log_10(100) = 2 and log_10(10) = 1, so 2 + 1 = 3.

Since 1000 is 10^3, log_10(1000) = 3.

Using the property of logarithms, log_5(25) = 2 and log_5(5) = 1. Therefore, log_5(25) + log_5(5) = 2 + 1 = 3, which is log_5(125).

Both 1/4^x and 4^(-x) represent the inverse of 4^x.

The product (x + 1)(x - 1) is a difference of squares, resulting in x^2 - 1.

The product of the roots of a quadratic polynomial ax^2 + bx + c is given by c/a. Here, c = 4 and a = 1, so the product is 4.

The sum of the roots is given by -b/a, which is -3/5 for this equation.

The vertex of the quadratic equation is given by the point (-b/2a, f(-b/2a)).

An exponential function approaches the x-axis as x approaches negative infinity but never actually touches it.

The function f(x) = 1/(x - 2) has a vertical asymptote at x = 2, where the function is undefined.

A horizontal line represents a function that is constant, meaning it neither increases nor decreases.

A parabola opening upwards is not one-to-one because it fails the horizontal line test; a horizontal line can intersect it at two points.

A strictly increasing function is one where, for any two points x1 and x2, if x1 < x2, then f(x1) < f(x2), which is represented by a graph that slopes upward from left to right.

A quadratic function is represented by a parabola, which can open either upwards or downwards.

A linear equation in two variables always forms a straight line when graphed.

Polynomial functions are continuous and smooth, meaning they do not have breaks, holes, or sharp corners.

A unique solution occurs when the equations intersect at exactly one point.

Exponential functions grow or decay at a constant percentage rate, which is a defining characteristic.

Harmonic progression can include fractions, as it is defined through the reciprocals of an arithmetic progression.

Harmonic progressions can contain negative numbers, but the terms themselves must be positive to maintain the definition of harmonic sequences.

The y-intercept is defined as the point where the line crosses the y-axis, which occurs when x is zero.

The y-intercept (b) is the value of y when x equals zero.

A quadratic polynomial is defined as a polynomial of degree 2, which is represented by x^2 + 2x + 1.

The polynomial x^2 - 9 can be factored as (x - 3)(x + 3).

All of the mentioned methods can be used to solve a quadratic equation.

A quadratic equation is one that can be expressed in the form ax^2 + bx + c = 0, which is satisfied by x^2 - 4x + 4 = 0.

The roots of the polynomial can be found by factoring it as (x-2)(x-3) = 0, giving roots 2 and 3.

Adding 3 to both sides gives 2x = 10, then dividing by 2 gives x = 5.

To solve for x, add 9 to both sides and then divide by 3: 3x = 9, thus x = 3.

Solving the inequality gives 3x < 9, thus x < 3.