Which graph represents the function f(x)=2⋅4x? An exponential function on a coordinate plane with x and y axis in increments of 1 increasing from negative 7 to 7. The function increases from left to right beginning infinitely close to the x axis in the second quadrant and passing through begin ordered pair 0 comma 2 end ordered pair. The function continues to increase through the first quadrant. An exponential function on a coordinate plane with x axis in increments of 1 increasing from negative 7 to 7 and y axis in increments of 1 increasing from negative 4 to 10. The function increases from left to right beginning infinitely close to the x axis in the second quadrant and passing through begin ordered pair 0 comma 1 end ordered pair. The function continues to increase through the first quadrant. An exponential function on a coordinate plane with x axis in increments of 1 increasing from negative 7 to 7 and y axis in increments of 1 increasing from negative 4 to 10. The function increases from left to right beginning infinitely close to the x axis in the second quadrant and passing through begin ordered pair 0 comma 1 end ordered pair. The function also passes through begin ordered pair 1 comma 4 end ordered pair. The function continues to increase through the first quadrant. An exponential function on a coordinate plane with x axis in increments of 1 increasing from negative 7 to 7 and y axis in increments of 1 increasing from negative 4 to 10. The function increases from left to right beginning infinitely close to the x axis in the second quadrant and passing through begin ordered pair 0 comma 4 end ordered pair. The function continues to increase through the first quadrant.

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

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: