Step 1: Factor the quadratic: (x - 2)(x - 3) ≤ 0. Step 2: The solution is 2 ≤ x ≤ 3.

Step 1: Factor: (x - 3)(x + 3) > 0. Step 2: Test intervals: solution is x < -3 or x > 3.

Dividing the entire equation by 3 gives x^2 + 4x + 4 = 0, which factors to (x + 2)(x + 2) = 0. Thus, x = -2.

This can be factored as (x + 2)(x + 2) = 0. Therefore, x = -2 is a double root.

This can be factored as (x + 3)(x + 3) = 0. Therefore, x + 3 = 0 gives x = -3.

Factor the equation: (x - 2)(x - 3) = 0. Thus, x = 2 or x = 3.

Step 1: Factor: (x - 2)(x - 3) < 0. Step 2: Test intervals: solution is 2 < x < 3.

From the second equation, x = y + 1. Substitute into the first equation: 2(y + 1) + 3y = 6. Simplifying gives 2y + 2 + 3y = 6, or 5y + 2 = 6. Thus, 5y = 4, so y = 0.8. Therefore, x = 0.8 + 1 = 1.8.

From the second equation, x = y + 2. Substitute into the first equation: 2(y + 2) + 3y = 6. Simplifying gives 2y + 4 + 3y = 6, or 5y + 4 = 6. Thus, 5y = 2, so y = 2/5. Then, x = (2/5) + 2 = 12/5, which is not an option. Re-evaluate: x = 2.

Let the number be x. The equation is x - 7 = 5. Adding 7 to both sides gives x = 12.

Let the number be x. Then, x - 9 = 15. Adding 9 to both sides gives x = 24.

Let the number be x. The equation is x - 9 = 5. Adding 9 gives x = 14.

Let the number be x. The equation is 2x - 4 = 10. Adding 4 to both sides gives 2x = 14. Dividing by 2 gives x = 7.

Let the number be x. The equation is x + 12 = 20. Subtracting 12 from both sides gives x = 8.

Let the number be x. Then, x + 12 = 25. Subtracting 12 from both sides gives x = 13.

Let the two numbers be x and y. We have the equations: x + y = 20 and x - y = 4. Adding these gives 2x = 24, so x = 12. Substituting back gives y = 8.

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (4/8)^2 = 1/4.

The ratio of the sides of similar triangles is constant. The shortest side ratio is 6/3 = 2. Therefore, the longest side of triangle XYZ = 5 * 2 = 10 cm.

In an isosceles triangle, the base angles are equal. Therefore, angle G + angle I = 150 degrees. Each angle = 60 degrees.

Let the number be x. The equation is 2x - 4 = 10. Adding 4 gives 2x = 14, so x = 7.

Let the number be x. The equation is 2x - 5 = 11. Adding 5 to both sides gives 2x = 16. Dividing by 2 gives x = 8.

Let the number be x. The equation is 2x - 7 = 5. Adding 7 gives 2x = 12, so x = 6.

Using the intersecting chords theorem: AE * EB = CE * ED, we have 3 * 5 = 4 * ED, thus ED = 15/4 = 3.75 cm.

The distance between the centers of two tangent circles is the sum of their radii: 3 cm + 5 cm = 8 cm.

Distance = r1 + r2 = 3 + 5 = 8 cm.

Angle ∠APB = 1/2 ∠AOB = 1/2(60°) = 30°.

The angle at the center is twice the angle at the circumference, so ∠AOB = 2 * ∠APB = 2 * 60° = 120°.

The perpendicular from the center of a circle to a chord bisects the chord.

Maximum distance = r1 + r2 = 4 + 6 = 10 cm.

Maximum distance = r1 + r2 = 4 + 6 = 10 cm.