How would your responses to the preceding question change if the annual payments were increased to $\$ 2,000,000$ per year for 15 years?

Answer the question, choosing one or more responses. Which of these might you find in a menagerie? a. monkeys b. a stuffed lion c. stars

Build rational expression into an equivalent rational expression with the indicated denominator. $1=\frac{?}{7}$.

How many different arrangements of the integers 1 through 20 are possible on a typical dartboard, assuming that 20 is always at the top?

Rewrite the following expression so that it is a difference of squares: x$^4$-y$^4$. Then factor the expression completely.

Solve each inequality and graph the solution set on a number line. $\frac{1}{2} x<4$

In this exercise, evaluate the given expression, or state that the expression is not a real number.

$$\sqrt{25-16}$$

Write your responses on a sheet of paper. Explain how scientists hypothesize that Earth is about 4.5 billion years old.

Do a trace of MergeSort(23, 5, 7, 13, 43, 21, 17, 2) using a top-down evaluation.

The quotient of a negative number and a positive number will _ be negative. (F) always (G) sometimes (H) never (J) not

Simplify algebraic expression, or explain why the expression cannot be simplified. $8 x^4+x^4$

Think About It Sketch the graph of an arbitrary function that does not have a point of inflection at $(c, f(c))$ even though $f^{\top}(c)=0$.

The ordered pair rule $(x, y) \rightarrow(y-7,-x+6)$ is what type of transformation?

Given a polynomial

$$p ( x ) = r _ { 0 } + r _ { 1 } x + \cdots + r _ { n } x ^ { n }$$

and a square matrix A, the matrix

$$p ( A ) = r _ { 0 } I + r _ { 1 } A + \cdots + r _ { n } A ^ { n }$$

is called the evaluation of p(x) at A. Let

$$B = P ^ { - 1 } A P$$

. Show that p(B)=

$$P ^ { - 1 } p ( A ) P$$

for all polynomials p(x).