11. solve for x: x3 + 3x2 + 3x + 2 = 0

x = -2,  (-1 + √3 i ) / 2  ,   (-1 - √3 i) / 2.

Step-by-step explanation:

x^3 + 3x^2 + 3x + 2 = 0

f(-2) = -8 + 3*4 - 6 + 2

= -8 + 12 - 6 + 2

= 0

So (x + 2) is a factor . Dividing:

            x^2  + x  + 1

x + 2)   x^3 + 3x^2 + 3x + 2

           x^3 + 2x^2

                       x^2 + 3x

                       x^2 + 2x

                                 x + 2

                                  x + 2.

Solving  x^2 + x + 1:

   x  = [ - 1 +/- sqrt(1 - 4*1*1) ] / 2

      =  (-1 + √3 i ) / 2  ,   (-1 - √3 i) / 2.

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional