Which of the following equations represents a line that is parallel to the line that passes through the points below?
(-3,6) (9,2)

See below

Step-by-step explanation:

Two lines are parallel if they have the same slope but different y-intercepts. So the slope that can be formed given the points (-3,6) and (9,2) is (9-(-3))/(2-6)=12/-4=-3

With y=-3x+b, we need b, which can be found by plugging in either point:

2=-3(9)+b

2=-27+b

29=b

So the y-intercept therefore cannot be 29 but it can be any real number.

So the equation y=-3x+2 works, y=-3x+3, y=-3x+4, and so on

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

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation: