What does the remainder theorem conclude given that f(x)/x+6 has a remainder of 14? Enter your answer by filling in the boxes.

Step-by-step explanation:

According to the remainder theorem, if a function f(x) is divided by (x-a), then the remainder is defined by f(a).

It is given that has a remainder of 14.

Here, the function f(x) is divided by (x+6). So, on comparing (x+6) and (x-a), we get

So, by remainder theorem, remainder of is f(-6).

Since the remainder is 14, therefore

Therefore, the answer for first blank is -6 and for second blank is 14, i.e., .

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