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.

Since D is opposite E, F sitting to the left of D means F is also opposite to E. Therefore, the person sitting to the right of E is F.

The arrangement can be visualized as A-B-C-E-D-F. Therefore, A is sitting to the left of E.

Since F is to the left of G and H is to the right of F, it follows that F must be to the left of H.

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

Since A cannot sit next to B, C, D, or E can be seated next to A. Therefore, C is a valid option.

Since W is to the immediate left of Y and Y is to the immediate right of Z, Y must be in the middle of the arrangement.

Since C is between A and D, and A is not next to B, E must be next to D.

Since C is between A and D, and A is not next to B, E must be next to B.

Arranging the friends based on the given information, we find that B is opposite to D.

P is between Q and R, which means Q is on one side of P and R on the other. Since S is opposite T, the only person next to R must be P.

Since R is between P and Q, we can place them in a circle. S must be placed such that T is directly opposite S, as there are only five friends.

Since R is between P and Q, we can place them in the circle. S will then be opposite T, as there are only five friends.

The union of two sets will always have at least as many elements as the larger of the two sets, including unique elements.

Hybrid sets can help reduce redundancy by combining different categories of data into a single representation.

With A between B and C, and D opposite A, F must be next to D in the arrangement.

Since C is opposite A, and A is next to B, D must be next to C.

If A is next to B and C is opposite A, then E must be to the right of C in the circular arrangement.

The arrangement is B-A-C. The person sitting opposite B would be E.