Rationalize the numerator.

$$\frac { \sqrt [ 3 ] { x ^ { 2 } z } } { y }$$

Find each indefinite integral and check the result by differentiating. $\int(3 x+5)^{2}(3) d x$

Choose the word from the list at the right that completes each statement. a. dependent b. determinant. c. feasible region. d. inconsistent. e. independent. f. matrix. g. parallel. h. perpendicular. i. slope. j substitution. k. x-intercept. l. y-intercept. In the equation y=2x-4, -4 is the ____.

Evaluate the indefinite integral. $\int(1+\tan \theta)^{5} \sec ^{2} \theta\ d \theta$

Rationalize the numerator. $\frac{1-\sqrt{5}}{3}$

Read each sentence and determine whether the subject refers to a person or a thing. Then, circle the correct relative pronoun to complete the sentence.

Los recursos con que / quienes trabajamos son escasos.

Evaluate each function. Round your answers to four decimal places. $\cot 11^{\circ} 15^{\prime}$

Answer true or false. Justify your answer by providing a counterexample if the statement is false or an outline of a proof if the statement is true. If A is an $(n \times n)$ matrix and c is a scalar, then $\operatorname{det}(c A)=c \operatorname{det}(A)$.

Write each number using calculator notation. $8 \times 10^{-}$

Suppose that a fellow student showed that the expression $n^{2}+n+1$ is prime for n = 1, 2, and 3. Explain why this is not a sufficient proof that the expression is prime for all positive integers n.

What is the molarity of a 2.4-liter solution containing 124 grams of HF?

Rationalize the numerator.

$$\sqrt [ 3 ] { \frac { 2 x } { 3 y } }$$

Answer true or false. Justify your answer by providing a counterexample if the statement is false or an outline of a proof if the statement is true. In each exercise, A is a real $(n \times n)$ matrix. If A is nonsingular with $A^{-1}=A^{T}$, then det(A) = 1.

Draw any $\triangle \mathrm{ABC}$ with A at the origin, side AB along the positive x-axis, and C in quadrant I. Show that the area of your triangle can be expressed as $\frac{1}{2} b c \sin \mathrm{A}$ or $\frac{1}{2} a c \sin \mathrm{B}$.