In the polynomial P(x), the coefficient of x^2 is -4.

In the polynomial P(x), the coefficient of the x^2 term is -4.

Let the cost price be x. Then, 80 = x - (20% of x) => 80 = x - 0.2x => 80 = 0.8x => x = 100.

Let the original price be x. After a 25% discount, the selling price is x - (0.25 * x) = 0.75x. Thus, 0.75x = $150, so x = $150 / 0.75 = $200.

A quadrilateral with one pair of parallel sides is classified as a trapezium.

The ratio of flour to sugar is 3:2. For 8 cups of sugar, the amount of flour needed is (3/2) × 8 = 12 cups.

Selling Price = $400 - (25% of $400) = $400 - $100 = $300. Profit = Selling Price - Cost Price = $300 - $250 = $50.

Substituting n = 5 into the equation gives a_5 = 3(5) + 2 = 15 + 2 = 17.

Let the marked price be x. Selling Price = x - (20% of x) = 0.80x. Thus, 0.80x = $80, so x = $80 / 0.80 = $100.

Let the cost price be x. Selling Price = Cost Price - (10% of Cost Price) = x - 0.10x = 0.90x. Thus, 0.90x = $90, so x = $90 / 0.90 = $100.

Let the marked price be x. Then, Selling Price = x - (20% of x) = 240 => 0.8x = 240 => x = 300.

Let the cost price be x. Selling price = cost price - loss = x - (0.10 * x) = 0.90x. Setting this equal to $90 gives 0.90x = $90, so x = $100.

Let the marked price be x. After a 20% discount, the selling price is x - (0.20 * x) = 0.80x. Setting this equal to $80 gives 0.80x = $80, so x = $100.

Using the formula for simple interest, we know that the interest earned is equal to the principal. Therefore, if the principal doubles in 5 years, the rate of interest can be calculated as (100 * Interest) / (Principal * Time) = (100 * Principal) / (Principal * 5) = 20%. Thus, the rate of interest is 20%.

Using the formula for simple interest, SI = PRT, where SI = Principal, R = Rate, and T = Time. If the principal doubles in 5 years, then SI = P. Therefore, P = PRT implies R = 1/5 = 20%. Hence, the rate of interest is 10%.

Using the rule of 72, we estimate the time to double as 72/12 = 6 years.

Using SI = PRT, SI = 8000 * 0.06 * 4 = $1920.

The number of ways to choose 4 players from 10 is given by 10C4 = 210.

a * b ≡ 2 * 3 ≡ 6 (mod 5), which is equivalent to 1.

All operations (addition, subtraction, multiplication) maintain congruence under modular arithmetic.

Supplementary angles sum up to 180 degrees. Therefore, angle B = 180 - 45 = 135 degrees.

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.

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

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.

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

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

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}.