Graph each linear system, either by hand or using a graphing device. Use the graph to determine whether the system has one solution, no solution, or infinitely many solutions. If there is exactly one solution, use the graph to find it.

$$\left\{\begin{aligned} 2 x + 6 y & = 0 \\ - 3 x - 9 y & = 18 \end{aligned} \right.$$

What fraction is half of 1/4?

Find a parametrization for the curve. the lower half of the parabola x - 1 = y2

Show that the range of the cotangent function is the set of all real numbers.

Graph the function. Describe the domain and range. $y=\frac{1}{x-3}$

Find the inverse of the function. Then graph the function and its inverse on one coordinate system. Show the line of symmetry on the graph.

$$f ( x ) = x ^ { 3 }$$

According to a 2011 poll, 55% of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that the existing American population experiences this consequence. a. Let $x$ represent a binomial random variable that represents the proportion of Americans in a sample of 17 chosen at random who are unaware that GOP stands for Grand Old Party. What other possible values may $x$ have? b. Determine the likelihood that, out of a random sample of 17 Americans, exactly 8 are unaware that GOP stands for Grand Old Party. Use the formula for the binomial probability distribution.

A 3-kg blob of putty moving at $10 \mathrm{~m} / \mathrm{s}$ hits a $2-\mathrm{kg}$ blob of putty at rest. Calculate the speed of the stuck-together blobs of putty immediately after the collision.

Give an example of a system of linear equations that can be solved by first adding the equations to eliminate one variable.

What is the second person singular present tense negative subjunctive form of the verb 'añadir' ?

Use substitution to solve each system of equations. If the system does not have exactly one solution, state whether it has no solutions or infinitely many solutions.

$$x+6 y=1$$

$$3 x-10 y=31$$

Graph the system and determine the number of solutions that it has. If it has one solution, name it. x + 2y = 6, 3x + 6y = 8

The following function gives the amount of a substance present at time $t$. Give the amount present initially (at $t=0$ ), state whether the function represents exponential growth or decay, and give the percent growth or decay rate.

$$A=100(1.07)^t$$

The grinding wheel has a mass of 250 kg and a moment of inertia of 500 kg. m^2. A torque of 100 N. m is applied to the grinding wheel. If the wheel starts from rest, what is the angular momentum of the wheel after 5.0 seconds?