Perform the given operations and simplify.

$$\frac{x^2+x-6}{x^2-2 x-3} \cdot \frac{2 x^2-3 x-9}{x^2-x-2} \div \frac{10 x^2+27 x+18}{x^2+2 x+1}$$

What does the real options model recognize that the NPV and IRR models do not?

Find a basis of solutions. Try to identify the series as expansions of known functions. Show the details of your work. xy''+y'-xy=0

$$\text { If } \left\{ v _ { 1 } , v _ { 2 } , \dots , v _ { n } \right\} \text { spans }\text { a vector space } V , \text { prove that some subset of the } v ^ { \prime } \text { 's a basis for } V .$$

Find the eigenvalues of each matrix and determine a basis for each eigenspace.

$$\begin{bmatrix}1&&3\\0&&-4\end{bmatrix}$$

Graph the parabola, showing the vertex with its coordinates and the axis of symmetry with its equation.

a. $y=3-(x-4)^2$

b. $x=3-(y-4)^2$

A parabola passes through the points (0, 5), (2, 1), and (6, 17). a. What is its equation? b. Where is its vertex?

Perform the operation and simplify when possible.

$$\frac { x ^ { 3 } + 3 x ^ { 2 } + 2 x } { 2 x ^ { 2 } - 2 x - 12 } \div \frac { x ^ { 3 } - 3 x ^ { 2 } - 4 x } { 3 x ^ { 2 } - 3 x } \cdot \frac { 2 x ^ { 2 } - 4 x - 16 } { x ^ { 2 } + 3 x + 2 }$$

Solve each equation by finding square roots. $4 x^{2}-20=0$

let M= $[m_{i j}]$, N=$[n_{i j}]$, and P=$[p_{i j}]$ be square matrices of the same size. Use the entries of M , N, and P to represent the entry in the ij-position of each of the following. (c) P(M + N)

Review the vocabulary list . Then, study each item below to categorize each group of words as all synonyms or as a mixture of antonyms and synonyms. If necessary, consult a dictionary. Then, explain your reasoning.

decorum, propriety, politeness

Find the roots of the polynomial equation:

$$x^3 -2x^2 + 10x + 136 = 0.$$

Determine the mass of each of the following: (a) 2.345 mol LiCl (b) 0.0872 mol acetylene, $\mathrm{C}_{2} \mathrm{H}_{2}$ (c) $3.3 \times 10^{-2} \mathrm{mol} \mathrm{Na}_{2} \mathrm{CO}_{3}$ (d) $1.23 \times 10^{3}$ mol fructose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}$ (e) 0.5758 mol $\mathrm{FeSO}_{4}\left(\mathrm{H}_{2} \mathrm{O}\right)_{7}$

Graph versus f, in the range $−4 < f < 4$ the magnitudes and phases of (a) $\mathrm{X}(f)=5 \operatorname{rect}(2 f) e^{+j 2 \pi f}$ (b) $\mathrm{X}(f)=j 5 \delta(f+2)-j 5 \delta(f-2)$ (c) $X(f)=(1 / 2) \delta_{1 / 4}(f) e^{-j \pi f}$