Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.x2 −2x + y2 − 6y = 26

Answers

Answer 1

Answer

The center of the circle is (1, 3) and its radius is 6

Step-by-step explanation

Given the equation:

\(x^2-2x+y^2-6y=26\)

we need to complete the square of the following expressions:

\(\begin{gathered} x^2-2x \\ y^2-6y \end{gathered}\)

To do this we need to divide the coefficient of the x-term, which is -2, and the y-term, which is -6, divide them by 2, and then square them, that is,

\(\begin{gathered} (-\frac{2}{2})^2=(-1)^2=1 \\ (-\frac{6}{2})^2=(-3)^2=9 \end{gathered}\)

Adding 1 and 9 at both sides of the equation:

\(\begin{gathered} x^2-2x+y^2-6y+1+9=26+1+9 \\ (x^2-2x+1)+(y^2-6y+9)=36 \\ (x-1)^2+(y-3)^2=36 \end{gathered}\)

This equation has the form:

\((x-h)^2+(y-k)^2=r^2\)

which is a circle centered at (h, k) with radius r.

Therefore, the center of the circle is (1, 3) and it radius is 6 (6² = 36)


Related Questions



Amir is in charge of getting oranges for today's soccer game. He buys 2 bags with
6 oranges in each bag. He also buys 4 loose oranges.
Choose all the expressions that can be used to find the number of oranges Amir gets
in all.

Answers

The expression that shows the total oranges amir got in total is x-12 = 4. And amir got 16 oranges in all

What is linear expressions?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.

example of linear expression is 2x+2y = 5. This is a linear expression with two variables x and y.

Let's represent the total no of oranges by x.

Therefore ,

2 bags of oranges with 6 in each bag will amount to 2×6 = 12 oranges.

an addition of 4 loose oranges . Therefore the total number of oranges = 12+4 = x

x = 12+4 or x-12 = 4

= 16

therefore amir got 16 oranges in all

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3.3x0.14 = ?
hazgxjklkkspkoxdh

Answers

Answer:

Step-by-step explanation:

0.462

Answer:

0.462 :) hope this helps and please put me as brainiest thankyou !!

Step-by-step explanation:

help me answer this please

help me answer this please

Answers

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Find the mode of the following: 75, 93, 89, 75

Answers

Answer:

75

Step-by-step explanation:

The mode is the number that appears most often!

Good luck!!!

Answer:

75

Step-by-step explanation:

The mode is the number that occurs most in the data set. In this case, 75 occurs 2 times.

hope this helped!

create a ppc curve and identify: efficiency, underutilization, specialization points (radical points), and an unattainable point. (just a sketch, does not have to be huge.)create a ppc curve and identify: efficiency, underutilization, specialization points (radical points), and an unattainable point. (just a sketch, does not have to be huge.

Answers

The production possibility curve is a graphical representation of the trade-off between two goods and the maximum combinations of goods that can be produced with limited resources.

A production possibility curve (PPC) is a graphical representation of the maximum combinations of two goods that can be produced with limited resources.

Efficiency: The point at which the production possibility curve is at its maximum efficiency is called the production possibility frontier (PPF). This is represented by a point on the curve that is tangent to the PPF.

Underutilization: If a society is producing below the production possibility frontier, it is considered underutilized.  This is represented by a point on the curve that is below the PPF.

Specialization Points (Radical Points): The radical points are the points on the curve where only one of the two goods is produced. This is represented by a point on the curve that is either the Y-intercept or the X-intercept.

Unattainable Point: The unattainable point is the point that is beyond the production possibility frontier. The curve represents the maximum possible production, so any point beyond the PPF is unattainable.

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Which relationship is NOT a function?

HELPPP!!!!!!!!!! HELP!!!!!!

Which relationship is NOT a function?HELPPP!!!!!!!!!! HELP!!!!!!

Answers

Answer:

I think that it is the one on the bottom left

Step-by-step explanation:

I am so sorry if it is wrong he he

Which of the following best describe this graph?

skewed left
skewed right
uniform distribution
center near 5
center near 7
data spread from 3 to 9
does not have an outlier

Which of the following best describe this graph?skewed leftskewed rightuniform distributioncenter near

Answers

The term that  best describe this graph attached is

does not have an outlier

What is outlier?

An outlier is a data point that significantly deviates from the general pattern or trend of a dataset. It is an observation that is noticeably different from other data points in terms of its magnitude or value.

Outliers can be either unusually high (positive outliers) or unusually low (negative outliers) compared to the rest of the data.

The graph is not exactly uniform even though it is not skewed

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if 6 people can walk 12 dogs, how many people are needed to walk 24 dogs

Answers

Answer:

12 people are need to walk 24 dogs

Step-by-step explanation:

12/2=6

24/2=12

Answer:

12 people can walk 24 dogs.

