To complete the square:
we take the coefficient ox "x" (which in this problem is -20)
we divide it by 2
square that number
then add it to both sides of the equation

-20 / 2 = -10
-10^2 = 100
then we add 100 to both sides of the equation:
x^2 -20x
x^2 -20x +100 = 100
******************************************************
To get the roots of the equation, we take the square root of both sides:
(x -10) * (x-10) = 10
(x-10) = square root (10)
x-10 = 3.1622776602 
x1 = 13.1622776602 
and don't forget that square root of 10 also equals -3.1622776602 
x2 = 10 - 3.1622776602
x2 = 6.8377223398

4 0

3 years ago

Tell whether the ordered pair is a solution of the equation y=5x; (15,-3)

n200080 [17]

Answer:

This ordered pair is NOT a solution of the equation.

Step-by-step explanation:

First, it is important to note that ordered pairs consist of (x, y) so in this case

x = 15 and y = -3. And that any variable directly next to a number calls for multiplication. So, plugging in the variables the equation would look like

"-3 = 5 x 15"

To see if 5 x 15 = -3 we will multiply them. 5 x 15 actually equals 75 not -3. So we know this ordered pair is NOT the solution for the problem.

3 0

3 years ago

Easy question

Ira Lisetskai [31]

Answer:

7/16

Step-by-step explanation:

Let the fraction be x/y

(x+5)/(y+5) = 4/7

7x + 35 = 4y + 20

7x + 15 = 4y

(x-1)/(y-1) = 2/5

5x - 5 = 2y - 2

2y = 5x - 3

7x + 15 = 2(5x - 3)

7x + 15 = 10x - 6

3x = 21

x = 7

2y = 5(7) - 3

2y = 32

y = 16

x/y = 7/16

5 0

3 years ago

Identify the radius and center. x^2 + y^2 - 2x + 4y - 11 = 0

miss Akunina [59]

<h2>Hello!</h2>

The answer is:

Center: (1,-2)

Radius: 4 units.

To solve the problem, using the given formula of a circle, we need to find its standard equation form which is equal to:

$(x-h)^{2}+(y-k)^{2}=r^{2}$

Where,

"h" and "k"are the coordinates of the center of the circle and "r" is its radius.

So, we need to complete the square for both variable "x" and "y".

The given equation is:

$x^2+y^2-2x+4y-11=0$

So, solving we have:

$x^2+y^2-2x+4y=11$

$(x^2-2x+(\frac{2}{2})^{2} )+(y^2+4y+(\frac{4}{2})^{2})=11+(\frac{2}{2})^{2} +(\frac{4}{2})^{2}\\\\(x^2-2x+1)+(y^2+4y+4)=11+1+4\\\\(x^2-1)+(y^2+2)=16$

$(x^2-1)+(y^2-(-2))=16$

Now, we have that:

$h=1\\k=-2\\r=\sqrt{16}=4$

So,

Center: (1,-2)

Radius: 4 units.

Have a nice day!

Note: I have attached a picture for better understanding.

5 0

3 years ago