Projection = (A · B / |B|^2) * B = (14 / 8) * (2i + 2j) = (7/4)(2i + 2j) = 3.5i + 3.5j.

Projection of A onto B = (A · B / |B|^2) * B = ((6*2 + 8*2) / (2^2 + 2^2)) * (2i + 2j) = (28/8)(2i + 2j) = 7i + 7j.

Range = Maximum - Minimum = 12 - 3 = 9

The rows of B are linearly dependent, hence the rank of B is 2.

The rows of D are linearly dependent, hence the rank of D is 2.

The rank of a matrix is the maximum number of linearly independent row vectors. Here, the first and third rows are independent, while the second row is zero. Thus, the rank is 2.

The rank of E is 2 because the rows are linearly dependent (the third row is a linear combination of the first two).

The real part of z is -2.

The real part of z is 3.

The real part of z = 4 + 5i is 4.

The real part of z is 4.

The recommended daily intake of fiber for adults is 25-30 grams to maintain digestive health.

The recommended daily intake is 5-7 servings of fruits and vegetables for optimal health.

The recommended daily intake of fruits and vegetables for adults is 5-7 servings to ensure adequate nutrient intake.

The recommended daily intake of protein for an average adult is about 50 grams.

Corresponding angles are equal when two parallel lines are cut by a transversal.

The loudness of a sound is directly proportional to the amplitude of the sound wave.

When two lines intersect, the angles formed are supplementary, meaning they add up to 180 degrees.

In an equilateral triangle, all three angles are equal and measure 60 degrees each.

When two parallel lines are cut by a transversal, the corresponding angles are equal.

In a rectangle, the diagonals are equal in length.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides.

The sum of the interior angles of a triangle is 180 degrees, and the angles formed by a transversal cutting through two parallel lines are supplementary, meaning they add up to 180 degrees.

Resistance R = ρ * (L/A). Here, R = (1.7 x 10^-8 Ωm) * (2 m / (1 x 10^-6 m²)) = 0.034 Ω.

(2x + 3)(2x - 3) = 4x² - 9 by the difference of squares.

(a - b)(a + b) = a² - b², which is the difference of squares.

(x + 1)² - (x - 1)² = [(x² + 2x + 1) - (x² - 2x + 1)] = 4x.

(x + y + z)² = x² + y² + z² + 2(xy + xz + yz) is the correct expansion.

(x + y)(x - y) = x² - y², which is the difference of squares.