A construction crew is extending the length of the center line on a highway. The length of the line starts out as 6 meters long, which is represented on a coordinate plane as the point (0,6). The crew works for 20 minutes and the line is now 17 meters long, which is represented as the point (20,17).

Complete the equation that represents the relationship between x, the number of minutes spent working, and y, the length of the line, in meters.

The equation that represents the relationship between x and y is

Explanation:

Given that a construction crew is extending the length of the center line on a highway.

The length of the line starts out as 6 meters long, which is represented on a coordinate plane as the point (0,6). The crew works for 20 minutes and the line is now 17 meters long, which is represented as the point (20,17).

Let x represents the number of minutes spent working.

Let y represents the length of the line in meters.

We need to determine the equation that represents the relationship between x and y.

The equation can be determined using the formula,

First, we shall determine the slope using the formula,

Substituting the coordinates and , we get,

Now, we shall substitute the slope and the coordinate in the formula , we have,

Simplifying, we get,

Thus, the equation that represents the relationship between x and y is

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

the answer is c)8

step-by-step explanaction: