Analyze the graph of the function. \( R(x)=\frac{x+4}{x(x+8)} \) (a) What is the domain of \( R(x) \) ? A. \( \{x \mid x \neq 0 \) and \( x \neq-8 \) and \( x \neq-4\} \) B. \( \{x \mid x \neq 0 \) and \( x \neq-4\} \) C. \( \{x \mid x \neq 0 \) and \( x \neq-8\} \) D. All real numbers (b) What is the equation of the vertical asymptote(s) of \( R(x) \) ? Select the correct choice below and fill in any answer boxes within your choice. A. \( x=\square \) (Use a comma to separate answers as needed. Type an integer or a fraction.)

Determine the implied domain of the following function. Express your answer in interval notation. \[ f(x)=\sqrt{x}-9 \] Answer

Find an equation for the hyperbola described. Graph the equation. Center at \( (-1,-7) ; \) focus at \( (-1,-10) ; \) vertex at \( (-1,-9) \) Write an equation for the hyperbola. \( \square-\square=1 \) (Type exact answers for each term, using fractions as needed.)

The number of U.S. travelers to other countries during the period from 1990 through 2009 can be modeled by the polynomial function \( P(x)=-0.00530 x^{3}+0.1366 x^{2}+1.250 x+46.49 \) where \( x=0 \) represents \( 1990, x=1 \) represents 1991 , and so on and \( P(x) \) is in millions. Use this function to approximate the number of \( U \).S. travelers to other countries in each given year. (a) 1990 (b) 2000 (c) 2009 (a) In 1990 , the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (b) In 2000, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (c) In 2009, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

What is the direction of a vector with a horizontal component of 2 and a vertical component of -4 ?

The function \( f(t)=60,000(2)^{\frac{1}{40}} \) gives the number of bacteria in a population \( t \) minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?