USING EQUATIONS to solve WORD PROBLEN Directions: Set up and solve an equation for each problem below. \( \begin{array}{l}\text { 2. Five less than twice a number is equal to one } \\ \text { half the difference of three times the number } \\ \text { and 13. Find the number. }\end{array} \)

4. A. B. C ve D sayılarının yerine \( 2,3,4,6 \) ve 8 sayılarından dört tanesi birer kez kullanıldığında aşağıdaki eşitlik sağlanmaktadır A、 \( \bar{B}= \) C、 \( \bar{D} \) Buna göre, bu beş sayıdan hangisi verilen eşitlikte yer almaz? \( \begin{array}{llll}\text { A) } 2 & \text { B) } 3 & \text { C) } 4 & \text { D) } 6\end{array} \) E) 8

Find the two natural numbers which differ by 5 and the sum of whose squares is 97.

Prove, by factoring, that \( A(x)=(x-2)(-x+1) \) Let \( F(x)=\frac{A(x)}{2} \)

If \( p=\{2,3,5,7,11\} \) and \( Q=\{1,3,5,11\} \) Rationalise the denominator of \( \frac{5+\sqrt{3}}{5-\sqrt{3}} \)

Hallar los autovalores reales \( y \) autovectores de \( \mathbb{R}^{n}, y \) una base de au- tovectores cuando sea posible, de las matrices: a) \( \left(\begin{array}{rr}4 & 6 \\ -3 & -5\end{array}\right) \), b) \( \left(\begin{array}{rr}5 & -1 \\ -1 & 1\end{array}\right) \), c) \( \left.\left(\begin{array}{cc}1 & -2 \\ -2 & 3\end{array}\right), d\right)\left(\begin{array}{rrr}2 & 2 & -1 \\ 0 & -2 & 0 \\ -1 & 0 & 0\end{array}\right) \)