What is the equation of the line that passes through the point (-5, 7) and
has a slope of - 1/5?

Step-by-step explanation:

We have the following equation

y=mx+b

where m is the slope

and b is the y intercept

we know that the slope is  -1/5 (or -.2)

which means that so far our equation looks like this

y= -.2x+b

which means we need to solve for b

we know that when x= -5 y= 7 which means we can plug in those values and solve for b

we have

7= (-.2*-5)+b

7=1+b

b=6

which means our equation is as follows

y= -1/5x+6

a² + b²= c²

24² + 7² = c²

c= 25

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12