9. Calcule razonadamente, el valor de \( k \) para que la ecuación \( 2 x^{2}-(4 k+6) x+8 k+6=0 \) tenga una solución real doble. SOLUCIÓN: \( k=4 \sqrt{3} \mathrm{y} k=-12 \);

Question \( 7:( \) June 2023\( ) \) If \( g(x)=-x^{2}-x+5 \), then \( g(-4) \) is equal to

5. \( \frac{(n+1)!}{(n-4)!}=6 n^{2}+6 n \) olduğuna göre, \( n \) kaçtır? \( \begin{array}{llll}\text { A) } 7 & \text { B) } 6 & \text { C) } 5 & \text { D) } 4 \\ \text { 5) } 3\end{array} \)

8 Olivia drove 170 miles each way (there and back) to visit her cousin. On the trip, Olivia drove an extra 20 miles to see the Grand Canyon. She also drove an extra 45 miles to see Lake Powell. Write one or more equations you could use to represent th number of miles Olivia drove on her trip.

Without actually calculating, find the value \( (-10)^{3}+(7)^{3}+(3)^{3} \) వాస్తవ గణన చేయకుండానే \( (-10)^{3}+(7)^{3}+(3)^{3} \) యొక్క విలువ కనుక్కోఁ

\[ \frac{(2 n-3)!\cdot(3 n-3)!}{(2 n-1)!\cdot(3 n-4)!}=\frac{1}{14} \] olduğuna göre, \( n \) kaçtır?