Which equation shows an example of the associative property of addition?
a.(–4 + i) + 4i = –4 + (i + 4i)
b.(–4 + i) + 4i = 4i + (–4i + i)
c.4i × (–4i + i) = (4i – 4i) + (4i × i)
d.(–4i + i) + 0 = (–4i + i)

a)yes

b) no

c) no

d) no

Step-by-step explanation:

Remember, that the associative property of the addition says that if then

(a+b)+c=a+(b+c).

Then

a) with a=-4, b=i, c=4i, says that

(a+b)+c=a+(b+c).

Then the equation (–4 + i) + 4i = –4 + (i + 4i) is an example of the associative property of addition.

b) Observe that with a=-4, b=i and c=4i, the equation (–4 + i) + 4i = 4i + (–4i + i) can be represented as

(a+b)+c=c+(a+b)

Which no represent the associative property

c) the equation is using the operator , that is, is using the multiplication. Then c doesn't represent the associative property of addition.

d) with a=-4i, b=i, c=0, the equation (–4 + i) + 0=(–4i + i) can be represented as

(a+b)+c=(a+b)

Then no show an example of the associative property of addition.

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.