Solve each equation by using the zero product property
(b-4)(3b-1)=0

Step-by-step explanation:

(b - 4)(3b - 1) is the factored form of some second degree polynomial.  Once you factor to this point, you can solve for the values of b using the Zero Product Property, which says that one of the those factors has to equal 0 for the product to equal 0 (cuz any number times 0 is equal to 0).  The first expression is b - 4.  If we set b - 4 equal to 0, we can solve for b:

b - 4 = 0 so

b = 4

Likewise with the second factor, 3b - 1.  Set it equal to 0 and solve for b:

3b - 1 = 0 and

3b = 1 so

b = 1/3

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

are ya tryin to ask something or is this a statement