How do I solve this question?

The correct answer is given by option a.

Step-by-step explanation:

Rational roots theorem:

In the rational roots theorem, we take the leading coefficient(which multiplies the term of x with the highest exponent) and the independent term(which does not multiply any value of x).

The possible roots have the format p/q, in which p are the factors of the independent term, and q are the factors of the leading coefficient.

In this question:

Leading coefficient: 3

Independent term: 15

Factors of the independent term: {1, 3, 5, 15} -> p

Factors of the leading coefficient: {1,3} -> q

Possible roots:

All possible values, positive or negative, in which p is divided by q. So

So, without the repeated terms, they are:

The correct answer is given by option a.

histogram or dot plot?

step-by-step explanation:

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