For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.

For the roots to be equal, the discriminant must be zero. Thus, (-5)^2 - 4(1)(k) = 0. Solving gives k = 6.25.

log_10(0.01) = log_10(10^-2) = -2.

log_2(1/8) = log_2(2^-3) = -3.

log_5(1) = 0 because 5^0 = 1.

In the equation y^2 = 4px, we have 4p = 20, thus p = 5.

According to the Pythagorean identity, sin² θ + cos² θ = 1 for any angle θ.

Calculating gives 2^3 = 8 and 3^2 = 9. Therefore, 2^3 + 3^2 = 8 + 9 = 17.

Calculating gives 4 × 5 - 5 = 20 - 5 = 15.

5! = 5 × 4 × 3 × 2 × 1 = 120.

5! = 120, 3! = 6, and 2! = 2. Thus, 120 / (6 * 2) = 10.

According to the order of operations, we first calculate 3 × 2 = 6, then add 7, giving 7 + 6 = 13.

The square root of 144 is 12, since 12 * 12 = 144.

Subtracting 5 from both sides gives 3x = 15. Dividing by 3 gives x = 5.

Rearranging gives 3x - 2x = 5 + 7, thus x = 12.

Adding 7 to both sides gives 4x = 16. Dividing by 4 gives x = 4.

The value of π (pi) is approximately 3.14.

Mean = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. Variance = [(1-3.5)² + (2-3.5)² + (3-3.5)² + (4-3.5)² + (5-3.5)² + (6-3.5)²] / 6 = 2.92 (approx 2.5).

Volume = side^3 = 4^3 = 64 cubic units.

Rearranging to slope-intercept form: -2y = -5x + 10, thus y = (5/2)x - 5. The y-intercept is -5.

A noun can function as a subject or object in a sentence, representing a person, place, thing, or idea.

A verb expresses an action or a state of being.

A noun is used to name a person, place, thing, or idea.

An adverb modifies a verb, an adjective, or another adverb, providing more detail about how, when, where, or to what extent.

An adjective provides more information about a noun.

The cell membrane is selectively permeable, allowing certain substances to pass while blocking others.

A matrix where all elements are zero is called a zero matrix.

The reaction CaCO3 → CaO + CO2 is a decomposition reaction, where one compound breaks down into two products.

An acid reacting with a base results in a neutralization reaction, producing salt and water.

The Non-Cooperation Movement aimed to resist British rule through non-violent means and promote self-governance.