Questions in mathematics

Questions in mathematics

[Done] Verify the trigonometric identity: \[ \cos^2 \theta - \sin^2 \theta = 1 - 2\sin^2 \theta \]

[Done] Transitive Property: Systems of Equations \[ y = 6x - 3 \] \[ y = -x + 4 \]

[Done] Which list shows the lengths of three line segments that could not form a triangle? A. 6 cm, 8 cm, 10 cm B. 5 cm, 6 cm, 7 cm C. 4 cm, 7 cm, 13 cm D. 3 cm, 6 cm, 6 cm

[Done] How do you write \(\frac{32}{100}\) in expanded form?

[Done] Solve the system of linear inequalities: 1. \(-2 \leq y \leq 6\) 2. \(3y \leq 4x + 26\) 3. \(y \leq -2x + 2\) Objective function: \(f(x, y) = -3x - 6y\)

[Done] The perimeter of a rectangle is 20 feet, and the length of each side is a whole number. How many rectangles with different shapes satisfy these conditions?

[Done] Model how to factor the polynomial \(2x^3 - 8x^2 + 3x - 12\) step by step.

[Done] How do you graph the equation \(\frac{1}{3}x - \frac{1}{6}y = 0\)?

[Done] Two movie tickets and three concert tickets cost $21. Three movie tickets and two concert tickets cost $19. Each ticket costs a whole number of dollars. How much does one movie ticket cost? How much does one concert ticket cost?

[Done] Solve the following system of linear equations: \[ 3x + 2y = 11 \] \[ 7x - y = 3 \]