The standard form of the equation that represents the number of quarters, \( q \), and the number of dimes, \( d \), that Austin has in his piggy bank is \( 5 q+2 d=270 \). Explain what the intercepts mean in terms of the context and how to find them.

2. La forma binómica del valor de \( z \) que satisface \( \frac{z}{i}+\frac{3 z-3 i}{1-i}=2-4 i \), es:

\( (2 x-3 y+z)(x+4 y-2 z) \) a) \( 2 x^{2}+5 x y-6 x z-12 y^{2}+13 y z-2 z^{2} \) b) \( 2 x^{2}+5 x y-4 x z-12 y^{2}+11 y z-2 z^{2} \) c) \( 2 x^{2}+8 x y-4 x z-12 y^{2}+11 y z-2 z^{2} \) d) \( 2 x^{2}-x y-4 x z-12 y^{2}+11 y z-2 z^{2} \)

Question If using the method of completing the square to solve the quadratic equation \( x^{2}+3 x-17=0 \), which number would have to be added to "complete the square"? Answer Attempt 2 out of 2

Solve the equation. (Round your answers to four decimal places \[ e^{2 x}-10 e^{x}+9=0 \] \( x=\square \) (smaller value) \( x=\square \) (larger value)

\( \left(2 x^{2} y-3 z\right)\left(x^{3} z+4 y^{2}\right) \) a) \( 2 x^{5} y z+8 x^{2} y^{3}-3 x^{3} z^{2}-12 z y^{2} \) b) \( 2 x^{5} y z+8 x^{2} y^{3}-3 x^{3} z^{2}-12 z^{2} y \) c) \( 2 x^{5} y z-8 x^{2} y^{3}+3 x^{3} z^{2}-12 z^{2} y \) d) \( 2 x^{5} y z+8 x^{2} y^{3}-3 x^{3} z^{2}-12 x^{2} z \)