Consider the following equation of a circle. x^(2)+y^(2)-2x+4y=20 Step 1 of 3 : Find the center, (h,k). Answer How to enter your answer (opens in new window )
Answers
The calculated center of the circle is (1, -2)
How to calculate the center of the circleFrom the question, we have the following parameters that can be used in our computation:
x² + y² - 2x + 4y = 20
Complete the square on the equation
So, we have
(x - 1)² + (y + 2)² = 5²
The equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
So, we have
Center = (1, -2)
Hence, the center of the circle is (1, -2)
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Related Questions
The plane with equation r= (1, 2, 3) + m(1, 2, 5) + n(1, 1, 3), m, n e R, intersects the x- and z-axes at the points A and B respectively. Determine the Cartesian equation of the line that contains these two points.
Answers
The Cartesian equation of the line that contains the points A and B, where A is the intersection point of the given plane with the x-axis and B is the intersection point with the z-axis, is x = 1 and z = 3.
To find the Cartesian equation of the line, we need to determine the values of x and z while allowing y to vary freely. Since point A lies on the x-axis, its y-coordinate is 0, so we have x = 1 and y = 0 for point A. Similarly, since point B lies on the z-axis, its y-coordinate is also 0, so we have z = 3 and y = 0 for point B.
Thus, the equation x = 1 represents the line that contains point A, and the equation z = 3 represents the line that contains point B. Since y can vary freely, we do not include it in the equations. Therefore, the Cartesian equation of the line that contains points A and B is x = 1 and z = 3.
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Find the circumference of a circle
with a diameter of 45.
Answers
Answer:
141.4 centimeters
Step-by-step explanation:
circumference = diameter * pi c = d * pi c = 45 * 3.1416 c = 141.4 (rounded)
Answer:
C= 141.37
Step-by-step explanation: go0gle
based on the statistical analysis of exoplanet data, approximately what fraction of stars in the milky way have an earth-size planet in the habitable zone?
Answers
The fraction of stars in the milky way having an earth-size planet in the habitable zone are around 10-20%.
Milky way is the galaxy comprising our solar system and therefore marking Earth's location in the universe. The milky way galaxy is just one among billions of different galaxies in the universe.
It contains numerous stars and the planets revolving it. Thus, the milky way galaxy can said to contain thousands of planetary systems. The planets in turn can be habitable or non-habitable owing to atmospheric conditions.
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Identify the volume of a cube with edge length 8 ft.
V = 512 ft^3
V = 256 ft^3
V = 514 ft^3
V = 324 ft^3
Answers
The volume of a cube with edge length 8 ft are V = 512 ft³
The volume of a cube is calculated by multiplying the length of one of its sides by itself three times (V = s³). Therefore, for a cube with an edge length of 8 ft, its volume would be V = 8³ = 512 ft³.
Therefore, the correct answer is: V = 512 ft³
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Help me I can't solve it!
Answers
The scientific notation of the given expression (7*10^{-6})(7*10^{-6}) will be 4.9 * 10^{-11}.
As per the question statement, we are supposed to find the scientific notation of the given expression (7*10^{-6})(7*10^{-6}).
Let x = (7*10^{-6})(7*10^{-6})
x = (7*7)(10^{-6})(10^{-6})
x = 49 * 10^{-6-6}
x = 49 * 10^{-12}
x = 4.9 * 10^{-11}
Hence, the scientific notation of the given expression (7*10^{-6})(7*10^{-6}) will be 4.9 * 10^{-11}.
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Evaluate the following, giving your answer in the simplest form.
a) 2 3/4 - 3 11/12
b) - 1 - ( - 5/6) + ( - 6/5)
Answers
a) -1 1/6
b) - 1 11/30
(A) 2 3/4 - 3 11/12
First we need to focus on the fractions, they need to have the same denominator to subtract.
12 is the common denominator
2 3/4 = 2 9/12
3 11/12 = 3 11/12
Now take 2 9/12 - 3 11/12 = - 1 2/12 simplified to - 1 1/6, your answer.
*note, your subtrahend is larger than your first number so you have a negative.
(B) -1 - (-5/6) + (-6/5)
First we need to have our fractions have the same denominator. Our common denominator here is 30.