Step-by-step explanation:

Given information,

→ 6 people can walk 12 dogs.

→ People required for 24 dogs = ?

Let us assume that,

→ Missing value = p

Forming the equation,

→ 6/12 = p/24

Then the value of p will be,

→ 6/12 = p/24

→ p/24 = 6/12

→ p × 12 = 6 × 24

→ 12p = 144

→ p = 144/12

→ [ p = 12 ]

Hence, the value of p is 12.

A petting zoo has 14 goats, 8 llamas, 2 pigs, and 6 mountain lions.

Use this information to write each ratio as a fraction in simplest form.



mountain lions to llamas

Answers

Answer:

goats 14/30 = 7/15

llamas 8/30 = 4/15

pigs 2/30 = 1/15

lions 6/30 = 1/5

Step-by-step explanation:

Which steps can be used to solve for the value of y?
2/3 (y+57)=178

A. Divide both sides by 2/3, then subtract 57 from both sides.

B. Subtract 57 from both sides, then divide both sides by 2/3.

C. Multiply both sides by 2/3, then subtract 57 from both sides.

D. Subtract 2/3 from both sides, then subtract 57 from both sides.

Answers

A is the correct answer

Keisha rented a truck for one day. There was a base fee of $13.75, and there was an additional charge of 10 cents for each mile driven. The total cost, C (in
dollars), for driving x miles is given by the following.

C=0.10x+13.75

What is the total rental cost if Keisha drove 40 miles?

Answers

Answer:

I believe the answer is $17.75

Step-by-step explanation:

As if you have a base fee of 13.75 then 0.10 for each additional mile. Then 40 miles x 0.10 is 4. Hope this helps.

: A cake recipe calls for 4 cups of flour and 2 cups of sugar.
(b) Express the unit rate of cups of sugar per
gar.
cup of flour.

Answers

Answer:

1 cup of sugar per 2 cups of flour

Step-by-step explanation:

I cup of sugar/ 2 cups of flour

The following bar chart shows the distances run by Jay's family in a race.
Find the median distance in km.

The following bar chart shows the distances run by Jay's family in a race. Find the median distance in

Answers

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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Place the indicated product in the proper location on the grid. (x 2 + 4)(x 2 - 4)

Answers

(x² + 4)(x² - 4) = x⁴ - 16 and the product is placed in the grid.

Given expression is: (x² + 4)(x² - 4) To multiply two polynomials, we use the distributive property.

We will multiply x² with both x² and -4 and 4 with both x² and -4 as shown below.x² * x² + x² * (-4) + 4 * x² + 4 * (-4)x⁴ - 4x² + 4x² - 16.

The above expression can be simplified further by combining like terms. 4x² gets canceled on adding -4x² and 4x².

Simplified expression is: x⁴ - 16

Hence, (x² + 4)(x² - 4) = x⁴ - 16 and the product is placed in the grid below:   

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Claim: Fewer than 92% of adults have a cell phone. In a reputable poll of 1207 adults, 85% said that they have a cell phone. Find the value of the test statistic,
Round to two decimal places as needed

Answers

Answer:

- 6.547

Step-by-step explanation:

Given that:

Sample size (n) = 1207

p = 0.85

p0 = 0.92

The test statistic :

Z = (p - p0) / √(p0(1 - p0) / n)

Z = (0.85 - 0.92) / √(0.92(1 - 0.85) / 1207)

Z = - 0.07 / √(0.92(0.15) / 1207)

Z = - 0.07 / √0.0001143

Z = - 0.07 / 0.0106926

Z = - 6.5465446

Z = - 6.547

If y = -5x + 3, determine the value of y when x = -4

Answers

Answer: Y = 23

Step-by-step explanation: -5 x -4 = positive 20 then add 3 which equals 23. 23 is the value of y

The function g is given by g(x) = ax^2 − b, where a and b are real numbers. If g(2) = −5 and g(−1) = 2, find the values of a and b.​

Answers

Answer:

a = 1

b = -1

Step-by-step explanation:

\(g(x)=ax^2-b \quad \quad \textsf{(where }\:a\:\textsf{ and }\:b\:\textsf{ are real numbers)}\)

Create 2 equations with b as the subject using the given information.

