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Questions in mathematics

📝 Answered - Simplify the following expression: 2/(1+a) + 1/(a-1) + (3a)/(1-a^2) + a/(1+a^3)

📝 Answered - Simplify: [tex]\sqrt{\frac{25}{441}}[/tex] The prime factorization of 25 is $\square$ . The prime factorization of 441 is $\square$ The expression [tex]\sqrt{\frac{25}{441}}[/tex] in simplest form is $\square$

📝 Answered - The a value of a function in the form [tex]$f(x)=a x^2+b x+c$[/tex] is negative. Which statement must be true? A. The vertex is a maximum. B. The [tex]$y$[/tex]-intercept is negative. C. The [tex]$x$[/tex]-intercepts are negative. D. The axis of symmetry is to the left of zero.

📝 Answered - The system of equations shown is solved using the linear combination method [tex] \begin{array}{l} 6 x-5 y=-8 \quad \rightarrow \quad 6 x-5 y=-8 \quad \rightarrow \quad 6 x-5 y=-8 \ -24 x+20 y=32 \rightarrow \frac{1}{4}(-24 x+20 y=32) \rightarrow \frac{-6 x+5 y=8}{0=0} \end{array} [/tex] What does [tex]$0=0$[/tex] mean regarding the solution to the system? A. There are no solutions to the system because the equations represent parallel lines. B. There are no solutions to the system because the equations represent the same line. C. There are infinitely many solutions to the system because the equations represent parallel lines. D. There are infinitely many solutions to the system because the equations represent the same line.

📝 Answered - The height of a plant over time is shown in the table below. Using a logarithmic model, what is the approximate age of the plant when it is 19 inches tall? | t, time in months | h, height in inches | |---|---| | 1 | 18 | | 2 | 18.21 | | 3 | 18.33 | | 4 | 18.42 | | 5 | 18.48 | | 6 | 18.54 | A. 10 months B. 14 months C. 16 months D. 28 months

📝 Answered - Simplify: (a) $\frac{x^2}{y(x-y)}+\frac{y^2}{x(y-x)}$

📝 Answered - Find the domain of the following [tex]f(x)=\frac{x+5}{x^2+1 x+2}[/tex] A. [tex]x \neq-5[/tex] B. All real numbers C. [tex]x \neq 2,-1,-5[/tex] D. [tex]x \neq 2,-1[/tex]

📝 Answered - Subtract the rational expressions: [tex]$\frac{a+1}{2 a}+\frac{3}{a^2}$[/tex] A) [tex]$\frac{(a+3)(a-2)}{2 a^2}$[/tex] B) [tex]$\frac{(a+1)(a-1)}{2 a^2}$[/tex]

📝 Answered - 8. En una tarea de ciencias se te pide hacer un experimento, a fin de que detectes el comportamiento en el crecimiento de población de ácaros. Tomas una muestra de una caja de vidrio de laboratorio (petri), la cual contiene una población inicial de mil ácaros, proporcionas alimento y registras a diario el crecimiento de la población. El registro de los tres días, fue el siguiente: [tex] \begin{array}{l} 1 \text { día }=4000 \\ 2 \text { días }=7000 \\ 3 \text { días }=10000 \end{array} [/tex] De acuerdo con este comportamiento, ¿cuál es el modelo matemático que lo representa? A) [tex]$y=3000 x+1000$[/tex] B) [tex]$y=1000 x+3000$[/tex] C) [tex]$y=x^3+1000 x$[/tex] D) [tex]$y=3000^x$[/tex]

📝 Answered - Complete the table for the function [tex]y=\log _{\frac{1}{2}}(x)[/tex]. [tex] \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline$\frac{1}{4}$ & $\square$ \\ \hline$\frac{1}{2}$ & $\square$ \\ \hline 1 & $\square$ \\ \hline 2 & $\square$ \\ \hline 4 & $\square$ \\ \hline \end{tabular} [/tex] Graph the function [tex]y=\log _{\frac{3}{4}}(x)[/tex]. Plot two points with integer coordinates to graph the function.