The Hinge Theorem is also known as the Side-Angle-Side Inequality Theorem or SAS Inequality Theorem. How are the requirements for applying the Hinge Theorem similar to the requirements for applying SAS? How are the requirements different?

Write an inequality relating the given side lengths. If there is not enough information to reach a conclusion, write no conclusion.

S T and M N

When two triangles have two pairs of congruent sides, how are the third pair of sides and the pair of angles opposite the third pair of sides related?

Venetta applies the Converse of the Hinge Theorem to conclude that the measurement of angle EKF > the measurement of angle HKG for the given triangles. Is Venetta correct? Explain your answer.

Use the definition of the derivative to find f'(x). $f(x)=\frac{1}{x-2}$

Determine all critical points of the function. f(x) = 6x^2 - x^3

Write the chemical formula for each substance mentioned in the fo llowing word descr iptions (use the front inside cover to find the symbols for the elements you do not know). Vanadium(III) bromide is a colored solid.

Kayak A and kayak B leave a dock. Which kayak is closer to the dock?

Order angle PTU, angle SQT, and angle QSR from least to greatest.

A woodworker uses a caliper to measure the widths of a bat to help him determine the widths for a new bat. The woodworker places the open tips of the caliper on the bat. The distance between the tips is a width of the bat.

Suppose a caliper opens to an angle of 25 degrees for one width of a bat and opens to an angle of 35 degrees for another. What can you conclude about the widths of the bat?

Use vector-matrix methods to find the general solution of the linear system where

$$\mathbf{x}=\left( \begin{array}{l}{x_{1}} \\ {x_{2}} \\ {x_{3}}\end{array}\right)$$

.

$$\mathbf{x}^{\prime}=\left( \begin{array}{rrr}{3} & {0} & {1} \\ {-1} & {4} & {1} \\ {4} & {-4} & {2}\end{array}\right) \mathbf{x}$$

Decide what number must be added to make each expression a perfect square trinomial. Then factor the trinomial. $x^{2}+\frac{1}{4} x+$

A data storage system consists of 3 disk drives sharing a common queue. An average of 50 storage requests arrive per second. The average time required to service a request is .03 second. Assuming that interarrival times and service times are exponential, determine: a. The probability that a given disk drive is busy b. The probability that no disk drives are busy c. The probability that a job will have to wait d. The average number of jobs present in the storage system

Translate into Latin: You (plural) ought not to fear the Druids.