Using the binomial theorem, the coefficient of x^3 in (x + 3)^5 is given by 5C3 * (3)^2 = 10 * 9 = 90.

Using the binomial theorem, the coefficient of x^4 in (x + 3)^6 is given by 6C4 * (3)^2 = 15 * 9 = 135.

The coefficient of x^5 in (x - 1)^8 is C(8,5) * (-1)^3 = 56 * (-1) = -56.

The term containing x^2 is given by C(6, 2) * (x)^2 * (-2)^(6-2) = 15 * x^2 * 16 = 240x^2, so the term is -80x^2.

The mode is 4, as it appears most frequently (three times) in the data set.

The mode is 4, as it appears most frequently (three times) in the data set.

The mode is 70, as it appears 3 times, which is more than any other score.

The mode is 8, as it appears 3 times, which is more than any other number.

The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.

Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.

Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.

Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.

Using the sine rule, HI/sin(60) = GH/sin(30). Therefore, HI = (10 * sin(60)) / sin(30) = 10 * (√3/2) / (1/2) = 10√3 cm.

The longest side of triangle GHI is GI, which measures 26 cm.

Perimeter = GH + HI + GI = 10 + 24 + 26 = 60 cm.

Since the sides are in the ratio 3:4:5, it follows the Pythagorean theorem, indicating it is a right-angled triangle.

Using Pythagoras theorem: JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12 cm.

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Semi-perimeter = (JK + KL + JL) / 2 = (15 + 20 + 25) / 2 = 30 cm.

Since 15² + 20² = 25² (225 + 400 = 625), triangle JKL is a right-angled triangle.

Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.

Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.

Semi-perimeter = (PQ + QR + PR) / 2 = (8 + 6 + 10) / 2 = 12 cm.

In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Therefore, XY = XZ / √2 = 10 / √2 = 5√2 cm.

In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.

The function f(x) = 1/(x-1) is not defined at x = 1, hence it is discontinuous at that point.

The function f(x) = sqrt(x) is continuous at x = 0 as it is defined and the limit exists.

The function f(x) = |x| is continuous at x = 0 because the left limit, right limit, and f(0) all equal 0.

Subtract 2x from both sides: x - 7 = 5. Then add 7: x = 12.

This is a separable equation. Separating variables and integrating gives ln|y| = 2x + C, hence y = Ce^(2x).