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

x

2

+6xy+9y

2

+4x+12y−5=0

Step-by-step explanation:

x

2

+6xy+9y

2

+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

2

h

2

−ab

∣

∣

∣

∣

∣

∣

tanθ=

∣

∣

∣

∣

∣

1+9

2

9−1×9

∣

∣

∣

∣

∣

=

9

0

tanθ=0

⇒θ=tan

−

(0)=0

∘

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

Hence proved

they used 313 gallons of paint

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %