To solve the equation 3x−2=4x−1 , veronica graphs the functions f(x)=3x−2 and g(x)=4x−1 on the same set of coordinate axes. which statement describes the solution of the equation 3x−2=4x−1? (a) the solution of the equation is the x-coordinate of the ordered pair where the graphs of the two functions intersect. (b) the solution of the equation cannot be found graphically. veronica should solve the equation algebraically. (c) the solution of the equation is the y-coordinate of the ordered pair where the graphs of the two functions intersect. (d) the solution of the equation is the y-intercept of the linear equations.

we have that

f(x)=3x-2

g(x)=4x-1

3x-2=4x-1-------------> 4x-3x=-2+1--- > x=-1

find the value of f(x) or g(x) for x=-1

f(x)=3x-2 ------->  f(-1)=3*(-1)-2 ------> f(-1)=-5

the solution is the point (-1,-5)

using a graph tool

see the attached figure

the answer is 

- "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."

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm