Find the common difference for the sequence shown.
56, 49, 42, 35, ...
-7
-12
7

-7

Step-by-step explanation:

Given  : sequence  56, 49, 42, 35, ...

To find : Find the common difference.

Solution : We have given that 56, 49, 42, 35, ...

By the common difference of an arithmetic sequence is:

d = a_{2} -a_{1}a2−a1

Where, a_{1}a1 is the first term and  a_{1}a1 is the second term.

Then common difference =  49 -56

                                          = -7 .

47

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is