Find the slope of the line described by each equation. y+2=7x

Use a graphing utility to graph the polar equation. Find an interval for $\theta$ for which the graph is traced only once. $r=2(1-2 \sin \theta)$

Write the corollary as a conditional statement and its converse. Then explain why each statement is true. Rhombus Corollary.

The voltage across a $12-\Omega$ resistor is given by $v(t) = 24\cos(2\pi t) \ V$. Calculate the energy delivered to the resistor between t = 0 and t = 2 s. The argument of the cosine function, $2\pi t$, is in radians.

(a) For ${r = 21}$, plot ${x}$ versus ${t}$ for the solutions starting at the initial points ${(3, 8, 0)}$, ${(5, 5, 5)}$, and ${(5, 5, 10)}$. Use a ${t}$ interval of at least ${0 \leq t \leq 30}$. (b) Repeat the calculation in part (a) for ${r = 22}$, ${r = 23}$, and ${r = 21}$. Increase the ${t}$ interval as necessary so that you can determine when each solution begins to converge to one of the critical points. Record the approximate duration of the chaotic transient in each case. Describe how this quantity depends on the value of ${r}$. (c) Repeat the calculations in parts (a) and (b) for values of ${r}$ slightly greater than ${24}$. Try to estimate the value of ${r}$ for which the duration of the chaotic transient approaches infinity.

Write the given expression as an algebraic expression in x.

$$\sin \left( 2 \tan ^ { -1 } x \right)$$

Use order of operations to simplify.

$$5 \times 4 - [ 3 \times ( 2 - 1 ) ]$$

In order to gauge the effectiveness of the OHaganBooks.com site, you recently commissioned a survey of online shoppers. According to the results, 2% of online shoppers visited OHaganBooks.com during a one-week period, while 5% of them visited at least one of OHaganBooks.com’s two main competitors: JungleBooks.com and FarmerBooks.com. Use this information to answer. Assuming that visiting OHaganBooks.com was independent of visiting a competitor, what percentage of online shoppers visited either OHaganBooks.com or a competitor?

Central Park is a rectangular shaped park in the middle of New York City. The area of the park is 3.41 km2. How many acres is the park to the nearest acre? (Note: 1 km2 = 247 acres) Use a unit multiplier and show your work.

When a 3.0-kg block is pushed against a massless spring of force constant 4.5 × 10³ N/m, the spring is compressed 8.0 cm. The block is released, and it slides 2.0 m (from the point at which it is released) across a horizontal surface before friction stops it. What is the coefficient of kinetic friction between the block and the surface?

Find an equation of each circle described. center (0, 0) and radius 8

Say whether the given distribution can be a relative frequency distribution. If your answer is no, indicate why not.

$$\begin{matrix} \text{Outcome} & \text{HH} & \text{HT} & \text{TH} & \text{TT}\\ \text{Rel. Frequency} & \text{.5} & \text{.4} & \text{.5} & \text{-.4}\\ \end{matrix}$$

Tell whether each situation is possible or impossible. If possible, draw a sketch of the graphs. If impossible, explain. Two different lines have the same slope.

Find the value of k that would make the left side of each equation a perfect square trinomial. $36 x^{2}-k x+1=0$