If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Perpendicular lines intersect at right angles, which measure 90 degrees.

Adjacent angles formed by intersecting lines are supplementary. Therefore, 180 - 70 = 110 degrees.

Alternate interior angles are equal when two parallel lines are cut by a transversal. Therefore, if one angle is 65 degrees, the other alternate interior angle is also 65 degrees.

The 3rd term is given by 6C2 * a^4 * b^2 = 15 * a^4 * b^2 = 15ab^5.

The 3rd term is given by C(6, 2) * (x)^2 * (2)^4 = 15 * x^2 * 16 = 240x^2.

The 4th term is given by C(6,3) * (3x)^3 * (2)^3 = 20 * 27x^3 * 8 = 4320x^3.

The 5th term is given by C(6, 4) * (3x)^4 * (-2)^2 = 15 * 81x^4 * 4 = 4860x^4.

The absolute value of -7 is 7.

The slopes of the lines are -2/3 and 4. The angle θ can be found using tan(θ) = |(m1 - m2) / (1 + m1*m2)|.

The slopes are m1 = 2 and m2 = -1/2. The angle θ between the lines is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)|, which results in 90 degrees.

Area = πr² = 3.14 * (4)² = 3.14 * 16 = 50.24 cm²

Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².

Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².

The area of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 8 * 5 = 20 cm².

Area = (√3/4) * side² = (√3/4) * 6² = (√3/4) * 36 = 9√3 cm².

The area under the curve is given by ∫(from 1 to 4) (1/x) dx = [ln(x)] from 1 to 4 = ln(4) - ln(1) = ln(4).

The area under the curve is given by ∫(from 0 to 2) (2x^2 + 3) dx = [(2/3)x^3 + 3x] from 0 to 2 = (16/3 + 6) = 10.

The axis of symmetry for a parabola in vertex form y = a(x - h)^2 + k is x = h. Here, h = 2.

The characteristic polynomial is given by det(G - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 3.

The circumference C of a circle is given by C = π * diameter. Here, C = π * 14 cm ≈ 3.14 * 14 ≈ 44 cm.

Circumference = 2 * π * radius = 2 * π * 7 = 14π cm

Using the binomial theorem, the coefficient of x^2 in (2x + 5)^4 is given by 4C2 * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.

The coefficient of x^2 in (2x - 5)^5 is given by 5C2 * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.

The coefficient of x^3 in (3x + 2)^5 is given by 5C3 * (3)^3 * (2)^2 = 10 * 27 * 4 = 1080.

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

Set f'(x) = 2x - 4 = 0; solving gives x = 2.

Find f'(x) = 2x - 4. Set f'(x) = 0, giving 2x - 4 = 0, hence x = 2.

A × B = |i  j  k| |1  2  3| |4  5  6| = -3i + 6j - 3k.

A × B = |i  j  k| |1  2  0| |3  4  0| = (0 - 0)i - (0 - 0)j + (4 - 6)k = -2k.