Questions in mathematics

Questions in mathematics

📝 Answered - Prove that the arithmetic sequence with first term [tex]\( \frac{1}{2} \)[/tex] and common difference [tex]\( \frac{1}{4} \)[/tex] contains all natural numbers.

📝 Answered - What are the $x$- and $y$-coordinates of point P on the directed line segment from $A$ to $B$ such that $P$ is $\frac{2}{3}$ the length of the line segment from $A$ to $B$? $x=\left(\frac{m}{m+n}\right)\left(x_2-x_1\right)+x_1$ $y=\left(\frac{m}{m+n}\right)\left(y_2-y_1\right)+y_1$ A. (2,-1) B. (4,-3) C. (-1,2) D. (3,-2)

📝 Answered - Louis plans to buy a new washing machine. The washing machine costs $560 and has an estimated annual operating cost of $48. Which rational function models the average annual cost in dollars of owning the washing machine for $x$ years? A. [tex]f(x)=\frac{560+48}{x}[/tex] B. [tex]f(x)=\frac{560 x+48 x}{x}[/tex] C. [tex]f(x)=\frac{560 x+48}{x}[/tex] D. [tex]f(x)=\frac{560+48 x}{x}[/tex]

📝 Answered - Add or subtract the fractions, then simplify the answer if needed. You can leave your answer as an improper fraction where needed. 1) [tex]$\frac{5}{4}+\frac{3}{4}=\frac{8}{4}$[/tex] 2) [tex]$\frac{9}{3}-\frac{5}{3}=\frac{4}{3}$[/tex] 3) [tex]$\frac{23}{6}-\frac{7}{6}=[/tex] 4) [tex]$\frac{9}{8}+\frac{12}{8}=[/tex] 5) [tex]$\frac{16}{9}+\frac{8}{9}=[/tex] 6) [tex]$\frac{23}{10}-\frac{11}{10}=[/tex] 7) [tex]$\frac{20}{7}-\frac{5}{7}=[/tex] 8) [tex]$\frac{19}{12}+\frac{5}{12}=[/tex] 9) [tex]$\frac{22}{15}-\frac{17}{15}=[/tex] 10) [tex]$\frac{15}{13}+\frac{8}{13}=[/tex] 11) [tex]$\frac{13}{11}+\frac{14}{11}=[/tex] 12) [tex]$\frac{21}{8}-\frac{7}{8}=[/tex] 13) [tex]$\frac{9}{14}+\frac{15}{14}=[/tex] 14) [tex]$\frac{31}{8}-\frac{11}{8}=[/tex] 15) [tex]$\frac{23}{4}-\frac{11}{4}=[/tex] 16) [tex]$\frac{17}{5}+\frac{9}{5}=[/tex] 17) [tex]$\frac{11}{6}+\frac{13}{6}=[/tex] 18) [tex]$\frac{23}{10}-\frac{7}{10}=[/tex]

📝 Answered - What number could be placed in the blank to make the following a perfect-square trinomial? _x

📝 Answered - [tex]$\begin{array}{l}5 x+3 y=9 \ 7 x-4 y=14\end{array}$[/tex]

📝 Answered - Divide. $0.3 \div 0.06=$

📝 Answered - Find the product $\frac{3}{20} \times \frac{4}{12}$ Enter your simplified answer.

📝 Answered - $0.05 \times \quad=0.5

📝 Answered - Solve the following exponential equation without using logarithms. [tex]4^{9 x-7}=256[/tex] The solution is [tex]x=[/tex] $\square$ . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)