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Questions in mathematics

📝 Answered - What is the solution for $x$ in the equation? $\frac{1}{2}-x+\frac{3}{2}=x-4$ A. $x=\frac{1}{3}$ B. $x=3$ C. $x=-3$ D. $x=-\frac{1}{3}$

📝 Answered - Translate the following phrase into an algebraic expression. Please use the variable x. The difference between -3 and twice the number

📝 Answered - Find the inverse of each of the given functions. [tex]f(x)=4 x-12[/tex] [tex]h(x)=\frac{2 x-4}{3}[/tex] [tex]f^{-1}(x)=\square x+\square[/tex] [tex]h^{-1}(x)=\frac{3 x-12}{2}[/tex] [tex]h^{-1}(x)=\frac{3}{(2 x-4)}[/tex] [tex]h^{-1}(x)=\frac{3 x+4}{2}[/tex]

📝 Answered - Given [tex]log _3 2 \approx 0.631[/tex] and [tex]log _3 7 \approx 1.771[/tex], what is [tex]log _3 14[/tex]?

📝 Answered - Select the correct answer. Consider the following equation. $-\left(\frac{3}{2}\right)^x+12=2 x-3$ Approximate the solution to the equation above using three iterations of successive approximation. Use the graph below as a starting point. A. $x \approx \frac{33}{8}$ B. $x \approx \frac{71}{16}$ C. $x \approx \frac{69}{16}$ D. $x \approx \frac{35}{8}$

📝 Answered - Which composition of similarity transformations maps polygon [tex]ABCD[/tex] to polygon [tex]A^{\prime} B^{\prime} C^{\prime} D^{\prime}[/tex]? A. a dilation with a scale factor of [tex]\frac{1}{4}[/tex] and then a rotation B. a dilation with a scale factor of [tex]\frac{1}{4}[/tex] and then a translation C. a dilation with a scale factor of 4 and then a rotation D. a dilation with a scale factor of 4 and then a translation

📝 Answered - Which statements about the graph of the function $y=\left(\frac{1}{3}\right)^x$ are true? * The function is increasing. * The function is decreasing. * The $x$-intercept is $(1,0)$. * The $y$-intercept is $(0,1)$. * The range of the function is all real numbers.

📝 Answered - Simplify the following rational expression: [tex]\frac{3 g^3 h^3}{g-h} \div \frac{4 g h}{h-g}[/tex]

📝 Answered - If [tex]$\log 32=1.505$[/tex], then what is the value of [tex]$\log _{1000} 32$[/tex]? A. 0.502 B. 001505 C. .000502 D. 1,505

📝 Answered - In the year 2000, the population of Ohio was 11.03 million people. By the year 2017, the population of Ohio was 11.66 million people. Create an equation modeling the population, p, of Ohio given the year, t. Round to the nearest hundredth if necessary. A. [tex]$p =11.1 t +232.14$[/tex] B. [tex]$p =11.1 t -11.66$[/tex] C. [tex]$p =0.09 t +191.93$[/tex] D. [tex]$p =0.04 x -68.97$[/tex]