What do the x- and y-intercepts of your graph represent?

Find the sum or difference. Write your answer in simplest form.

$$12 \frac { 3 } { 4 } - 6 \frac { 1 } { 6 }$$

Solve each system of equations using matrices.

$$\left\{ \begin{array} { r } { x - 2 y + z = 2 } \\ { 2 x - y - z = 1 } \end{array} \right.$$

Which measures the average kinetic energy of air molecules? A. humidity B. pressure C. speed D. temperature

Determine whether the equation represents a linear or nonlinear function. Explain.

$$y = \sqrt [ 3 ] { 8 } - x$$

What positive number is the same as its reciprocal?

Find the probability of winning a lottery using the given rules. Assume that lottery numbers are selected at random. You must correctly select 4 numbers, each an integer from 0 to 9. The order is important.

The Chebyshev equation is(1−x2)y''−xy'+α2y=0,whereαis a constant; see Problem 10 of Section 5.3.(a) Show that x=1 and x=−1 are regular singular points, and find the exponents at each of these singularities.(b) Find two solutions about x=1.

Define a relation R on the set Z of all integers as follows: For all m,

$$n \in Z$$

,

$$m R n \Leftrightarrow$$

every prime factor of m is a prime factor of n. Is R a partial order relation? Prove or give a counterexample.

Choose the correct term to complete each sentence. • biconditional • conjecture • contrapositive • converse • deductive reasoning • inductive reasoning • Law of Detachment • Law of Syllogism • postulate • theorem. Arriving at a conclusion by observing patterns is _____.

Z is the standard normal distribution. Find the indicated probabilities. $P(0.5 \leq Z \leq 1.5)$

Why do Earth-based optical telescopes work best at night, while radio telescopes work all day and all night long?

a. What is a glacier? b. What occurs during an ice age? c. Compare the climate today with it during an ice age.

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. Identify any asymptotes of the graph. $f(x)=2^{x-1}$