Carbon is not an exceptionally abundant element but it is the most essential element for life on our planet. Why?

The lithosphere includes the crust and the top part of the (a) asthenosphere. (b) mantle. $(c)$ core. (d) lower mantle.

Find the specified term of each geometric sequence.

$$320,80,20,5 , \dots ; t _ { 8 }$$

What is the source of water for an oasis?

On a separate sheet of paper, answer the questions below. Make sure you read carefully and answer all parts of the questions. Describe Jean-Jacques Rousseau's political philosophy explained in his work The Social Contract.

Find the equilibrium solution, or critical point of the system

$$\begin{gather*} x' = - x - 4y - 4, \,\,\, y' = x - y - 6 \end{gather*}$$

and describe how solutions of the system behave in the vicinity of the critical point, and then use a computer to draw a direction field and phase portrait centered at the critical point.

Write the partial fraction decomposition of each rational expression. $\frac{x^{2}+1}{x^{3}+x^{2}-5 x+3}$

The Scwimmers' cost for cable television is given by C=75+25x, where x is the number of months of service. (a) Graph C=75+25x, for x≤50. (b) From the graph, estimate the Schwimmers' cost for 30 months of cable television. (c) If the Schwimmers' total cost for cable television is $975, estimate the number of months of service.

Identify the terms, like terms, coefficients, and constant terms. 12 - 7k + 9 - k

use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically.

$$2ln(x+3)-3=0$$

$$5x+3-2x=7x+3$$

Express each expanded form as a Hindu-Arabic numeral. $\left(5 \times 10^{3}\right)+\left(3 \times 10^{-2}\right)$

For each of the functions in a-d: (i) Copy and complete the table. Put a X in any cells that cannot be completed. (ii) Write down the domain. (iii) Decide if y = 0 is in the range of the function. Justify your decision. a. y = 2x

$$\begin{matrix} \text{x} & {-\frac{1}{2}} & \text{0} & \text{1} & \text{3.5}\\ \text{y = 2x} & \text{ } & \text{ } & \text{ } & \text{ } & \text{12}\\ \end{matrix}$$

b. $y=x^{2}+1$

$$\begin{matrix} \text{x} & \text{-3} & \text{0} & \text{2} & {\frac{1}{4}} & \text{ } & \text{ }\\ {y=x^{2}+1} & \text{ } & \text{ } & \text{ } & \text{ } & \text{5} & \text{5}\\\end{matrix}$$

c. $y=\frac{1}{x+1}, x \neq-1$

$$\begin{matrix} \text{x} & \text{-2} & \text{-1} & \text{0} & {\frac{1}{2}} & \text{3} & \text{ }\\ {y=\frac{1}{x+1}} & \text{ } & \text{ } & \text{ } & \text{ } & \text{ } & {\frac{1}{6}}\\ \end{matrix}$$

d. $y=\sqrt{x}, x \geq 0$

$$\begin{matrix} \text{x} & \text{-3} & \text{0} & {\frac{1}{4}} & \text{ } & \text{9} & \text{ }\\ y=\sqrt{x} & \text{ } & \text{ } & \text{ } & \text{1} & \text{ } & \text{10}\\ \end{matrix}$$

Find the magnitude and direction angle of the vector. Use an algebraic method and approximate exact answers with a calculator when appropriate. <3,4>