2. All 120 seats in a hall were filled for a concert. The tickets cost \( \$ 10 \) for adults and \( \$ 6 \) for students. The total proceeds were \( \$ 980 \). How many adults attended the concert? How many students?

3. Résoudre les équations suivantes: (a) \( \log _{x}(x-2)=\log _{x-2}(x) \)

10. a. Show that the roots of the equation \( 2\left(a^{2}+b^{2}\right) x^{2}+2(a+b) x+1=0 \) can never be real unless \( a=b \). b. Prove that the roots of the equation \( x^{2}+(2 k-1) x+k^{2}=0 \) are real roots if \( k \leq \frac{1}{4} \).

\( a^{2}=4 a+4 \) \( b^{2}=4 b+4 \) olduğuna göre, \( \frac{a-4}{a^{2}}+\frac{4}{b^{2}} \) kaçtır?

27. Dada la matriz \( A=\left[\begin{array}{cc}a & b \\ -b & a\end{array}\right] \) [video guia: https://voutu.be/m580)hu2MnIPsi=t|Gfe9fJKvVSr7KH] a. Determine valores propios y los vectores propios complejos asociados b. Encuentre los valores caracteristicos de la matriz \( B=A^{T} A \) c. Si los valores caracteristicos de \( \left[\begin{array}{ll}a & b \\ 0 & d\end{array}\right] \) son 0 y 1 , halle los posibles valores de \( a \) y \( d \)

Diberikan polinomial \( P(x)=x^{3}-5 x^{2}+4 x+4 \) \( Q(x)=-x^{2}-7 x+9 \) Nilai dari \( P(x)-Q(x)=\cdots \) A. \( \quad x^{3}-6 x^{2}-3 x+13 \) B. \( x^{3}-6 x^{2}-2 x+13 \) C. \( x^{3}+6 x^{2}-3 x+13 \) D. \( x^{3}+6 x^{2}-2 x+13 \) E. \( \quad x^{3}+6 x^{2}+3 x+13 \)