The essence of the author's argument is that innovation drives progress, as emphasized throughout the passage.

The phrase 'A necessary change for a better future' encapsulates the passage's message about the need for progress.

The phrase 'the main point' accurately captures the essence of 'the crux of the matter'.

Industrial expansion contradicts the theme of environmental conservation, while the others promote it.

A stitch in time saves nine is about timely action, while the others focus on the value of actions or habits.

Individual effort is paramount contradicts the theme of teamwork, which emphasizes collaboration.

He was unprepared contradicts the positive outcomes suggested by the other phrases.

The benefits of a healthy diet do not connect with the theme of education and learning.

The phrase 'a cycle of disadvantage' reflects the ongoing nature of systemic inequality discussed in the passage.

The phrase 'On the contrary,' signals a shift in the author's argument, introducing a contrasting viewpoint.

The phrase 'We must strive for equity' indicates a call to action, urging readers to take steps towards addressing inequalities.

Industrial expansion often leads to increased resource consumption and environmental degradation, making it the least related to sustainability.

Isolation and solitude are contrary to the theme of friendship, which is built on connection and companionship.

The distance from the origin to a point (x, y) is given by √(x² + y²). The point (0, 1) has a distance of 1, which is the smallest.

The point (2, 3) is the midpoint of the segment joining (1, 2) and (3, 4), making it equidistant from both.

Substituting x = 2 into the equation y = 2(2) + 1 gives y = 5, so the point (2, 5) lies on the line.

A concave hexagon has at least one interior angle greater than 180 degrees, which makes it a non-convex polygon.

The number of diagonals in a polygon is given by n(n-3)/2. For a hexagon (n=6), it has 9 diagonals, which is more than the others.

A star-shaped polygon has at least one interior angle greater than 180 degrees, making it concave.

A star-shaped polygon is an example of a non-convex polygon because it has points that point inward.

A concave hexagon has at least one interior angle greater than 180 degrees, making it a non-convex polygon.

The polynomial x^2 + 4x + 4 can be factored as (x + 2)^2, making it a perfect square.

A quadratic polynomial is defined as a polynomial of degree 2, which is 2x^2 + 3x - 5.

A quadratic equation has a maximum value when the coefficient of x² is negative. Here, all options have a positive coefficient, but the first option can be rewritten to show its vertex form.

The discriminant of x^2 + 4x + 5 is negative (16 - 20), indicating complex roots.

A rhombus has all sides equal and opposite angles equal.

In a rectangle, the diagonals are equal in length but not perpendicular.

In a rectangle, the diagonals are equal in length but are not necessarily perpendicular.

In a rectangle, the diagonals are equal in length.

In a kite, the diagonals bisect each other but are not equal in length.