What is d n e? given sets in photo

OPTION B: {5, 7, 9}

Step-by-step explanation:

D E is the collection of elements that are present in both D and E.

Given the set D = {5, 6, 7, 8, 9, 10}

and                 E = {1, 3, 5, 7, 9, 11}

So, the elements present in both D and E are: {5, 7, 9}.

Hence, D E = {5, 7, 9}.

OPTION B is the answer.

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.

47 - 90 = 43

43 - 180 = x

x = 137