Cicero and Themistocles run for the same political office. Cicero received www votes in the election, and Themistocles received vvv votes. Which of the following expressions always represents how many more votes the winner received than the loser?
A. w - v
B.∣w−v∣
C. None of above

[w-v]           b is answer

Step-by-step explanation:

How many more votes the winner received than the loser can be thought of as the distance between the two numbers of votes on the number line.

Hint #22 / 5

The distance between two numbers is equal to the absolute value of their difference.

For example, | a - b|∣a−b∣vertical bar, a, minus, b, vertical bar is the distance between aaa and bbb.

Hint #33 / 5

We want to find the distance between \blue{w}wstart color #6495ed, w, end color #6495ed and \pink{v}vstart color #ff00af, v, end color #ff00af.

Hint #44 / 5

The distance between \blue{w}wstart color #6495ed, w, end color #6495ed and \pink{v}vstart color #ff00af, v, end color #ff00af is |\blue{w} - \pink{v}|∣w−v∣vertical bar, start color #6495ed, w, end color #6495ed, minus, start color #ff00af, v, end color #ff00af, vertical bar or |\pink{v}-\blue{w}|∣v−w∣vertical bar, start color #ff00af, v, end color #ff00af, minus, start color #6495ed, w, end color #6495ed, vertical bar.

Hint #55 / 5

\left\lvert \blue w- \pink v\right\rvert∣w−v∣open vertical bar, start color #6495ed, w, end color #6495ed, minus, start color #ff00af, v, end color #ff00af, close vertical bar always represents how many more votes the winner received than the loser.

B |w-v|

Step-by-step explanation:

khan academy

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3