Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: $(0, 4), (0, 0)$; passes through the point $(\sqrt{5},-1)$

Find the 17th term of each sequence. $a_{18}=18, d=-4$

Express each probability as a fraction reduced to lowest terms. you are dealt one card from a standard 52-card deck. Find the probability of being dealt a club.

Graph the function. Compare the graph with the graph of f(x) = x. g(x) = x + 5

Solve the equation by completing the square. Round to the nearest tenth if necessary.

$$x^2 + 4x = 6$$

The correlation between the number of visitors to the state of Florida and the number of shark attacks since 1990 is 0.946. Should the number of visitors to Florida be reduced in an attempt to reduce shark attacks? Explain your reasoning.

Solve each equation. Check your solution.

$$z - 19 = 34$$

Both the forward reaction and the reverse reaction in the following equilibrium are believed to be elementary steps:

$$\mathrm { CO } ( g ) + \mathrm { Cl } _ { 2 } ( g ) \rightleftharpoons \operatorname { COCl } ( g ) + \mathrm { Cl } ( g )$$

At

$$25 ^ { \circ } \mathrm { C }$$

the rate constants for the forward and reverse reactions are

$$1.4 \times 10 ^ { - 28 } M ^ { - 1 } \mathrm { s } ^ { - 1 }$$

and

$$9.3 \times 10 ^ { 10 } \mathrm { M } ^ { - 1 } \mathrm { s } ^ { - 1 }$$

respectively. What is the value for the equilibrium constant at

$$25 ^ { \circ } \mathrm { C } ?$$

draw a scatter diagram

$$\begin{array}{ccccccc}{X} & {0} & {1.2} & {1.8} & {2.3} & {3.5} & {4.1} \\ \hline Y & {2} & {6.4} & {7} & {7.3} & {4.5} & {2.4} \\ \hline\end{array}$$

Find the value of k that would make the left side of each equation a perfect square trinomial. $25 x^{2}-k x+1=0$

Evaluate each determinant.

$$\left| \begin{array} { c c } { - 5 } & { - 1 } \\ { - 2 } & { - 7 } \end{array} \right|$$

Use Pascal’s Triangle to find the binomial coefficient. $_7C_2$

Use the Intermediate Value Theorem and Rolle’s Theorem to prove that the equation has exactly one real solution. 2x² + 7x - 1 = 0

Find the first five terms of each sequence described.

$$a _ { 1 } = 6 , a _ { n + 1 } = 3 a _ { n } - n$$