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Travka [436]
3 years ago
5

Use a common denominator What does 1/9 equal?

Mathematics
1 answer:
dem82 [27]3 years ago
8 0

Answer:

2/18

Step-by-step explanation:

because i multiplied 1/9 by 2

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Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5).
NemiM [27]

Let the coordinates of the circumcentre O of the triangle DEF be (x, y). Circumcentre of a triangle is equidistant from each of the vertices.

1. Distance OD=distance OE, then:

(x-1)^2+(y-3)^2=(x-8)^2+(y-3)^2.

2. Distance OD=distance OE, then:

(x-1)^2+(y-3)^2=(x-1)^2+(y+5)^2.

Solve the system:

\left\{\begin{array}{l}          (x-1)^2+(y-3)^2=(x-8)^2+(y-3)^2 \\          (x-1)^2+(y-3)^2=(x-1)^2+(y+5)^2         \end{array}\right.,

\left\{\begin{array}{l}          x^2-2x+1+y^2-6y+9=x^2-16x+64+y^2-6y+9 \\          x^2-2x+1+y^2-6y+9=x^2-2x+1+y^2+10y+25         \end{array}\right.,

\left\{\begin{array}{l}          14x=63 \\          -16y=16         \end{array}\right..

Then

x=\dfrac{63}{14} =\dfrac{9}{2} =4.5,\\  \\ y=-1.

Answer: the coordinates of the circumcenter for ∆DEF are x=4.5, y=-1.


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