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Questions in mathematics

[Answered] If [tex]$f(x)=a x^3+\frac{b}{x}+5$[/tex] has local minimum at [tex]$(2,-3)$[/tex], then what are the values of [tex]$a$[/tex] and [tex]$b$[/tex]?

[Answered] What is the probability of rolling a sum of 10 when rolling two number cubes? [tex]$\frac{1}{12}$[/tex] [tex]$\frac{1}{9}$[/tex] [tex]$\frac{1}{3}$[/tex] [tex]$\frac{5}{12}$[/tex]

[Answered] Which is equivalent to $64^{\frac{1}{4}}$ ? $2 \sqrt[4]{4}$ 4 16 $16 \sqrt[4]{4}$

[Answered] Evaluate the following. $\begin{array}{r} |-6|=\square \\ |9|=\square \end{array}$

[Answered] The vertex of this parabola is at $(1,3)$. Which of the following could be its equation? A. $y=3(x+1)^2-3$ B. $x=3(y-3)^2-1$ C. $y=3(x+1)^2+3$ D. $x=3(y-3)^2+1$

[Answered] Describe generators and relations for all dihedral groups [tex]$D_{2 n}$[/tex]. (Hint: Let [tex]$x$[/tex] be reflection about a line through the center of a regular n-gon and a vertex, and let [tex]$y$[/tex] be counterclockwise rotation by [tex]$2 \pi / n$[/tex]. The group [tex]$D_{2 n}$[/tex] will be generated by [tex]$x$[/tex] and [tex]$y$[/tex], subject to three relations. To see that these relations really determine [tex]$D_{2 n}$[/tex], use them to show that any product [tex]$x^{i_1} y^{i_2} x^{i_3} y^{i_4} \cdots$[/tex] equals [tex]$x^i y^j$[/tex] for some [tex]$i, j$[/tex] with [tex]$(0 \leq i \leq 1,0 \leq j\ \textless \ n)$[/tex].

[Answered] Consider the equation $\log _5(x+5)=x^2$. What are the approximate solutions of the equation? Check all that apply. A. $x \approx-0.93$ B. $x=0$ C. $x \approx 0.87$ D. $x \approx 1.06$

[Answered] $y \geq x^2+5$ What is the $x$-intercept? What is the $y$-intercept?

[Answered] 9. The 5th and 10th terms of an arithmetic sequence are 23 and 48 respectively. a) Write down the general term of the arithmetic sequence. b) Find the common difference and first term of the sequence. c) Is the 15th term of the sequence 74?

[Answered] Simplify the following complex fraction. [tex]$\frac{\frac{z+6}{z-4}}{\frac{z^2-36}{z^2-16}}$[/tex]