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Questions in mathematics

[Done] Simplify the following algebraic expression: $7(11 x-3) =$

[Done] Complete the steps in order to write the inverse of [tex]f(x)=[/tex] 1. $\square =x+5$ 2. $\square =y+5$ 3. $\square =y$ 4. $\square =x-5$

[Done] $(a x+4)(3 x+b)=18 x^2+c x+12$ If the equation is defined for all values of $x$, what is the value of $c$?

[Done] Which equation has the solutions [tex]$x=\frac{5 \pm 2 \sqrt{7}}{3}$[/tex]? [tex]$3 x^2-5 x+7=0$[/tex] [tex]$3 x^2-5 x-1=0$[/tex] [tex]$3 x^2-10 x+6=0$[/tex] [tex]$3 x^2-10 x-1=0$[/tex]

[Done] Make an estimate - what is the average fee to take money out of a non-network ATM?

[Done] What is the simplified form of this expression? $(8 x-7)+(-2 x-9)-(4 x-3)$

[Done] For [tex]f(x)=\left\lfloor\frac{95}{x}\right\rfloor[/tex], evaluate [tex]f(12)[/tex]. *This function uses greatest integer notation.

[Done] Is the solution shown below correct? Explain. $\begin{array}{l} 9 x+2=8 x^2+6 x \\ -8 x^2+3 x+2=0 \\ x=\frac{-3 \\pm \\sqrt{(3)^2-(4)(-8)(2)}}{-16} \\ x=\frac{-3 \\pm \\sqrt{9-(64)}}{-16} \\ x=\frac{3 \\pm \\sqrt{55 i}}{16} \end{array}$

[Done] Find the value of $c$ and $YZ$ if $Y$ is between $X$ and $Z$. $XY = 11, YZ = 4c, XZ = 83$ $c = $ $YZ = $

[Done] Review the proof of de Moivre's theorem (not in order). Which steps must be switched to put the proof in order? Proof of de Moivre's Theorem A = [cos (\theta)+i sin (\theta)]^k \cdot[cos (\theta)+i sin (\theta)]^1 B = cos (k \theta+\theta)+i sin (k \theta+\theta) C = cos (k \theta) cos (\theta)-sin (k \theta) sin (\theta)+i[sin (k \theta) cos (\theta)+ cos (k \theta) sin (\theta)] D = [cos (k \theta)+i sin (k \theta)] \cdot[cos (\theta)+i sin (\theta)] E = cos [(k+1) \theta]+i sin [(k+1) \theta] A. steps B and C B. steps B and D C. steps C and D D. steps C and E