- 5/6 = - 25/30
- 6/5 = - 36/30
Now our equation
-1 - (-25/30) + (- 36/30)
* note: a minus negative makes 25/30 a positive
-5/30 - 36/30 = -41/30
Simplify
- 1 11/30
Problems solved
abc is a right triangle with ab=ac. bisector of <a meets bc at d. prove that bc = 2ad.
Answers
Answer:
Let ac=ab=5
With this, bc= 5√2
Step-by-step explanation:
So to find ad, Let ad be x
5√2=(2)(x)
(5√2/2)= x
This proves that bc=2ad
The Cartesian coordinates of a point are (−1,−3–√). (i) Find polar coordinates (r,θ) of the point, where r>0 and 0≤θ<2π. r= 2 θ= 4pi/3 (ii) Find polar coordinates (r,θ) of the point, where r<0 and 0≤θ<2π. r= -2 θ= pi/3 (b) The Cartesian coordinates of a point are (−2,3). (i) Find polar coordinates (r,θ) of the point, where r>0 and 0≤θ<2π. r= sqrt(13) θ= (ii) Find polar coordinates (r,θ) of the point, where r<0 and 0≤θ<2π. r= -sqrt(13) θ=
Answers
(i) For the point (-1, -3-√): r=2, θ=4π/3 | (ii) For the point (-1, -3-√): r=-2, θ=π/3 | For the point (-2, 3): (i) r=√(13), θ= | (ii) r=-√(13), θ=
What are the polar coordinates (r, θ) of the point (-1, -3-√) for both r > 0 and r < 0, as well as the polar coordinates for the point (-2, 3) in both cases?(i) For the point (-1, -3-√) with r > 0 and 0 ≤ θ < 2π:
r = 2
θ = 4π/3
(ii) For the point (-1, -3-√) with r < 0 and 0 ≤ θ < 2π:
r = -2
θ = π/3
For the point (-2, 3):
(i) With r > 0 and 0 ≤ θ < 2π:
r = √(13)
θ =
(ii) With r < 0 and 0 ≤ θ < 2π:
r = -√(13)
θ =
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An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:
93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4
Answers
The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.
The sample variance is a measure of how much the individual data points in a sample vary from the mean.
It is calculated by finding the average of the squared differences between each data point and the mean.
To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:
Calculate the mean (average) of the data set:
Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90
Subtract the mean from each data point and square the result:
(93 - 90)^2 = 9
(89 - 90)^2 = 1
(91 - 90)^2 = 1
(87 - 90)^2 = 9
(91 - 90)^2 = 1
(89 - 90)^2 = 1
Calculate the sum of the squared differences:
9 + 1 + 1 + 9 + 1 + 1 = 22
Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):
Variance = 22 / 5 = 4.4
It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.
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Find the equation of the line that passes through (-5,3) and (1,1)
Answers
The equation of the line that passes through (-5,3) and (1,1) is y = (-1/3)x + 3.
To find the equation of the line that passes through the given points, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line. The slope formula is:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the given points, we get:
m = (1 - 3) / (1 - (-5))
m = (-2) / (6)
m = -1/3
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is:
y - y₁ = m(x - x₁)
Plugging in the slope and one of the given points, we get:
y - 3 = (-1/3)(x - (-5))
y - 3 = (-1/3)(x + 5)
y - 3 = (-1/3)x - (5/3)
y = (-1/3)x + (9/3)
y = (-1/3)x + 3
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x-4 in word form
Please help!
Answers
Answer:
x minus four
Step-by-step explanation:
can i have brainliest plz?
Answer and Step-by-step explanation:
The word form of the expression X - 4 is:
X minus four.
It can also be written as:
Some number minus four. (By user: iwaoiismyotp)
Any number in place of x minus 4.
A value substituted for x minus 4.
#teamtrees #PAW (Plant And Water)
If z is directly proportional to the product of x and y and if z is 10 when x is 4 and y is 5, then x, y, and z are related by the equation
Answers
The equation relating x, y, and z is:
z = 0.5 * x * y.
In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.
To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.
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Maria said that 40% of her family's tomato plants produced tomatoes this year. They had 70 tomato plants. How many plants produced tomatoes
Answers
Answer:
28 plants
Step-by-step explanation:
40% of 70 = 28
Can someone please explain to me how to do this I don't understand it at alll!
