{1}{2}(x-1)}\)
Step-by-step explanation:
The point-slope form of an equation of a line:
\(y-y_1=m(x-x_1)\)
\(m\)- slope
\((x_1;\ y_1)\) - point on a line
We have
\(m=\dfrac{1}{2};\ (1;\ 3)\to x_1=1;\ y_1=3\)
Substitute:
\(y-3=\dfrac{1}{2}(x-1)\)
Use the distance formula to find the area of the square:
Answers
Answer:
10
Step-by-step explanation:
Distance formula:
d = √(x₂-x₁)²+(y₂-y₁)²
A (1,2) D (4,3)
d = √(4-1)²+(3-2)² = 3.16227766
All 4 sides of a square are equal lengths.
The equation for the area of a square:
A = a²
A = (3.16227766)² = 10
If anybody knows how to do this pls anwser thansdk
Answers
Answer:
Either A or B.
Step-by-step explanation:
Each number in the sequence is being added by 6.
So you can use the equation: x+6
The ninth term in the sequence would be 36 because 30+6=36
When Joseph first starts working at a grocery store, his hourly rate is $10dollar sign, 10. For each year he works at the grocery store, his hourly rate increases by $0.50dollar sign, 0, point, 50.
Joseph's hourly rate R, in dollars, is a function of t, the number of years he works at the grocery store.
Write the function's formula.
Answers
Answer:
R(t)=10+0.50t
Step-by-step explanation:
Let t be the number of years.
We have been given that When Joseph first starts working at a grocery store, his hourly rate is $10.
For each year he works at the grocery store, his hourly rate increases by $0.50.
So the hourly rates after t years will be 10 plus 0.50t.We can represent this information in an equation as: R(t)=10+0.50t
Therefore, the function R(t)=10+0.50t represents Joseph's hourly rates after t years.
(Hope this helps pls can I have brainlist have a great day )
If the number of bacteria in a colony doubles every 21 hours and there is currently a population of 150 bacteria, what will the population be 42 hours from now?
Answers
Answer:
450
Step-by-step explanation:
i think thats right
Please help
Given: P(1, 3)P(1,3)
and
Q(3,7)Q(3,7)
What is the slope of PQPQJ
Answers
Answer:
Slope = 2
Step-by-step explanation:
(1,3) and (3,7)
m = (7-3)/3-1)
= 4/2
= 2
Please please help help
Answers
option b is correct answer please Like me and Follow me
Find the following using identities (190)²
Answers
\(\boxed{36100}\)
You want to estimate the average GMAT score for all students who took the Logitano GMAT Preparation course during the past 2 years. You select a random sample of 100 such students from a comprehensive list of all students who took the course over the last two years and find that the average GMAT score for the sample was 1040. Suppose now you build a 95% confidence interval estimate of the average score for the population of Logitano students represented here and the interval turns out to be 1040 ± 10 points. How would you interpret your result?
We can be 95% confident that the interval 1030 to 1050 contains the average score for the entire population of Logitano students.
The score for 95% of all Logitano students will be between 1030 and 1050.
There is a 5% chance that not all Logitano students scored between 1030 and 1050.
We can be 95% confident that all of Logitano students scored between 1030 and 1050.
Ninety-five percent of the scores for all Logitano students will be between 1030 and 1050.
Answers
The correct interpretation is: We can be 95% confident that the interval 1030 to 1050 contains the average score for the entire population of Logitano students.
The statement is referring to a confidence interval estimate for the average score of the entire population of Logitano students who took the GMAT Preparation course during the past two years. The interval 1030 to 1050 is constructed based on a sample of students and provides a plausible range for the true population average.
The interpretation "We can be 95% confident that the interval 1030 to 1050 contains the average score for the entire population of Logitano students" means that if we were to repeat the process of taking samples and constructing confidence intervals multiple times, about 95% of those intervals would contain the true average score of all Logitano students who took the course.
In other words, the statement implies that we have a high level of confidence that the true population average score falls within the interval 1030 to 1050. This level of confidence is derived from the statistical methods used to estimate the population parameter (average score) based on the sample data. The 95% confidence level indicates that there is a 95% probability that the true population average lies within the stated interval.
It's important to note that this interpretation is based on the assumptions and conditions of the statistical analysis performed, such as the random sampling of students, the validity of the estimation method, and the assumption of normality in the population distribution.
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eacher: ""the first triangle is an isosceles triangle. the second triangle is an isosceles triangle. the third triangle is not an isosceles triangle. based on your observations alone what should be the definition of an isosceles triangle?""what does this question illustrate about the geometry teacher’s questioning techniques?
Answers
We have demonstrated the definition of an isosceles triangle.
What is an isosceles triangle?
An isosceles triangle is a triangle with at least two equal-length sides in geometry. It is sometimes specified as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter version including the equilateral triangle as a special case.
The isosceles triangle has both two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). A triangle with all sides equal is called an equilateral triangle, and a triangle with no sides equal is called a scalene triangle.
The given diagram shows an isosceles triangle.
Hence, we have demonstrated the definition of an isosceles triangle.
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