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Questions in mathematics

[Done] \begin{tabular}{|cc|c|} \hline & \\ \hline 6. & $\frac{2}{3}(6 k-30)+k=100$ & \\ & & \\ \hline \end{tabular}

[Done] -7-7(-x-1)=6-(-2x-3)

[Done] Solve: [tex]$\frac{x^2-x-6}{x^2}=\frac{x-6}{2 x}+\frac{2 x+12}{x}$[/tex] After multiplying each side of the equation by the LCD and simplifying, the resulting equation is [tex]$3 x^2+20 x+12=0$[/tex]. What are the solutions to the equation? A. [tex]$x=-6$[/tex] and [tex]$x=-\frac{2}{3}$[/tex] B. [tex]$x=-6$[/tex] and [tex]$x=\frac{2}{3}$[/tex] C. [tex]$x=6$[/tex] and [tex]$x=\frac{2}{3}$[/tex]

[Done] Solve for all values of $a$ in simplest form. $|-3 a+5|=9$

[Done] c.) The ruins also contain a math room (for math purposes) at a location that is the same distance away from the exit (-2,8) and the library (-8,1) Where is the math room located?

[Done] Rewrite the expression using only positive integer exponents. $\left(m^{\frac{2}{3}} n^{-\frac{1}{3}}\right)^6$ A. $\frac{m^9}{n^{18}}$ B. $\frac{n^{18}}{m^5}$ C. $\frac{m^4}{n^2}$ D. $\frac{n^2}{m^4}$

[Done] Part A: Complete the square to rewrite the following equation in standard form. Show all necessary work. [tex]$x^2+2 x+y^2+4 y=20$[/tex] Part B: What are the center and radius of the circle?

[Done] $6 \longdiv { 6 4 6 }$

[Done] Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which equation relates the total amount of gasoline in the tank, [tex]$y$[/tex], to the number of gallons that she put in the tank, [tex]$x$[/tex]? [tex]$y=4+x$[/tex] [tex]$y=x-4$[/tex] [tex]$y=4 \cdot x$[/tex] [tex]$y=x+4$[/tex]

[Done] For $y=-25+x^2$, determine the vertex, axis of symmetry, domain, and range. Vertex $\square$ Axis of Symmetry $\square$ Domain $\square$ Range $\square$