What is the center of a circle whose equation is x^2+y^2-12x-2y+12=0
Answers
Answer:
\((6,\, 1)\).
Step-by-step explanation:
Let \((a,\, b)\) denote the center of this circle (where \(a \) and \(b\) are to be found.) If the radius of this circle is \(r\), the equation of this circle would be:
\((x - a)^{2} + (y - b)^{2} = r^{2}\).
Expand this equation using binomial theorem:
\(x^{2} - 2\, a\, x + a^{2} + y^{2} - 2\, b\, y + b^{2} = r^{2}\).
Both this equation and the given equation \(x^{2} + y^{2} - 12\, x - 2\, y + 12 = 0\) describe the same circle. Therefore, corresponding coefficients of the two equations should match one another:
The coefficient of the \(x\) term should match in the two equations. Therefore: \((-2\, a) = (-12)\).The coefficient of the \(y\) term should also match in the two equations. Therefore: \((-2\, b) = (-2)\).Solve these two equation for \(a\) and \(b\): \(a = 6\) and \(b = 1\).
Substitute \(a = 6\) and \(b = 1\) into \((a,\, b)\) to find the center of this circle: \((6,\, 1)\).
Related Questions
Solve the system of linear equations by elimination. 8x−7y=−3 6x−5y=−1
Answers
What is the value of x?
75
28°
67°
F
Answers
Answer:
114 degrees
Step-by-step explanation:
Leah worked for 8 hours and earned $48.At this rate , how many hours would it take her to earn $60.
Answers
The number of hours required to earn $60 will be 10 hours.
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that Leah worked for 8 hours and earned $48.At this rate,
The number of hours required to earn $60 will be calculated as:-
$48 = 8 hours
$1 = 8 / 48 hours
To earn $60 time required will be,
$60 = ( 1 / 6 ) x 60
$60 = 10 hours
Therefore, the number of hours required to earn $60 will be 10 hours.
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You model your investment account using the formula y = 20000(1.035)x where x represents the
number of years and y represents the account balance after x years. What is the growth rate of your
investment?
Answers
Answer:
Step-by-step explanation:
The growth rate of the investment is represented by the constant multiplier in the exponential term of the formula y = 20000(1.035)x. In this case, the constant multiplier is 1.035, which represents the annual growth rate of the investment account.
To calculate the growth rate as a percentage, we can subtract 1 from the constant multiplier, and then multiply the result by 100.
So, the growth rate of the investment is:
1.035 - 1 = 0.035
0.035 * 100 = 3.5%
Therefore, the growth rate of the investment is 3.5%.
The growth rate of the investment can be found by subtracting 1 from the base of the exponential function and converting the result to a percentage:
growth rate = (base - 1) x 100%
growth rate = (1.035 - 1) x 100%
growth rate = 0.035 x 100%
growth rate = 3.5%
Therefore, the growth rate of the investment is 3.5%.
Helpppppppppppppppppppppp ASAP
Answers
9514 1404 393
Answer:
B. G(x) = (x -0.5)³ -(x -0.5)
Step-by-step explanation:
The desired equation can be found by translating the function left one unit. That is accomplished by replacing x with x+1. Then you have ...
G(x) = ((x +1) -1.5)³ -((x +1) -1.5)
G(x) = (x -0.5)³ -(x -0.5) . . . . . . . . matches choice B
51 is a multiple of 2,3,5,6,9,10 or none
Answers
Based on the numbers given, we can say that 51 is a multiple of 3.
What is 51 a multiple of?51 is not a prime number which means that it has factors and it is a multiple of several numbers.
The factors of 51 include:
1, 3, 17, and 51
Out of the numbers given of 2,3,5,6,9,10, it therefore means that 51 is a multiple of only one number which is 3. When 3 is multiplied by 17, it gives 51.
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36% of what is 99? Please help
Answers
Answer:
99 is 36% of 275.
Step-by-step explanation:
To find this, we need to set up our equation. We will have 99 be 36% of the number we are trying to find, while we are going to have x equal the number we are looking for. Then, on the right side of the equation we are making, we will have the percent.
99/x=36/100
Next, we cross multiply.
36x=9900
Now, divide both sides by 36 to get x by itself.
x=275
So 99 is 36% of 275.
.............. ......
Please help asap due soon!!
Answers
The domain and the range of the composite function are given as follows:
a) Domain: {3, 5, 6, 7}.
b) Range: {0, 9}.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the following rule:
(f ∘ g)(x) = f(g(x)).
It means that the output of the inside function serves as the input for the outside function.
The points on the composite function are given as follows:
g(f(1)) = g(0) = undefined.g(f(3)) = g(7) = 9.g(f(5)) = g(3) = 9.g(f(6)) = g(3) = 9.g(f(7)) = g(2) = 0.The domain is the set of input values, hence it is given by:
{3, 5, 6, 7}.
The range is the set of output values, hence it is given by:
{0, 9}.
