Certainly! Here are some common formulas and concepts typically covered in 9th-grade mathematics. These formulas are useful for solving problems in algebra, geometry, and trigonometry:

Algebra:

1. Quadratic Formula: For the quadratic equation ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 – 4ac)) / 2a

2. Distance Formula: The distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane is:
d = √((x₂ – x₁)² + (y₂ – y₁)²)

3. Slope of a Line: The slope (m) of a line passing through points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ – y₁) / (x₂ – x₁)

4. Slope-Intercept Form of a Line: The equation of a line with slope m and y-intercept b is:
y = mx + b

Geometry:

1. Pythagorean Theorem: In a right-angled triangle, where c is the hypotenuse and a, b are the other two sides:
c² = a² + b²

2. Area of a Triangle: The area (A) of a triangle with base (b) and height (h) is:
A = 0.5 * b * h

3. Area of a Circle: The area (A) of a circle with radius (r) is:
A = π * r²

4. Circumference of a Circle: The circumference (C) of a circle with radius (r) is:
C = 2 * π * r

Trigonometry:

1. Sine, Cosine, and Tangent: In a right-angled triangle, for an angle θ:
sin(θ) = opposite / hypotenuse