A 2-column table with 7 rows. Column 1 is labeled Power of 3 with entries 3 cubed, 3 squared, 3 Superscript 1, 3 Superscript 0, 3 Superscript negative 1, 3 Superscript negative 2, 3 Superscript negative 3. Column 2 is labeled Value with entries 27, 9, 3, a, b, StartFraction 1 Over 9 EndFraction, c.

Answer these questions about the powers of 3.

What is the pattern as the exponents decrease?

What is the value of each variable?

a =

b =

c =

a=1, b=1/3, c=1/27

Step-by-step explanation:

The table is given below:

(a)As the exponents decrease, the next term is gotten by a division of the previous term by 3.

(b)

a=1, b=1/3, c=1/27

quit

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