The number of inmates \( N \) (measured in thousands) in federal and state prisons can be approximated by the equation \( N=-2.09 x^{2}+77.85 x+746 \), where \( x \) is the number of years since 1990. In what year was the number of inmates expected to be \( 1,404,840 \) ? The number of inmates was expected to be \( 1,404,840 \) in the year

\( ( 4,9 ) \quad \left\{ \begin{array} { l } { y = \frac { 3 } { 4 } x + 6 } \\ { 4 x - y = 7 } \end{array} \right. \)

\( (4 \mathrm{p}) \) a) \( 5 x^{2}-3 x=0 \) \( (4 \mathrm{p}) \) b) \( 6 x^{2}+12 x=0 \) \( (4 \mathrm{p}) \) c) \( 8 x^{2}-24=0 \) \( (4 \mathrm{p}) \) d) \( -4 x^{2}+100=0 \) (4p) e) \( x^{2}+8 x-33=0 \) \( (4 p) \) f) \( x^{2}+9 x+20=0 \)

Solve. \( 14 x^{2}-45 x>14 \) What is the solution? Select the correct choice below and, if necessary, fill in any answer boxes within your choice. (Simplify your answer.) A. \( \quad<x< \) B. \( x<\square \) or \( x> \) C. \( x=\square \) D. All real numbers satisfy the inequality. E. No real numbers satisfy the inequality.

\( ( 6,4 ) \quad \left\{ \begin{array} { l } { y = \frac { 3 } { 2 } x - 5 } \\ { y = x - 10 } \end{array} \right. \)

5 Show that if \( n \) is a whole number, \( n^{2}+n+2 \) must always be even.