Questions in mathematics

Questions in mathematics

📝 Answered - Simplify the expression. $512^{-\frac{5}{3}}$ Simplify $512^{-\frac{5}{3}}$ completely. Choose the correct answer below. A. $\sqrt[3]{512^{-5}}$ B. -32768 C. $\frac{1}{(\sqrt[3]{512})^5}$ D. $\frac{1}{32768}$

📝 Answered - Graph this line using the slope and y-intercept: y - 4 = 5(x + 2)

📝 Answered - $4 x^2-8 x+3 \leqslant 0$

📝 Answered - Which of the following is the graph of [tex]f(x)=-0.5|x+3|-2[/tex]?

📝 Answered - Enter the correct answer in the box. The function [tex]$f(x)=2^x-1$[/tex] is transformed to function [tex]$g$[/tex] through a horizontal shift of 7 units left. What is the equation of function [tex]$g$[/tex]? Replace the values of [tex]$h$[/tex] and [tex]$k$[/tex] in the equation. [tex]$g(x)=2^{x+h}+k$[/tex]

📝 Answered - Which equation represents a line that is parallel to the line that passes through the points $(-6,9)$ and $(7,-17)$? A. $y=2 x+13$ B. $y=-2 x+13$ C. $y=\frac{1}{2} x+13$ D. $y=-\frac{1}{2} x+13

📝 Answered - What are the solution(s) of $-\frac{1}{2} x+4=x+1$?

📝 Answered - Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. [tex] \log _2 60 [/tex] [tex]\log _2 60=[/tex] (Simplify your answer. Do not round until the final answer. Then round to four decimal places as needed.)

📝 Answered - Study the pattern produced by division of numbers ending with 1 by 9. $\frac{1}{9}=0.1111111111 \ldots$ $\frac{11}{9}=1.2222222222 \ldots$ $\frac{21}{9}=2.3333333333 \ldots$ $\frac{31}{9}=3.4444444444 \ldots$ $\frac{101}{9}=11.222222222 \ldots$ What is the answer to $\frac{100001}{9}$?

📝 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])