And show work the product of a number, x, and five is half the sum of the number and two. which answer represents this situation? a. 5 = 1 2 + 2 b. 5 + 1 2 ( + 2) c. 10 = 1 2 ( + 2) d.10 + 1 2 + 3

In the given problem, the number is taken by a variable x.

Let us break the given statement into smaller parts.

First part : " product of a number, x, and five"

Product represents multiplication operation.

Therefore, product of a number, x, and five can be written as an expression

5*x = 5x.

Second part : "half the sum of the number and two".

Half could be represent by fraction 1/2, and sum of a number x and 2 by (x+2).

Therefore, second part of the expression could be written as

1/2 (x+2).

On combining both parts together, we get final expression

5x = 1/2 (x+2)

Therefore, option B is correct, that is 5x = 1/2 (x+2).

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be