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3 years ago

Find the angle between the following pairs of lines x^2+6xy +9y^2-4x +12y-5 =0

Mathematics

1 answer:

wlad13 [49]3 years ago

3 0

Answer:

+6xy+9y

+4x+12y−5=0

Step-by-step explanation:

+6xy+9y

+4x+12y−5=0

Comparing the equation with the general equation of second degree gives

a=1,b=9,h=3,g=2,f=6,c=−5

Angle between a pair of straight lines that is tanθ=

∣

a+b

−ab

∣

tanθ=

∣

1+9

9−1×9

∣

tanθ=0

⇒θ=tan

−

(0)=0

∘

Angle between the pair of straight lines is zero therefore the lines are parallel.

Hence proved

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Marat540 [252]

Answer: Option C

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Step-by-step explanation:

If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a', b', c' then:

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So:

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Then

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Finally the answer is:

$y=5$ , $x=10$

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3 years ago

Determine g(x+a)−g(x) for the following function.<br> g(x)=4x2−6x

Ilia_Sergeevich [38]

Answer:

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Step-by-step explanation:

g(x)=4x²−6x

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= 4(x+a)² - 6(x+a)

= 4( x² + 2ax + a²) - 6x - 6a

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= [4x² + (8a - 6)x + (4a²- 6a)] - (4x²−6x)

= 4x² + (8a - 6)x + (4a²- 6a) - 4x² + 6x

= (8a - 6)x + (4a²- 6a) + 6x

= (8a - 6 + 6)x + (4a²- 6a)

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4 years ago

Find the angle between the following pairs of lines x^2+6xy +9y^2-4x +12y-5 =0​

Find the angle between the following pairs of lines x^2+6xy +9y^2-4x +12y-5 =0