Supplementary angles sum to 180 degrees. Therefore, angle B = 180 - 75 = 105 degrees.

By definition, supplementary angles add up to 180 degrees.

The complement of an angle is found by subtracting it from 90 degrees. Thus, angle B = 90 - 30 = 60 degrees.

According to the exponent rule, any non-zero number raised to the power of zero equals 1.

By convention, 0^0 is often defined as 1 in combinatorics, although it can be considered indeterminate in other contexts.

The exponent zero indicates the multiplicative identity, meaning any non-zero number raised to the power of zero equals one.

Using the property of exponents, a^3 * a^(-2) = a^(3 - 2) = a^1, hence x = 1.

Substituting a = 2, we have 2^3 * b^2 = 64, which simplifies to 8b^2 = 64. Thus, b^2 = 8, leading to b = 4.

From a^3 = b^2, we can express b in terms of a as b = a^(3/2).

According to the laws of exponents, when multiplying like bases, we add the exponents: p = m + n.

The property of exponents states that when multiplying like bases, you add the exponents: m + n = p.

If a = b, then a^x = b^y implies x must equal y for the equality to hold.

Substituting x = 1 into the function gives f(1) = 3(1)^2 + 2(1) - 5 = 3 + 2 - 5 = 0.

Since 8 is 2^3, log_2(8) equals 3.

log_2(x) + 2 = 5 implies log_2(x) = 3, thus x = 2^3 = 8.

Since 27 is 3^3, log_3(27) = 3.

The expression log_a(b) = c can be rewritten in exponential form as a^c = b.

The definition of logarithms states that if log_a(b) = c, then a raised to the power of c equals b, hence a^c = b.

By the definition of logarithms, if log_a(b) = x, then b = a^x.

The definition of logarithms states that if log_b(x) = y, then b raised to the power of y equals x, hence b^y = x.

Profits should be divided in accordance with their capital contributions, which are 60% for A and 40% for B.

Despite the capital contribution, the partners agreed to split profits equally, hence 50% to each.

In the absence of any other agreement, profits are typically divided in the ratio of capital contributions.

Profits should be divided in accordance with their capital contributions, so A receives 60% and B receives 40%.

Profits should be divided in accordance with their capital contributions, hence 60% to A and 40% to B.

The difference A - B includes elements in A that are not in B, which are {1, 2}.

The intersection of sets A and B includes the elements that are common to both sets. Therefore, the intersection is {3, 4}.

A - B represents the elements in A that are not in B. Thus, A - B = {1}.

The intersection A ∩ B includes elements that are both even and prime, which is {2}.

The intersection of sets A and B is the set of elements that are common to both sets. Therefore, the intersection is {3, 4}.