P and q are complex numbers such that |p|=3/4x+2, |q|=2x+1, and |p+q|=2/3x-2. On what interval must x fall on?

Answer choices:

a.(-infinity, -13/5]

b.[3, infinity)

c.[-8/3,-13/5]

d.[-8/3, -1/2]

B

( - 3 , infinity )

Step-by-step explanation:

Given that

|p| = 3/4x+2

|q| = 2x+1

|p+q| = 2/3x-2

|p| + |q| = |p+q|

That is

3/4x+2 + 2x+1 = 2/3x-2

(3x + 8)/4 + 2x + 1 = (2x - 6)/3

(3x + 8 + 8x + 4)/4 = (2x - 6)/3

Cross multiply

9x + 24 + 24x + 12 = 8x - 24

Collect the like terms

33x + 36 = 8x - 24

33x - 8x = - 24 - 36

25x = - 60

X = -60/25

X = - 2.4

X should fall on the interval of

( -3, infinity)

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

you can not drow on this

step-by-step explanation: