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Karo-lina-s [1.5K]
3 years ago
7

The equation x2 + y2 − 2x + 2y − 1 = 0 is the general form of the equation of a circle. What is the standard form of the equatio

n?
Mathematics
2 answers:
Alla [95]3 years ago
8 0
X^2 + y^2 - 2x + 2y - 1 = 0

(x^2 - 2x) + (y^2 + 2y) - 1 = 0

(x^2 - 2x + 1) + (y^2 + 2y + 1) - 1 - 1 - 1 = 0

(x - 1)^2 + (y + 1)^2 - 3 = 0

(x - 1)^2 + (y + 1)^2 = 3


qaws [65]3 years ago
7 0

Answer:

(x-1)^2+ (y+1)^2=3

Step-by-step explanation:

x^2 + y^2 - 2x + 2y - 1 = 0

Standard form of the equation is (x-h)^2 + (y-k)^2= r^2

To get standard form we apply completing the square method

x^2-2x+ y^2+ 2y - 1 = 0

Take coefficient of x  and y . Divide it by 2 and then square it

\frac{2}{2} =1 and 1^2=1

Add and subtract 1

(x^2-2x)+(y^2+ 2y) - 1 = 0

(x^2-2x+1-1)+(y^2+ 2y+1-1) - 1 = 0

(x^2-2x+1)+(y^2+ 2y+1)-1-1- 1 = 0

(x^2-2x+1)+(y^2+ 2y+1)-3= 0

Now write the parenthesis in square form

(x-1)(x-1)+ (y+1)(y+1)-3= 0

(x-1)^2+ (y+1)^2-3= 0 , add 3 on both sides

(x-1)^2+ (y+1)^2=3 is the standard form

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Elina [12.6K]
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x= 15m * (sin 35)

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5 0
3 years ago
Solve the system of linear equations using the Gauss-Jordan elimination method. 2x + 3y 6212 3x + (x, y. z)
Gekata [30.6K]

Answer:

The solution of the system of linear equations is x=3, y=4, z=1

Step-by-step explanation:

We have the system of linear equations:

2x+3y-6z=12\\x-2y+3z=-2\\3x+y=13

Gauss-Jordan elimination method is the process of performing row operations to transform any matrix into reduced row-echelon form.

The first step is to transform the system of linear equations into the matrix form. A system of linear equations can be represented in matrix form (Ax=b) using a coefficient matrix (A), a variable matrix (x), and a constant matrix(b).

From the system of linear equations that we have, the coefficient matrix is

\left[\begin{array}{ccc}2&3&-6\\1&-2&3\\3&1&0\end{array}\right]

the variable matrix is

\left[\begin{array}{c}x&y&z\end{array}\right]

and the constant matrix is

\left[\begin{array}{c}12&-2&13\end{array}\right]

We also need the augmented matrix, this matrix is the result of joining the columns of the coefficient matrix and the constant matrix divided by a vertical bar, so

\left[\begin{array}{ccc|c}2&3&-6&12\\1&-2&3&-2\\3&1&0&13\end{array}\right]

To transform the augmented matrix to reduced row-echelon form we need to follow these row operations:

  • multiply the 1st row by 1/2

\left[\begin{array}{ccc|c}1&3/2&-3&6\\1&-2&3&-2\\3&1&0&13\end{array}\right]

  • add -1 times the 1st row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\3&1&0&13\end{array}\right]

  • add -3 times the 1st row to the 3rd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&-7/2&6&-8\\0&-7/2&9&-5\end{array}\right]

  • multiply the 2nd row by -2/7

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&-7/2&9&-5\end{array}\right]

  • add 7/2 times the 2nd row to the 3rd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&3&3\end{array}\right]

  • multiply the 3rd row by 1/3

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&-12/7&16/7\\0&0&1&1\end{array}\right]

  • add 12/7 times the 3rd row to the 2nd row

\left[\begin{array}{ccc|c}1&3/2&-3&6\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add 3 times the 3rd row to the 1st row

\left[\begin{array}{ccc|c}1&3/2&0&9\\0&1&0&4\\0&0&1&1\end{array}\right]

  • add -3/2 times the 2nd row to the 1st row

\left[\begin{array}{ccc|c}1&0&0&3\\0&1&0&4\\0&0&1&1\end{array}\right]

From the reduced row echelon form we have that

x=3\\y=4\\z=1

Since every column in the coefficient part of the matrix has a leading entry that means our system has a unique solution.

7 0
3 years ago
In 2015,in buffalo,new York there were 8.625 arrest,2.678 robberies,865 assaults and 20 murders.The population of Buffalo is 258
Kisachek [45]

<u>Answer:</u>

\frac { 8 6 5 } { 2 6 7 8 }

<u>Step-by-step explanation:</u>

We are given the following information for year 2015:

Number of arrests = 8625  

Number of robberies = 2678

Number of assaults = 865

Number of murders = 20

Population of Buffalo = 258959

We are to find the ratio of number of assaults to the number of robberies in simplest form.

Ratio of number of assaults to number of robberies = \frac{865}{2678}

4 0
3 years ago
The original price of a shirt is $25, and it’s on sale for 20% off the original price. To determine the sale price of the shirt,
Pani-rosa [81]
The price of the shift is $20.

20% off of $25 means to subtract $5 off of $25, making it $20.
4 0
3 years ago
Read 2 more answers
An ant moves 18 millimeters every 5 seconds
vaieri [72.5K]

Answer:

Step-by-step explanation:

First we need to find their rate of speed.

r = d / t

For ant,

Convert millimeters to inches.

1 inch = 25.4 mm

18 mm = 0.7 inch

r = 0.7 / 5

r = 0.14 inches per second

For beetle,

r = 8 / 3

r = 2.7 inches per second

From the rates, you can tell that the beetle crosses the Garden first.

To know how long it takes for the ant to cross is by dividing the length by the rate.

1 yard = 36 inches

13 yards = 468 inches

468 ÷ 0.14 = 668.5 ≈ 669 seconds

In terms of minutes:

11 minutes and 15 seconds

The ant would cross the garden in 11 minutes and 15 seconds (or 669 seconds <em>up to you</em>).

7 0
3 years ago
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