Answers
Answer:
Sitting pretty in the prime of light. I'm so tasty if the price is right :) BOOM BOOM BOOM BOOM
Step-by-step explanation:
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what is the distance between P(9,-5) and Q(-2,3) round to nearest tenth if necessary
Answers
Answer:
3.6
Step-by-step explanation:
find the rationalizing factor of:
a)³√16
b)√27
c) ³√4
plz solve these questions,I will make u brainliest if correct.
Answers
Answer:
Check out the answer. Hope it helps!!
if there is an average of 1.4 of 10 people, how much is there for 600
for example, out of 10 people surveyed for how many pets they have, the avg is 1.4, so out of 650 people surveyed what would the avg be??
Answers
Answer: For 600 ppl: 84 & for 650 ppl: 91
Step-by-step explanation:
If the average is 1.4 of 10 ppl, you can use that to solve for 600 people and for 650 people.
Divide 600 by 10, and you get 60.
Multiply that by 1.4, and you get 84, which is the answer.
For 650 people:
Divide 650 by 10, and you get 65.
Multiply that by 1.4, and you get 91, which is the answer.
find the coefficient of xr in (x 5 x 6 x 7 ···)
Answers
The cofficient of xʳ in the expansion of the expression, (x⁵ + x⁶ + x⁷ ···)⁸ is equals to the \(= \frac{ 8.9.10....( 8 + r - 41) }{(r - 40)!}\), r≥ 40.
This provide problem involves the application of binomial theorem to determine the coefficient of a term. The binomial theorem simply helps us to find the required coefficient easily using combinatorics. The formula of the binomial theorem is, \((a+b)^n =∑_{i=0}^{n} ⁿC_r a^rb_{n−r}\). Cofficient is an constant number that is written along with a variable or it is multiplied by the variable. We have an algebraic expression, (x⁵ + x⁶ + x⁷ + .... )⁸ and we have to solve it to determine the cofficient of x^r. So, first rewrite the expression, (x⁵ + x⁶ + x⁷ + .... )⁸ = [x⁵( 1 + x + x² +.....)]⁸
= x⁴⁰( 1 + x + x² +.....)⁸
= x⁴⁰ ( 1 - x) -8
Using binomial expansion,
\( ( 1 - x)^{-8} = 1 + 8x + \frac{8.9}{2!}x² +....\)
\((x⁵ + x⁶ + x⁷ + .... )⁸ = x⁴⁰( 1 + 8x + \frac{8.9}{2!}x² +....) \\ \)
Now, we have determine the cofficient of
\(x^r\). The required cofficient is
\(= \frac{ 8.9.10....( 8 + r - 41) }{(r - 40)!}\) for r ≥ 40.
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Complete question:
find the coefficient of x^r in (x ^5 + x^6 + x ^7 ···)⁸
6>2k+4
WONDERINGGGGGGGGGGGGGGGGGGGGGGGGGGGG
Answers
Answer:
is it 1?
Step-by-step explanation:
flowcharts are used to group of answer choices show the relative sizes of the parts of a whole. illustrate processes and procedures. show how something looks or operates. summarize large amounts of statistical data. indicate trends over time.
Answers
Flowcharts are used to summarize large amounts of statistical data and indicate trends over time. The correct options for the flow charts are to summarize large amounts of statistical data and indicate trends over time
Flowcharts are a powerful tool for both technical and non-technical people, providing a visual representation of complex information. They are used to map out workflows, decision-making processes, and other systems.
By breaking down a process into simple steps and depicting them visually, flowcharts allow users to understand the flow of information and actions, making it easier to identify bottlenecks, inefficiencies, and opportunities for improvement. Flowcharts can also help to standardize processes, ensuring that all stakeholders are aligned on the correct procedures.
Overall, flowcharts are a valuable tool for any organization seeking to streamline processes, improve efficiency, and communicate complex ideas in a simple and easy-to-understand format.
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Please solve the equation with a rational coefficients,
then choose your answer.
-1.4m = 2.1
Answers:
-1.5
1.5
5
15
Answers
m = - 1.5
Step-by-step explanation:Hi there !
- 1.4m = 2.1
m = 2.1 : - 1/4
m = - 1.5
Good luck !
LuAnn is playing a math game. She chooses three cards. The value of each of her cards is shown. • First card: -12 • Second card: 3 • Third card: -5 What is the sum of the values of LuAnn's three cards?
Answers
The sum of all the cards of Luann is -14.
