Substituting x = 0: 4(0) - 5y = 20 => -5y = 20 => y = -4.

Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.

Population after 2 years = 100,000 * (1 + 0.05)^2 = 100,000 * 1.1025 = 110,250.

Population after 1 year = 1000 * 1.10 = 1100. Population after 2 years = 1100 * 1.10 = 1210.

Probability of not occurring = 1 - P(event) = 1 - 0.3 = 0.7.

By Vieta's formulas, the sum of the roots p + q = -b/a.

The equation can be factored as (x + 1)(x + 1) = 0, giving the root -1 with multiplicity 2.

Substituting x = -1 into the equation gives (-1)^2 + 2(-1) + k = 0, leading to 1 - 2 + k = 0, thus k = 1.

Using Vieta's formulas, p = -(3 + 4) = -7 and q = 3 * 4 = 12. Therefore, p + q = -7 + 12 = 5.

Circumference = 2πr = 2π × 7 cm = 14π cm.

Circumference = 2πr = 2 × 3.14 × 7 cm = 43.96 cm.

Circumference = 2 * π * radius = 2 * π * 7 = 14π units.

The area of a circle is given by A = πr². If the radius is doubled (r becomes 2r), the new area is A' = π(2r)² = 4πr², which is four times the original area.

Elected members = Total members - Nominated members = 245 - 12 = 233.

Percentage of nominated members = (12 / 245) * 100 = 4.89%.

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 28, giving 7x = 28, so x = 4. Thus, A's age = 3x = 12.

Let A's age be 3x and B's age be 4x. Then, 3x + 4x = 28, so 7x = 28, giving x = 4. Thus, A's age = 3x = 12.

Let the sides be 3x, 4x, and 5x. Then, 3x + 4x + 5x = 36. Thus, 12x = 36, giving x = 3. The longest side is 5x = 15 cm.

A triangle with sides in the ratio 3:4:5 is a right-angled triangle.

Using a dew point calculator or approximation, the dew point at 80% relative humidity and 25°C is approximately 22°C.

Using the formula for dew point, the approximate dew point at 80% humidity and 30°C is around 20°C.

The discriminant is given by b^2 - 4ac. Here, b = 2, a = 1, c = 1, so the discriminant is 2^2 - 4*1*1 = 0.

The sum of the roots is -1 + -3 = -4, and the product is (-1)(-3) = 3. Thus, k = 3.

Using Vieta's formulas, k = (-1)(-2) = 2.

For the roots to be equal, the discriminant must be zero. Thus, 4^2 - 4*1*k = 0 leads to k = 4.

The product of the roots ab is given by c/a. Here, c = 6 and a = 1, so ab = 6.

The discriminant must be greater than zero for real and distinct roots: (-4)^2 - 4*1*k > 0, which simplifies to 16 - 4k > 0, or k < 4.

For real and distinct roots, the discriminant must be greater than zero: (-6)^2 - 4*1*k > 0, leading to k < 9.

A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.

Vertical drop = Distance × Slope = 2000 m × (1/1000) = 2 m.