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Sergeeva-Olga [200]
3 years ago
15

Which ordered pair is a solution of the system of equation y=x-4

Mathematics
1 answer:
enyata [817]3 years ago
7 0
There are many solutions, probably too many to list 
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X^2+4x+y^2-10y+20=30 find the center of the circle by completing the square
swat32

Answer:

a). Center of the circle = (-2, 5)

b). Equation of the line ⇒ y = -\frac{4}{5}x+\frac{58}{5}

Step-by-step explanation:

Equation of the circle is,

x² + 4x + y²- 10y + 20 = 30

a). [x² + 2(2)x + 4 - 4] + [y²- 2(5)y + 25] - 25 + 20 = 30

   [x² + 2(2)x + 4] - 4 + [y² - 2(5)y + 25] - 25 + 20 = 30

   (x + 2)² + (y - 5)²- 29 + 20 = 30

   (x + 2)² + (y - 5)²- 9 = 30

   (x + 2)² + (y - 5)² = 39

By comparing this equation with the standard equation of a circle,

    Center of the circle is (-2, 5).

b). A point (2, 10) lies on this circle.

    Slope of the line joining this point to the center (-2, 5),

    m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

          = \frac{10-5}{2+2}

          = \frac{5}{4}

    Let the slope of the tangent which is perpendicular to this line is 'm_{2}'

    Then by the property of perpendicular lines,

          m_{1}\times m_{2}=-1

          \frac{5}{4}\times m_{2}=-1

                 m_{2}=-\frac{4}{5}

   Now the equation of the line passing though (2, 10) having slope m_{2}=-\frac{4}{5}

           y - y' = m_{2}(x-x')

           y - 10 = -\frac{4}{5}(x-2)

           y - 10 = -\frac{4}{5}x+\frac{8}{5}

                  y = -\frac{4}{5}x+\frac{8}{5}+10

                  y = -\frac{4}{5}x+\frac{58}{5}

Therefore, equation of the line will be, y = -\frac{4}{5}x+\frac{58}{5}

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3 years ago
How does the value of the digit 4 in 3.546 compare to the value of the digit 4 in 4.23
JulijaS [17]

Answer:

the digit 4 in 3.546 is called hundredth because it is after the decimal point you add -th behind it while the digit 4 in 4.23 is called a unit

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4 years ago
What is40.99 times 2.1
inessss [21]

Answer:

40.99* 2.1= 86.079

Step-by-step explanation:

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3х + 4 = 9x - 8<br> What is the value of X to make the equation true?
givi [52]

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x=2

Step-by-step explanation:

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Han is hiring laborers to cut down and remove 8 large trees from his
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company a

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if the work for company b takes more than two days is gonna be more than 1,000 dollars and if he pick company a he would owe 1,000 no matter how many days it takes

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