The area of a sector of a circle and the measure of its central angle are given. Find the radius of the circle. $A=377 \text { in }^{2}, \theta=\frac{5 \pi}{3}$

Neatly graph the points (-2, 9), (-3, 7) and (-5, 10) on a four-quadrant graph. Connect them to make a triangle. Then, for each transformation described below: i) Write and simplify an expression to find the new coordinates. ii) Check your answer on your graph. a. Slide the triangle right 4 units and down 6 units. b. Reflect the triangle across the y-axis.

Factor each polynomial using the given factor and long division. Assume n>0. $x^{3 n}+x^{2 n}-12 x^{n}+10 ; x^{n}-1$

Set up a definite integral that represents the area bounded by the graphs of the indicated equations over the given interval. Find the areas to three decimal places. $y=-\sqrt{36-x^{2}} ; y=0 ;-6 \leq x \leq 0$

Use the given trigonometric function value of the acute angle $\theta$ to find the exact values of the five remaining trigonometric function values of $\theta$. $\than \theta=3$

Humble Management Services opened for business and completed these transactions in September.

$$\begin{matrix} \text{Sep. 1} & \text{Henry Humble, the owner, invested \$38,000 cash along with office equipment valued at \$15,000 in the company in exchange for common stock.}\\ \text{2} & \text{The company prepaid \$9,000 cash for 12 months’ rent for office space.}\\ \text{4} & \text{The company made credit purchases for \$8,000 in office equipment and \$2,400 in office supplies. Payment is due within 10 days.}\\ \text{8} & \text{The company completed work for a client and immediately received \$3,280 cash}\\ \text{12} & \text{The company completed a \$15,400 project for a client, who must pay within 30 days.}\\ \text{13} & \text{The company paid \$10,400 cash to settle the payable created on September 4.}\\ \text{19} & \text{The company paid \$1,900 cash for the premium on an 18-month insurance policy.}\\ \text{22} & \text{The company received \$7,700 cash as partial payment for the work completed on September 12.}\\ \text{24} & \text{The company completed work for another client for \$2,100 on credit.}\\ \text{28} & \text{The company paid \$5,300 cash in dividends.}\\ \text{29} & \text{The company purchased \$550 of additional office supplies on credit.}\\ \text{30} & \text{The company paid \$860 cash for this month’s utility bill.}\\ \end{matrix}$$

1. Prepare general journal entries to record these transactions (use account titles listed in part 2). 2. Open the following ledger accounts—their account numbers are in parentheses (use the balance column format): Cash (101); Accounts Receivable (106); Office Supplies (124); Prepaid Insurance (128); Prepaid Rent (131); Office Equipment (163); Accounts Payable (201); Common Stock (307); Dividends (319); Services Revenue (401); and Utilities Expense (690). Post journal entries from part 1 to the ledger accounts and enter the balance after each posting. 3. Prepare a trial balance as of the end of September.

Graph each function over the indicated interval. $y=\left(\frac{1}{3}\right)^{x}=3^{-x} ;[-3,3]$

Determine if the nth term of the sequence defines an arithmetic sequence, a geometric sequence, or neither. If the sequence is arithmetic, find the common difference d. If the sequence is geometric, find the common ratio r. $a_{n}=5+\sqrt{2} n$

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity. Filling a cup

Locate the vertical asymptotes, and sketch the graph of each function. and=-than 3x

Graph the solutlon set.

$$5 x \leq 6 y$$

Perform the indicated operations if possible.

$$\scriptstyle A=\left[\begin{array}{rrr}4 & 1 & -3 \\ 2 & 4 & 6\end{array}\right] \quad B=\left[\begin{array}{rr}1 & 9 \\ 0 & -1 \\ 3 & 5\end{array}\right] \quad C=\left[\begin{array}{rrr}0 & 1 & -4 \\ 2 & -1 & 8\end{array}\right]$$

BA

Verify each identity. $\frac{\cos \theta}{1+\sin \theta}+\than \theta=\sec \theta$

If k is nonnegative, find the interval for x for which each inequality is true. $(xk)(x-k)<0$