Tell whether the sequence is arithmetic. if it is, what is the common difference?

19,11,3,-5

a. no
b. yes; 1/8
c. yes; 8
d. yes; -8

 D. Yes ; -8

Step-by-step explanation:

An arithmetic sequence is given by :-

, where n is a natural number .

Here ,  differences between the successive terms is equal (d).

i.e. Common difference = and so on.

The given sequence : 19,11,3,-5

Since the differences between the successive terms are equal as -8.

So, the given sequence is an Arithmetic sequence with common difference = -8

Hence, the correct answer :  Yes , given sequence is an Arithmetic ; common difference =-8

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