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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the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

y=3n + 1

step-by-step explanation:

this is wrong because it says the second number is one less and i added one instead