Sea \( R \) la relación de los números naturales: \( N=\{0,1,2,3, \ldots \ldots . . . . \).\( \} definida por cl \) cnunciado formal; ' \( 2 x+y=10 \) ", hallar: a) \( R_{4}=\{(x, y) \in N \times N / 2 x+y=10\} \) b) Hallar el dominio de la relación c) Hallar el rango de la relación

2. Expand and simplify \( \begin{array}{ll}\text { a. } 2(x+3) & \text { b. } \quad x\left(x^{2}-3 x\right) \\ \text { c. } \quad(x+7)(x-5) & \text { d. } \quad(x-3)^{2}\end{array} \)

The number of incarcerated adults N (measured in thousands) in a certain country can be approximated by the equation \( \mathrm{N}=-2.8 \mathrm{x}^{2}+72.4 \mathrm{x}+1914 \), where x is the number of years since 2000. In 2012 , the number of incarcerated adults peaked. How many adults were incarcerated in that year? There were \( \square \) incarcerated adults in 2012.

a) \( 2 / 6=9 / x \) b) \( 1 / 3=x / 12 \) c) \( x / 10=6 / 5 \) d) \( \delta / x=2 / 15 \)

4. \( 4 x-2 x+2=2 x-2-2 x \)

Solve for \( M \). Assume that all other variables are nonzero. \( Q=\frac{2 \text { twM }^{2}}{3 c} \) \( M=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.