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raketka [301]
4 years ago
6

Someone please help me with this

Mathematics
1 answer:
hram777 [196]4 years ago
5 0

Answer:

3/2 and -2

Step-by-step explanation:

The quadratic formula is x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}. Here a=2, b=1, and c=-6.

Substitute and you'll have:

x=\frac{-b+/-\sqrt{b^2-4ac} }{2a} =\frac{-1+/-\sqrt{1^2-4(2)(-6)} }{2(2)}=\frac{-1+/-\sqrt{1+48} }{4)}

\frac{-1+/-\sqrt{1+48} }{4}=\frac{-1+/-\sqrt{49} }{4}=\frac{-1+/-7 }{4}= \frac{3}{2} , -2


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Step-by-step explanation:

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3 0
3 years ago
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}

7 0
3 years ago
Value of m varies directly as value of n and n=5 when m=12. What is n when m=18?
ohaa [14]
Simplify the problem down, so:

m = 12 & n = 5
m = 6 & n = 2.5 <span>(divided each number by 20)
</span>
Now m is a factor of 18. Multiply each number by 3.
Answer: m = 18 & <span>n = 7.5</span>
6 0
4 years ago
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