Questions in mathematics

Questions in mathematics

[Done] If the total length of all the edges of a cube is 4 feet, what is the volume of the cube?

[Done] What is \(3\sqrt{24} - 4\sqrt{54}\)?

[Done] Use the substitution method to solve the system of equations: 1. [tex]x = 4[/tex] 2. [tex]2x - 3y = -19[/tex]

[Done] Substitution Method 1) \[ \begin{cases} 3x + y = 7 \\ 4x + 2y = 16 \end{cases} \] 2) \[ \begin{cases} 2x + 2y = 4 \\ x - 2y = 0 \end{cases} \]

[Done] 3. Factor. \[ 9x^2 + 15x \] A. \( x(3x + 5) \) B. \( 3x(3x + 5) \) C. \( 9x(x + 5) \) D. \( 3x^2(3x + 5) \) 4. Factor. \[ 20mn − 30m \] A. \( 2m − 3 \) B. \( 10m(2n − 3) \) C. \( 10mn(2m + 3n) \) D. \( 10n(2m − 3) \) 5. Factor. \[ 8x^2y^2 − 4x^2y − 12xy \] A. \( 4(2xy − 4x^2y − 12xy) \) B. \( 4(8x^2y^2 − x − 12xy) \) C. \( 4x^2y^2(2xy − xy − 3) \) D. \( 4xy(2xy − x − 3) \)

[Done] Use the elimination method to solve the following systems of equations: 1) \[ \begin{align} -4x + y &= -12 \\ 4x + 2y &= 6 \\ \end{align} \] 2) \[ \begin{align} 5x + 2y &= 12 \\ -6x - 2y &= -14 \\ \end{align} \] 3) \[ \begin{align} 5x + 4y &= 12 \\ 7x - 6y &= 40 \\ \end{align} \] 4) \[ \begin{align} 5m + 2n &= -8 \\ 4m + 3n &= 2 \\ \end{align} \]

[Done] Graph the line for this problem: \[ y = 3x + 6 \]

[Done] Oil consumption is increasing at a rate of 1.8% per year. By what factor will oil consumption increase in 6 years? Use the approximate doubling time formula (rule of 70).

[Done] What is bigger: 2.5 feet or 32 inches?

[Done] Graph the function [tex]y = \frac{1}{2}\sin(x - \frac{\pi}{4})[/tex].