The examples are used to illustrate the complexity of inequalities, reinforcing the author's argument.

The vertex of a quadratic function is the point at which the function reaches its maximum or minimum value.

The x-intercepts of a function are the points where the graph crosses the x-axis, meaning the output of the function is zero at those points.

Using the property of exponents (a^m)^n = a^(m*n), we have (2^3)^2 = 2^(3*2) = 2^6.

Using the power of a product property, we have (x^2 * y^3)^(2) = x^(2*2) * y^(3*2) = x^4 * y^6.

Using the property of exponents, we have (x^3 * x^2) / x^4 = x^(3+2-4) = x^1.

The smallest 3-digit number is 100. The first number greater than or equal to 100 that is divisible by 9 is 108.

The smallest multiple of 9 greater than 50 is 54.

Solving the inequality gives 2x < 4, thus x < 2.

Solving the system gives x = 2 and y = 3, thus the solution set is (2, 3).

'101' is 5 and '110' is 6 in decimal. Their sum is 5 + 6 = 11.

The sum of the digits in '1011' is 1 + 0 + 1 + 1 = 3.

The sum of the first n terms S_n = n/2 * (2a + (n-1)d). Here, S_15 = 15/2 * (2*2 + 14*4) = 15/2 * (4 + 56) = 15/2 * 60 = 450.

The sum of the first n terms of a GP is given by S_n = a(1 - r^n) / (1 - r). Here, S_5 = 2(1 - 3^5) / (1 - 3) = 2(1 - 243) / (-2) = 242.

The sum of the interior angles of any quadrilateral is 360 degrees.

In binary, '101' + '110' = '1011'.

'12' in base-3 is 3 and '21' is 7. Their sum is 10, which is '100' in base-3.

The sum of the roots is given by -b/a = 3/2.

The sum of the roots is given by -b/a = 8/2 = 4.

Surface area = 6 * (side)² = 6 * (5)² = 6 * 25 = 150 cm².

A general partner has unlimited liability, meaning they are personally responsible for the debts of the partnership.

A polygon that has all sides and angles equal is called a regular polygon.

A concave polygon is defined as a polygon that has at least one interior angle greater than 180 degrees.

A polygon with all sides and angles equal is known as a regular polygon.

The tone of the passage is cautious but hopeful, acknowledging challenges while emphasizing potential solutions.

The author maintains an optimistic tone, suggesting that change is possible and necessary.

The total surface area of a sphere is given by SA = 4πr². Here, r = 7, so SA = 4π(7)² = 196π.

Calculating each term, we have 5^0 = 1, 5^1 = 5, and 5^2 = 25. Therefore, 1 + 5 + 25 = 31.

Using the property of exponents, (5^3 * 5^2) = 5^(3+2) = 5^5. Thus, (5^5) / (5^4) = 5^(5-4) = 5^1 = 5.

5^(-2) is equal to 1/(5^2) = 1/25 = 0.04.