Equation 1

\(\begin{aligned}g(2) &=-5\\\implies a(2)^2-b &=-5\\4a-b &=5\\ b&=4a-5\end{aligned}\)

Equation 2

\(\begin{aligned}g(-1) &=2\\\implies a(-1)^2-b &=2\\a-b &=2\\ b &=a-2\end{aligned}\)

Equate the equations and solve for a:

\(\begin{aligned}b & =b\\\implies 4a-5 & = a-2\\3a & = 3\\a & = 1\\\end{aligned}\)

Substitute the value of a into Equation 2 and solve for b:

\(\begin{aligned}b & =a-2\\a=1 \implies b & =1-2\\b & = -1\end{aligned}\)

Answer:

a = -7/3

b = -13/3

Step-by-step explanation:

Making equations in terms of 'a' and 'b' :

g(2) = -5 = a(2)² - b ⇒ 4a - b = -5 [Equation 1]g(-1) = 2 = a(-1)² - b ⇒ a - b = 2     [Equation 2]

Subtract : Equation 1 - Equation 2

4a - b - a + b = -5 - 23a = -7a = -7/3

Finding b :

-7/3 - b = 2b = -7/3 - 6/3b = -13/3

Solve the equation
z³=27

Answers

Answer: z = 3, -1.5 + 1.5\(\sqrt{3}\)i, -1.5 - 1.5\(\sqrt{3}\)i

Step-by-step explanation:

      A cubic equation will have three solutions. This equatoin will give us one real solution. We will also have two complex solutions. These are solutions that involve "imaginary numbers" and will utilize the value i. We will write the equation in standard form and factor it.

              z³ - 27 = 0

              (z - 3)(z² + 3z + 9) = 0

      The first factor gives us z = 3, because 3 - 3 = 0. Now, we will look at when the second factor equals 0. Let us complete the square.

              z² + 3z + 9 = 0

              (z² + 3z + 2.25) + 9 - 1.5 = 0

              (z² + 3z + 2.25) + 6.75 = 0

              (z + 1.5)² + 6.75 = 0

      Lastly, we can continue solving. We will subtract 7.5 from both sides of the equation and then take the square root of both sides. Then, we will subtract 1.5 from both sides of the equation and simplify the radical.  \(i=\sqrt{-1}\).

              (z + 1.5)² = -6.75

              z + 1.5 = ±\(\sqrt{6.75}\)i

              z = -1.5 ±1.5\(\sqrt{3}\)i

Answer:

  z = 3, -1.5+1.5√3i, -1.5-1.5√3i

Step-by-step explanation:

You want the solutions to the equation z³ = 27.

Cubic

A cubic equation has three solutions. This one has one positive real solution and two complex conjugate solutions.

We can rewrite the equation to standard form, then factor the difference of cubes.

  z³ -27 = 0

  (z -3)(z² +3z +9) = 0

The first factor will be zero when z = 3, so that is one solution.

The second factor will be zero when ...

  (z +1.5)² +6.75 = 0 . . . . . . . complete the square

  (z +1.5) = ±√(-6.75) = ±√(-27/4) = ±(3/2)√(-3) . . . subtract 6.75; square root

  z = -1.5 ±1.5√3i

The three solutions to the equation are ...

z = 3z = -1.5+1.5(√3)iz = -1.5-1.5(√3)i

<95141404393>

Solve the following inequality. 2x−6>3x−11

Answers

Answer:  x < 5

Step-by-step explanation:

The graph of g is a translation 1 unit down of the graph of f(x) = 3|x| – 4. The rate of change of g over the interval 2 ≤ x ≤ 5 is

Answers

The solution is:  the rate of change is 3.

Here, we have,

Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):

g(x) = f(x) - 1

f(x) = 3|x| – 4

so, we get,

g(x) = 3|x| – 4 - 1

      = 3|x| – 5

Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:

rate = g(5) - g(2)/ 5-2

so, we get,

rate = 9/3 = 3

Therefore the rate of change is 3.

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2 kilometers to 72 meters write each ratio in simplest form

Answers

Hi there!

1:36

1.Find common denominator:

\(2*2/72*2\)

Commonest denominator: 2

2.Divide the two terms:

\(2*2=1/72*2=36\)

3.Convert into rate form:

\(1,36=1:36\)

This means, 2 kilometers to 72 meters simplest form is 1:36.

Algebra transformation

f(x) =
f(x) =
f(x) =
f(x) =

Algebra transformationf(x) =f(x) =f(x) =f(x) =

Answers

Algebra transformation

for  Graph1 f(x)=f(x)+4

for  Graph2 f(x)=-f(x-4)

for  Graph3 f(x)=f(x-7)

for  Graph4 f(x)=f(x-2)-5

Define reflection of graph

In mathematics, the reflection of a graph is a transformation that produces a mirror image of the original graph across a specific line or point. The line or point across which the reflection occurs is called the axis of reflection.

