For the following system to be consistent, \( \left\{\begin{array}{l}6 x_{1}-3 x_{2}-2 x_{3}=-6 \\ 5 x_{1}-8 x_{2}+k x_{3}=-4 \\ -7 x_{1}+4 x_{2}+7 x_{3}=8\end{array}\right. \) we must have \( k \neq \square \) You may enter your answer as a fraction.

Find the nth term of the geometric sequence whose initial term is \( a_{1}=5 \) and common ratio is 10 . \( a_{n}=\square \) Next Question answer must be a function of \( n \).) .

Question 2 of 25 After the drama club sold 100 tickets to a show, it had \( \$ 300 \) in profit. After the next show, it had sold a total of 200 tickets and had a total of \( \$ 700 \) profit. Which equation models the total profit, \( y \), based on the number of tickets sold, \( x \) ?

Use the elimination method to find all solutions of the system: \( \left\{\begin{array}{l}x^{2}-2 y=7 \\ x^{2}+5 y=14\end{array}\right. \) The two solutions of the system are: (the one with \( x<0 \) is) \( x=\square \) \( y=\square \) (the one with \( x>0 \) is) \( x=\square \) \( y=\square \)

14. Uttrycken nedan har samma positiva värde på \( a \). Vilka tal ska stå i rutorna så att likheterna stämmer? \( a^{\frac{1}{3}}=\square \quad a^{\frac{2}{3}}=9 \)

Find dif \( a_{1}=-17 \) and \( a_{13}=-29 \)