One of the four fundamental operations for arithmetic on integers, decimals, fractions, real and complex numbers, as well as in algebraic expressions or on structures related to them, including vector spaces, is sum (also known as addition).
The terms, addends, or summands collectively refer to the numbers or objects that need to be added in general addition; this nomenclature also applies to the summation of several terms. This should be distinguished from multiplied factors.Addition or sum follows the commutative , associative and distributive properties.The given numbers on the cards are given as - 12 , 3 and - 5 .
Therefore the addition or sum is equal to :
-12 + 3 + ( - 5 ) = - 17 + 3 = - 14
Hence the sum of all the cards in LuAnn's card games is -14.
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I need help on this one problem, honestly I've tried this question like 4 times and was all wrong so I don't know. I will send a pic
Answers
Let's use the formula provided:
\(\begin{gathered} A=P(1+r)^t \\ \text{Where:} \\ P=3000 \\ r=0.05 \\ t=4 \\ A=3000(1+0.05)^4 \\ A=3000(1.05)^4 \\ A=3646.51857 \end{gathered}\)hlo friends
H. C. F of 64 and 96 is ____.
Answers
The highest common factors of 64 and 96 is 32
How to find the highest common factor(HCF)Find the factors of 64 and 96 respectively
64 = 1, 2, 4, 8, 16, 32 and 6496 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96The common factors of 64 and 96 are 1, 2, 4, 8, 16, 32
Therefore, the highest common factors of 64 and 96 is 32
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5 dollars for 4 cans of tuna
Answers
Answer:
1.25 for each can
Step-by-step explanation:
Answer: $1.25 per can of tuna
Hope this helps :)
Please mark me as Brainliest
Solve for x.
5(x - 10) = 30 – 15x
A. x = 1
B. x = 4
C. x = 5
D. x = 8
Answers
30+50= 80
-15x - 5x = -20x
-20x = 80
20/80
4
Anwer B.
x=4
Step-by-step explanation:
Distrubutive property: 5x-50=30-15x
get x on one side: 5x-50+15x=30
combine like terms: 20x-50=30
subtract on both sides: 20x=30+50
20x=80
simplify: 20/20=80/20
x=4
PLEASE HELP URGENT DO NOT WASTE ANSWERS
Answers
Answer:
(1/2)(1/2)
Step-by-step explanation:
Answer:
b or the second one because there are no letters
Step-by-step explanation:
The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate
Answers
The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.
The time Jasmine spends biking is indeed a function of the distance she bikes.
The formula to calculate the time Jasmine takes to bike a certain distance is equal to,
time = distance / speed __(1)
Here the speed is the rate at which Jasmine bikes = 18 miles per hour.
Let us consider 'd' be the distance representing the number of miles Jasmine bikes.
This implies,
The function that represents the time Jasmine spends biking in terms of the distance .
Function f(d) representing the time Jasmine spends biking for a distance of d miles
Substitute all the values in the formula (1) we get,
⇒ f(d) = d / 18
Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.
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The above question is incomplete , the complete question is:
The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.
Write the function representing the time Jasmine spends biking in terms of the distance?
A function f(x) is graphed.
What is the slope of the function?
ma
What is the y-intercept of the function?
b.
Which equatich represents the graph of the function?
Answers
Answer:
slope:1/2
y intercept:-1/2
equation of the line: y=1/2x-1/2
Step-by-step explanation:
choose two points from the line( I chose (3,1) and (-1,-1)) and then using y1-y2/x1-x2, do 1 - -1/3 - -1 which is 2/4 simplified to 1/2. the slope is 1/2.
now to find the y intercept, you just have to plug in the numbers from one of the sets of points you chose and your slope using y = mx +b(I will be using the point (-1,-1)). equational look like this: -1=1/2•-1+b
since b is the y intercept, solve for b and you get b= -1/2.
so nowsince you know the slope and the y intercept you just plug it in to the equation
y = mx + b and you get y=1/2x-1/2.
A line intercepts the points (3, -4) and has a slope of 17. What is the slope-intercept equation for this line?
Y=?x+?
PLZ, HELP WILL GIVE BRAINLY!!!!
Answers
Answer:
y=17x-55
Step-by-step explanation:
y=ax+b
y=17x+b
-4=17(3)+b
-4=51+b
-55=b
y=17x-55