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n200080 [17]
3 years ago
8

Consider the rational expression.

Mathematics
1 answer:
xxMikexx [17]3 years ago
4 0

Answer:

The options 1,2 and 4 are correct.

Step-by-step explanation:

The given rational expression

\frac{6x+12}{x^2+8x+12}

From the given expression it is noticed 12 is a term in both the numerator and denominator. Option 1 is correct.

The denominator has 3 terms. Option 4 is correct.

\frac{6(x+2)}{x^2+6x+2x+12}

\frac{6(x+2)}{x(x+6)+2(x+6)}

\frac{6(x+2)}{(x+6)(x+2)}

From the above expression it is clear that (x+2) is a factor of the numerator. Option 2 is correct.

Therefore options 1,2 and 4 are correct.

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The quadrilateral ABCD on a coordinate plane has the following characteristics.
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Answer with explanation:

Property of Quadrilateral A B CD

⇒Equation of Line AD is, y= -3 x.

⇒Equation of Line BC is, y= -3 x +11

Coordinates of CD = C(2,5) and D(-1,3)

Equation of line CD will be

  \frac{y-5}{x-2}=\frac{3-5}{-1-2}\\\\-3 \times (y-5)=-2\times (x-2)\\\\-3 y +15=-2 x +4\\\\2 x -3 y +11=0

Equation of line AB will be, which is parallel to CD, as opposite sides of parallelogram are parallel and equal,is equal to

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Because when lines are parallel their slopes are equal.

→→Equation of line AD is , y= - 3 x.

Coordinates of point A can be calculated by

→2 x -3 × (-3 x ) +k=0

→2 x +9 x +k=0

\rightarrow x=\frac{-k}{11}\\\\\rightarrow y=\frac{3k}{11}

→→→Similarly, Coordinate of point D can be calculated by solving these two lines:

   y = -3 x + 11

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→2 x -3 × (-3 x +11) +k=0

→2 x +9 x -33 +k=0

→11 x =33 -k

x=\frac{33-k}{11}

y=-3 \times \frac{33-k}{11}+11\\\\y=\frac{-99+3 k+121}{11}\\\\y=\frac{22+3 k}{11}

→→Coordinates of A is (\frac{-k}{11},\frac{3k}{11})

Coordinates of Point D is (\frac{33-k}{11},\frac{22+3k}{11}).

you, can get infinite number of ordered pairs, for different value of k.

For, k=0 ,

A= (0,0)

D=(3,2)

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