The following statements concern the modulus. which statement is false?
the modulus represents the distance between the complex number and the origin.
the algorithm to find the modulus is based on the pythagorean theorem.
the modulus is sometimes negative because of the computations with i.
the modulus is an extension of the absolute value in the complex plane.

30 feet

step-by-step explanation:

that would be 2 1/2 * 12

= 24 + 6

= 30 feet   (answer)

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)

the answer is b.

64

step-by-step explanation:

c=2πr=2·π·8≈64

42.4 6th grade students prefer hip hop

step-by-step explanation:

40 percent of 106 = 42.4