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ioda
3 years ago
11

Please help! Thanks

Mathematics
1 answer:
9966 [12]3 years ago
5 0

Answer:

x = +-sqrt(3) and they are the actual solutions

Step-by-step explanation:

x^2/ (2x-6) = 9/(6x-18)

get a common denominator of 6x-18

x^2/ (2x-6) * 3/3 = 9/(6x-18)

3x^2/ (6x-18) = 9/(6x-18)

since the denominators are the same, the numerators must be the same

3x^2 = 9

divide by 3 on each side

x^2 = 3

take the square root of each side

sqrt(x^2) = +-sqrt(3)

x = +-sqrt(3)



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Answer:

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3 years ago
In a 30cm by 25cm rectangle, a quadrant of a circle of radius 7cm has been cut away from each corner. What is the perimeter of t
lidiya [134]

Answer:

Perimeter = 98 cm

Area = 596 cm^{2}

Step-by-step explanation:

Please refer to the attached image for the resultant figure when a quadrant of circle with radius 7 cm is cut from a rectangle of sides 30 cm and 25 cm.

Perimeter of a figure = Sum of all its sides + Perimeter of circle

Quadrant of a circle is one fourth of a circle and there are 4 such quadrant of a circle, so eventually there is one complete circle in this figure.

The sides of this resultant figure = 30 - 14 = 16 cm

and 25 - 14 = 11 cm

So perimeter of this figure = 16 + 11 + 16 + 11 + Perimeter of circle

\Rightarrow 54 + 2 \pi r\\\Rightarrow 54 + 2 \times \dfrac{22}{7} \times 7\\\Rightarrow 54 + 44 = 98 cm

To find area of this figure = Area of rectangle - Area of circle

Area of rectangle = Length \times Width

\Rightarrow 30 \times 25 = 750\ cm^{2}

Area of circle = \pi r^{2}

\Rightarrow \dfrac{22}{7} \times 7^{2} = 154\ cm^{2}

So, area of figure = 750 - 154 = 596 cm^{2}

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3 years ago
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Suppose KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. Prove that A is equidistant from LM and KN.
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Answer:

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 Step-by-step explanation:

Given KLMN is a parallelogram, and that the bisectors of ∠K and ∠L meet at A. we have to prove that A is equidistant from LM and KN i.e we have to prove that AP=AQ

we know that the diagonals of parallelogram bisect each other therefore the the bisectors of ∠K and ∠L must be the diagonals.

In ΔAPN and ΔAQL

∠PNA=∠ALQ    (∵alternate angles)  

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∴ By ASA rule ΔAPN ≅ ΔAQL

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Hence, A is equidistant from LM and KN.

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