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ill give the crown things
Members of the drama club sold T-shirts for their upcoming musical. Of the 80 shirts sold, 45% were size medium. How many of the T-shirts sold were size medium?
Answers
Answer:
36
Step-by-step explanation:
45% = \(\frac{45}{100}\)
No. of T-shirts size medium = \(\frac{45}{100}\) × 80
= 36
what is the slope of the line on the graph?
Answers
Answer:
1/6
Step-by-step explanation:
A (6,1)
B (12,2)
slope = (2-1)/(12-6)
1/6
A person has a rectangular garden with a width of 5 feet and a length of 7 feet. To form a border of uniform width, he plans to place mulch around the outside of the garden. If he has just enough mulch to cover 64 square feet of land, determine the width of the border.
PLEASE HELP!!!!!!!!!!!
Answers
Answer:
I think the answer is c
Step-by-step explanation:
What 9+10?................................................
Answers
Answer:
21
9= 3*3
10= 5*2
Therefore 5*3 + 3*2
= 15+6 = 21
On a standardized exam, the scores are normally distributed with a mean of
195 and a standard deviation of 50. Find the z-score of a person who scored
330 on the exam.
Answers
The z-score of a person who scored 330 on the exam is approximately 2.7.
To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:
z = (x - μ) / σ
where:
z is the z-score
x is the raw score (330 in this case)
μ is the mean (195 in this case)
σ is the standard deviation (50 in this case)
Substituting the values into the formula, we get:
z = (330 - 195) / 50
z = 135 / 50
z = 2.7
The z-score of a person who scored 330 on the exam is 2.7.
The z-score measures the number of standard deviations a particular data point is away from the mean.
In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.
The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.
A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.
In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.
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Pls, help!!!
In 1846 the depth of the river was 5 feet deep.
In 1847 it dropped to 4.3 feet.
This year, 1848, it rose to 6 feet.
Find the percent change from EACH CHANGE
Answers
First, 5 to 4.3 feet, to make it a bit easier, let’s multiply by 2, now we have 10 and 8.6. Since 8.6 - 10 = -1.4, the river dropped 14% in 1846-1847.
Second, we will find the change from 4.3 to 6, and 6 - 4.3 = 1.7, but we need to multiply it by 1.66…7, which approximately equals a 28.32% gain. Hope this helped ☺️
DONT IGNORE PLEASE!! What is the measure of angle c
A. 94°
B. 86°
C. 18°
D. 274°
Answers
Answer:
B
Step-by-step explanation:
the sum of the 3 angles in a triangle is 180° , so
∠ c + 56° + 38° = 180°
∠ c + 94° = 180° ( subtract 94° from both sides )
∠ c = 86°
What is the population standard deviation?
{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2.
Answers
5, 8, 8, 5 has a population standard deviation of 3
Given,
The population is
{5, 8, 8, 5}
The population's mean is calculated as follows:
Sum of terms / Number of terms
Calculate the values and then replace them in the equation.
Sum equals 5 + 8 + 8 + 5 = 26
Number of terms = 4
The population's average is 26 / 4 = 6.5
The population's variance is equal to (5 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (5 - 6.5)²
= (-1.5) (-1.5)² + (1.5) (1.5)² + 1.5² + (-1.5) (-1.5)²
= 2.25 + 2.25 + 2.25 + 2.25
= 9
The population's standard deviation is equal to
= 3
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John worked 18hrs last week. He earned $171. What was his hourly rate? Explain
Answers
Explanation: To calculate his hourly pay you have to divide $171 by 18 hrs
171/18 is 9.5
Now just convert that to dollars and you’ll get $9.50
Answer:
$9.5
Step-by-step explanation:
First, you have to find the unit rate for the hourly rate. So just divide 171 by 18 and you get 9.5 So John made $9.50 per hour.
Can someone help find the surface area, then round the answer to the nearest whole number please?
Answers
The Surface Area of cylinders are: 100 yd² , 264 m², 226 mm²
The Surface Area of Can is 219 cm².
We know the formula for Surface Area of Cylinder
= 2πrh
1. Radius = 2 yd
Height = 8 yd
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 2 x 8
= 100 yd²
2. Radius = 7 m
Height = 6 m
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 6 x 7
= 264 m²
3. Radius = 3 mm
Height = 12 mm
So, Surface Area of Cylinder
= 2πrh
= 2 x 3.14 x 3 x 12
= 226 mm²
4. Radius = 3.5 cm
Height = 10 cm
So, Surface Area of Can
= 2πrh
= 2 x 3.14 x 3.5 x 10
= 219 cm²
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Which statements are true regarding the expression below? Choose three answers. 8 ^-1. 8 ^-3. 8
Answers
The statements that are true regarding the expression with the exponents -1, -3, and 1 are;
An equivalent expression is 8⁷·8⁻¹⁰The sum of the exponent is -3The value of the expression is 1/512What is an exponent?An exponent is a quantity or power to which a value, expression or number is to be raised.