Graph1

Transform the graph by +4 units in y direction.

f(x)=f(x)+4

Graph2

Transform the graph by +4 units in x direction.

f(x)=f(x-4)

Now take the reflection of graph about x axis

f(x)=-f(x-4)

Graph3

Transform the graph by +7 units in x direction.

f(x)=f(x-7)

Graph5

Transform the graph by -5 units in y direction.

f(x)=f(x)-5

Now Transform the graph by -2 units in x direction.

f(x)=f(x-2)-5

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Find the first five terms of the following sequence, starting with n=1.

Find the first five terms of the following sequence, starting with n=1.

Answers

Answer:

-2,1,6,13,22

Step-by-step explanation:

cn = n^2 -3

Let n=1

c1 = 1^2 -3 = 1-3 = -2

Let n=2

c2 = 2^2 -3 = 4-3 = 1

Let n=3

c3 = 3^2 -3 = 9-3 = 6

Let n=4

c4 = 4^2 -3 = 16-3 = 13

Let n=5

c5 = 5^2 -3 = 25-3 = 22

Find the perimeter of this shape

Find the perimeter of this shape

Answers

The perimeter of the given shape as represented in the task content is; 29 cm.

What is the perimeter of the given shape?

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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Help me out please please

Help me out please please

Answers

Answer:

490000

Step-by-step explanation:

Substituting \(x=40\),

\(I=-425(40)^2 + 45500(40) - 650000=490000\)

Which person earns a living wage?
A. Paulo earns $350 per week, and his weekly costs are $400.
B. DeMarcus earns $350 per week, and his weekly costs are
$300.
c. Vivienne earns $250 per week, and her weekly costs are
$400.
D. Claudia earns $250 per week, and her weekly costs are
$300.

Answers

Answer:

B becouse he earns 350 and spends 300 so he is earning 50 extra

Step-by-step explanation:

Answer:

B. DeMarcus earns $350 per week, and his weekly costs are $300.

Step-by-step explanation:

What is a living wage?

The minimum income necessary for a worker to meet their cost-of-living expenses and to provide some discretionary income.

Therefore, a person earns a living wage if their earnings are greater than their weekly costs.

The only person who earns more than their weekly costs is DeMarcus.

Since DeMarcus earns $350 per week and his weekly costs are $300, his income is enough to meet his basic needs with $50 left over.

I dont get this question equation

y=0.5 (6) - 4

I know that 0.5 is equivalent to 1/2 but I just don’t get this question

Answers

The equation y = 0.5(6) - 4 is a linear equation in which y represents the value of the dependent variable and 0.5(6) - 4 represents the value of the independent variable.

To solve the equation, you first need to simplify 0.5(6) to get 3, since 0.5 is equivalent to 1/2 and multiplying 6 by 1/2 gives you 3. So the equation becomes:

y = 3 - 4

Next, you need to subtract 4 from 3 to get -1. So the solution to the equation is:

y = -1

Therefore, when the value of the independent variable is 6, the value of the dependent variable is -1.

Answer

\(\pink\sf{y=-1}\)

Step-by-step explanation

I'm assuming that this exercise is asking us to simplify the equation \(\sf{y=0.5(6)-4}\).

We know that 0.5 (6) means 0.5 multiplied by 6. That is the same as 6 divided by 2, which is 3:

\(\sf{y=3-4}\)

And now we just simplify the last part:

\(\sf{y=-1}\)

∴ answer: y = -1

Adding and Subtracting Polynomials
Feb 09, 10:57:07 AM
Find the sum of 9x² + 5x + 8 and 9x – 7.
-

Answers

9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.

What is Polynomial?

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

We need to find the sum of  9x² + 5x + 8 and 9x – 7.

Summation is the addition of a sequence of any kind of numbers.

So add  9x² + 5x + 8 and 9x – 7.

9x² + 5x + 8 + 9x – 7.

Add the like terms

9x² + 14x +1

Hence, 9x² + 14x +1 is the sum of polynomials 9x² + 5x + 8 and 9x – 7.

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Whalen recorded the amount of money people spent for gasoline to the nearest dollar. Which type of graph would be the most appropriate to illustrate Whalen’s information?

Whalen recorded the amount of money people spent for gasoline to the nearest dollar. Which type of graph

Answers

Answer:

c :)

Step-by-step explanation:

i guessed and got it right <3

32) Write a compound inequality that represents the given graph:



A. 6≤x 10
D. 6

32) Write a compound inequality that represents the given graph:A. 6x 10D. 6

Answers

Answer:

6 < x ≤ 10

Step-by-step explanation:

The graph given shows that the possible value of x greater 6 (does not include 6 because the circle is not full) and also is less than or equal to 10 (includes 10 because the circle is full).

That is: x > 6 and x ≤ 10

This can be written as: 6 < x ≤ 10

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