Solve the system of equations by using the row-reduction method.

$$\left\{\begin{array}{l}{3 x+4 y=1} \\ {8 x+11 y=4}\end{array}\right.$$

Let

$$f(x)=\left\{\begin{array}{l}{x^{2}-3 \text { for } x \leq 2} \\ {5-x \text { for } x>2}\end{array}\right.$$

Evaluate the following limits. If the lumit does not exist, explain why it does not exist. a. $\lim _{x \rightarrow 2^{+}} f(x)$ b. $\lim _{x \rightarrow 2^{-}} f(x)$ c. $\lim _{x \rightarrow 2} f(x)$

Find the indicated sides of the right triangle. b = 5600, c = 6500, a = ?

True or False. Two triangles are congruent if two angles and the included side of one equals two angles and the included side of the other.

Multiply or divide, as indicated, and write scientific notation for the result:

$$(3.1 \times 10^7)(2.1 \times 10^{- 4})$$

A block of wood has a mass of 120 g and a volume of

$$200 \mathrm { cm } ^ { 3 }$$

What is the density of the wood?

A spring hangs from the ceiling. Describe how a single coil moves as a longitudal wave passes through the spring.

Even on a cloudy day, you can get sunburned outside. However, inside a glass greenhouse, you won’t get sunburned. Which type of electromagnetic waves will pass through clouds, but not glass?

Plot each complex number in the complex plane and write it in polar form. Express the argument in degrees. $-2+3 i$

The improper fraction 3/2 equals what mixed number?

If P is a polynomial of degree k, then $\int{P(x)e^x}dx=[P(x)-P'(x)+\cdots\pm P^{(k)}(x)]e^x+C$ Verify this statement. For simplicity, take k = 4.

Combine each pair of simple sentences to form a compound sentence. Use a comma and coordinating conjunction or a semicolon to separate the independent clauses. Odysseus yelled insults at Polyphemus. The Cyclops hurled a rock at the ship.

Decompose v into two vectors, one parallel to w and the other orthogonal to w. $\mathbf{v}=-\mathbf{i}+2 \mathbf{j} ; \mathbf{w}=3 \mathbf{i}-\mathbf{j}$

John has a balance of $3000 on his Discover card that charges 1% interest per month on any unpaid balance. John can afford to pay$100 toward the balance each month. His balance each month after making a $100 payment is given by the recursively defined sequence$B_{0}=$3000 \quad B_{n}=1.01 B_{n-1}-100.$ Determine John’s balance after making the first payment. That is, determine $B_{1}.$