Hal earns n dollars per hour. Next month he will receive a 2 percent raise in pay per hour The expression n+0.02n is one way to represent Hal's pay per hour after the raise. Write an equivalent simplified expression that will represent his pay per hour after the raise.

Use an adjacency matrix to implement a class supporting a simplified graph ADT that does not include update methods. Your class should include a constructor method that takes two collections-a collection $V$ of vertex elements and a collection $E$ of pairs of vertex elements-and produces the graph $G$ that these two collections represent.

When simplified, which expressions would be equal to -1? Check all that apply. A. $\csc \theta \sin (-\theta)$ B. $\cos \theta \sec (-\theta)$ C. $\sin ^{2} \theta+\cos ^{2} \theta$ D. $\cot (-\theta) \tan \theta$ E. $\sec ^{2}(-\theta)-\tan ^{2}(-\theta)$

Using the Expression Mat, the value -3 can be shown in several ways, two of which are shown at right. Note that in these examples, the diagram on the left side uses negative tiles in the"+" region, while the diagram on the right side uses positive tiles in the"-" region. a. Build two different representations for $-2x$ using an Expression Mat. b. Similarly, build $3x-(-4)$. How many different ways can you build $3x-(-4)$?

Miguel is planning a trip to Turkey. Before he leaves, he wants to exchange his money to the Turkish lira, the official currency of Turkey. The exchange rate at the time of his trip is $2$ lira per $1$ U.S. dollar.

Write an equation for the inverse of the problem situation. Use the same variable representations, where $r$ represents the number of lira, and $d$ represents the number of U.S. dollars. Does this equation represent a function?

Find the length of the hypotenuse of each right triangle with the given leg lengths. Express the answer as a simplified radical. legs: 11 ft and 60 ft. legs: 7 mm and 8 mm. legs: 40 cm and 41 cm. legs: 20 in. and 99 in. legs: 16 ft and 23 ft

The Channel Tunnel is a tunnel that runs under the English Channel. It is cylindrical in shape. Write the volume to lateral area ratio as a simplified rational expression. Then find the ratio given that the tunnel has an inner diameter of 7.6 meters. (Hint: The lateral area of a cylinder is the same as the surface area minus the area of the bases.)

For the exercise, indicate "expression" if an expression is to be simplified or "equation" if an equation is to be solved. Then simplify the expression or solve the equation.

$$\dfrac{2 k^2-3 k}{20 k^2-5 k} \div \dfrac{2 k^2-5 k+3}{4 k^2+11 k-3}$$

An important derivative operation in many applications is called the Laplacian; in Cartesian coordinates, for z=f(x, y), the Laplacian is

$$z _ { x x } + z _ { y y }$$

. Determine the Laplacian in polar coordinates using the following steps. Use the Chain Rule to find

$$z _ { x x } = \frac { \partial } { \partial x } \left( z _ { x } \right)$$

. There should be two major terms, which, when expanded and simplified, result in five terms.

Use the Pythagorean Theorem and the square root property to solve this exercise. Express answers in simplified radical form. Then find a decimal approximation to the nearest tenth.

A supporting wire is to be attached to the top of a $70$ -foot antenna. If the wire must be anchored $70$ feet from the base of the antenna, what length of wire is required?

Jill is studying a strange bacteria. When she first looks at the bacteria, there are 1000 cells in her sample. The next day, it has doubled (there are 2000 cells). Intrigued, she comes back the next day to find that there are 4000 cells! Create multiple representations (table, graph, rule) of the function whose inputs are the days that have passed after she first began to study the sample and whose outputs are the number of cells of bacteria.

What is the simplified form of $\left(2 x^{2}+4 x-3\right)(3 x+1)$? A. $6 x^{3}+10 x^{2}-5 x+3$ B. $6 x^{3}+14 x^{2}+5 x-3$ C. $6 x^{3}+14 x^{2}-5 x-3$ D. $6 x^{3}-10 x^{2}-5 x-3$

Lucy wants to be a farmer,just like her dad. Her father says he will give her some cows to raise if she can build them a good pen. Lucy saves her money and buys 30 meters of fencing material. She will use it to build a rectangular pen against one wall of her family's barn, as shown in the picture at right. Lucy has come to you for help. She wants to build a pen for her cows that gives them the most possible area to roam. How long should each side of the fence be to give the cows as much roaming area as possible? How can you convince Lucy that the pen you suggest has the largest roaming area? Create a poster showing all four representations of this situation. On your poster, include a drawing of the pen with the largest possible area. State its dimensions (width and length) and its area. Use multiple representations to justify your conclusion that this is the largest pen.

Which of the following is a simplified form of the given expression? Assume the denominator is not $0$.

$$\left(\frac{15 n^5 m^3}{5 m^4 n^2}\right)^2$$

A. $\frac{3 n^6}{m^2}$

B. $\frac{9 n^6}{m^2}$

C. $\frac{9 n^5}{m^3}$

D. $9 m^2 n^2$