For the following, find the discriminant; \( b^{2}-4 a c \), and then determine whether one real-number solution, two different real-number solutions, or two different imaginary number solutions exist. \( x^{2}+4 x+7=0 \) What is the discriminant, \( b^{2}-4 a c \) ? (Simplify your answer.) What is the nature of the solution(s)? A. There is one real-number solution. B. There are two different imaginary-number solutions. C. There are two different real-number solutions.

втопарке \( 92 \% \) всех автомобилей - отечественные, остальные - импортные. \( 22 \% \) омобилей неисправны. При этом \( 78 \% \) огечественных автомобилей исправны. Схоль оцентов импортных автомобилей ненсправны?

Determine the solution of the system of equations represented by the lines in the graph. Check your solution by substituting into bot, equations. \[ \begin{array}{l}y=2 \\ x=-4\end{array} \]

Given that the point \( (-84,13) \) is on the terminal side of an angle, \( \theta \), find the exact value of the following: \[ \begin{array}{l}\sin (\theta)= \\ \qquad \frac{\tan (\theta)}{\tan (\theta)}= \\ \frac{1}{\sin (\theta)}=\square \\ \frac{1}{\cos (\theta)}=\square\end{array} \]

Solve for \( x \) \[ 9^{x+5}=27 \]

1. Derive as seguintes funcoses: a) \( f(x)=x^{4}-\frac{x^{2}}{3}+\sqrt{2} x-\sqrt{5} \) b) \( f(x)=\left(\frac{2 x+3}{x-1}\right)^{2} \)