There are several sets of different numbers which can be chosen from {0,1,2,3,4,5,6,7,8,9}. d How many sets can be formed (including empty set)

Step-by-step explanation:

The number of sets that can be generated from the given set is determined by calculating the power of the set. Power of a set is expressed as 2ⁿ where:

n represents the number of elements in the set.

Given the set S = {0,1,2,3,4,5,6,7,8,9}.

n(S) = 10

The Power of the set = 2^n(S)

Power of the set = 2^10 = 1,024

This means that 1,024 different sets can be formed from the given set including the empty set.

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.