The specified expression can be presented as follows;
8⁻¹ × 8⁻³ × 8
Therefore; 8⁻¹ × 8⁻³ × 8 = 8⁽⁻¹ ⁺ ⁻³ ⁺ ¹⁾ = 8⁻³ = 1/8³
The sum of the exponent is; -1 + (-3) + 1 = -31/8³ = 1/512
Therefore, the value of the expression is; 1/512Similarly, we get; 8⁷ × 8⁻¹⁰ = 8⁽⁷ ⁻ ¹⁰⁾ = 8⁻³ = 1/8³
Therefore, 8⁷ × 8⁻¹⁰ and 8⁻¹ × 8⁻³ × 8 are equivalent expressionsLearn more on exponents here: https://brainly.com/question/29831670
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You have found a house that you would like to purchase. The amount of the home is $525,000. You would like to finance the home through your local credit union but they require a 8% down payment. Determine the amount needed for the down payment so that the bank will finance the home purchase. a. $525,000 c. $42,000 b. $420,000 d. $4,200
Answers
Answer:
The Answer Is C
958499596858+9538468648545
Answers
Answer:
1.0496968e+13
Step-by-step explanation:
Answer:
bro how are u do u remeber me
Step-by-step explanation:
Find the value of each variable.
Answers
Answer:
Step-by-step explanation:
The sum of exterior angles in a quadrilateral is always 360 degrees.
So, 2x+x+4x+3x=10x=360
Soling for x, we get x=36 degrees.
Question 6 of 19 Step 1 of 1 Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4. Using Chebyshev's Theorem, state the range in which at least 75% of the data will reside. Please do not round your answers. Answer(How to Enter) 4 Points to
Answers
Suppose that quiz scores in a beginning statistics class have a mean of 7.1 with a standard deviation of 0.4, the range in which at least 75% of the data will reside is from 6.3 to 7.9.
Chebyshev's Theorem is a statistical tool that provides a range for how much data is likely to fall within a certain number of standard deviations from the mean.
Specifically, it tells us that, for any set of data, no matter how it is distributed, at least 1 - (1/k^2) of the data will fall within k standard deviations from the mean, where k is any positive number greater than 1.
In this case, we want to find the range in which at least 75% of the data will reside. We can use Chebyshev's Theorem to determine the minimum value of k that will give us this range. We know that at least 75% of the data should fall within two standard deviations from the mean, so we can set k = 2.
Using Chebyshev's Theorem, we can say that at least 1 - (1/2^2) = 75% of the data will fall within 2 standard deviations from the mean. The standard deviation is 0.4, so two standard deviations would be 2 * 0.4 = 0.8.
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.1 years, and standard deviation of 0.6 years.
If you randomly purchase one item, what is the probability it will last longer than 2 years?
Answers
The probability will last longer than 2 years will be 3.3%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
First let us calculate the z score using the formula:
\(z = \dfrac{(x- \mu)} { s}\)
where x = 2, u is the mean = 3.1 years, and s is the standard deviation
\(z =\dfrac{ (2 - 3.1) }{ 0.6}\)
z = -1.83
From the standard probability tables, the p-value at z = -1.83 is:
P = 0.033 = 3.3%
Therefore the probability that will last longer than 2 years will be 3.3%.
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Solve the system of equation. Show your work.
-6x+4y=-28
-9x+5y=-33
Answers
y=-9
Hope this helps :)
Ava plays on the softball team at her school. The team won 8 of its first 12 games. At that rate, how many games will Ava's team win if it plays 60 games in all?
Answers
Answer:
She wins 40 games
Step-by-step explanation:
I'm not the best at explaining but 5x12=60 so then we multiply 8 by 5 aswell and bam we have 40.
An arborist is preparing the fuel mix for her chainsaw before climbing a tree to remove a dead limb. The two-stroke chainsaw
requires a 5% mix of engine oil to gas-that is, the amount of oil should be 5% of the amount of gas. How much engine oil should
be added to a jerry can that contains 3.8 gallons of gas?
(Type a whole number or a decimal)
Answers
Answer:
To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:
0.05 x 3.8 = 0.19
So, 0.19 gallons of engine oil should be added to the jerry can.
Evaluate the function at the given value
f(x) = 4.753(0.9421)^x
x = 5
Answers
Answer:more info pl
Z
Step-by-step explanation:
11. If AD = 8 centimeters, what is BD?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
Answers
Hello please, I did not understand this exercise. In the plane referred to an orthonormal reference (o, i, j) place the points A, B, C and D defined by: A(6; 4); B(3; 7); C(12; -2); D(9; 7).
Show that C is the image of A by dilation with center B and ratio 3.
Answers
We have shown that C is the image of A by dilation with center B and ratio 3.
Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:
Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:
AB = A - B = (6 - 3, 4 - 7) = (3, -3)
Multiply the vector AB by the dilation ratio of 3:
3 AB = 3 (3, -3) = (9, -9)
Add the resulting vector to the coordinates of the center B:
BC = B + 3 AB = (3, 7) + (9, -9)
BC = (12, -2)
Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:
BC = (12, -2) = C
Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.
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