Use the segment to complete the statements.
the value of x is
the length of ab in inches is
the length of bc in inches is

x = 5

AB = 5 inches

BC = 15 inches

Step-by-step explanation:

If AC = 20

then AB + BC = AC

; 3x + x = 20

where 4x = 20

; x = 5

AB = x = 5 inches

BC = 3x = 3(5) = 15 inches

a). x = 5 inches

b). AB = 5 inches

c). BC = 15 inches

Step-by-step explanation:

From the given diagram, sum of the length of segment AB and length of segment BC will be equal to the length of AC.

That means, AB + BC = AC

Since AB = x inches

BC = 3x inches

and AC = 20 inches

A). x + 3x = 20

4x = 20

x =

  = 5 inches

B). AB = x = 5 inches

C). BC = 3x = 3×5 = 15 inches

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.