Gandalf the grey started in the forest of mirkwood at a point with coordinates (2,1)(2,1) and arrived in the iron hills at the point with coordinates (3,6)(3,6). if he began walking in the direction of the vector v¯¯¯=5i+1jv¯=5i+1j and changed direction only once, when he turned at a right angle, at what point did he make the turn?

Answer is x = -24/13,  y = 3/13

Step-by-step explanation:

The vector equation of line is;

(x,y) = () + t (v)  ...............  1

we know that;

() = (2,1)    

and

v = 5i + 1j

put in equation 1

The parametric equation becomes;

by comparison we get;

multiply equation 3 by -5 and add it to equation 2

we know that;

so, m = 5

we can find the family of lines that are perpendicular to the above line by swapping the coefficients and change the sign of one of them:

So, the equation of other line is

multiply equation 5 by -5

put this value of y in equation 5.

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answer: 1,380

step-by-step explanation:

1: you turn %15 into a decimal by moving the decimal point two places to the left.

2: and then you multiply .15 by 1,200 , which will get you 180.00

3: from there you will add 180 to 1,200

4: which will get you 1,380

hope it *im kind of slow so idk if my answer is right*

y=3x+4

step-by-step explanation:

given the points a(0,4) and b(-4, -8)

eqn of line ab: (y-4)/(x-0)=(-8-4)/(-4-0)

(y-4)/x=-12/-4=3

y=3x+4