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Questions in mathematics

📝 Answered - If $y$ varies directly as $x$, and $y$ is 48 when $x$ is 6, which expression can be used to find the value of $y$ when $x$ is 2? A. $y=\frac{48}{6}(2)$ B. $y=\frac{6}{48}(2)$ C. $y=\frac{?}{2}$ D. $y=\frac{2}{(48)(6)}$

📝 Answered - The length of a standard jewel case is 4 cm more than its width. The area of the rectangular top of the case is 320 cm. Find the length and width of the jewel case.

📝 Answered - The function [tex]$f(x)=\frac{1}{x+3}$[/tex] has a horizontal asymptote at A. [tex]$x=0$[/tex] B. [tex]$f(x)=0$[/tex] C. [tex]$f(x)=-3$[/tex] D. [tex]$f(x)=3$[/tex]

📝 Answered - What is the following quotient? [tex]\frac{3 \sqrt{8}}{4 \sqrt{6}}[/tex] A. [tex]\frac{12 \sqrt{2}-6 \sqrt{3}}{5}[/tex] B. [tex]\frac{3 \sqrt{6}-4 \sqrt{3}}{24}[/tex] C. [tex]\frac{\sqrt{3}}{12}[/tex] D. [tex]\frac{\sqrt{3}}{2}[/tex]

📝 Answered - Complete the work shown to find a possible solution of the equation. $\begin{array}{l} (x-5)^{\frac{1}{2}}+5=2 \\ (x-5)^{\frac{1}{2}}=-3 \\ {\left[(x-5)^{\frac{1}{2}}\right]^2=(-3)^2} \end{array}$ A possible solution of the equation is $\square$ .

📝 Answered - A coordinate grid has a line labeled 3y = 2x - 9 passing through points (0, -3) and (3, -1). Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations is 3y = 2x - 9. Which could be the other equation? A) 2y = x - 4.5 B) y = (2/3)x - 3 C) 6y = 6x - 27 D) y = (3/2)x - 4.5

📝 Answered - Express the following octal numbers into their equivalent decimal numbers: (i) 145 (ii) 6760 (iii) 455 (iv) 10.75

📝 Answered - Sum of three times a number and four times another number is 68. Subtracting two times the second number from four times the first number gives 10. What are the numbers?

📝 Answered - The population of a town grows at the rate of 20% every 5 years. In how many years will it double itself (approximately)? (a) 12 (b) 15 (c) 16 (d) 20

📝 Answered - On shifting the origin to the point \(\left(\frac{1}{2}, -\frac{1}{3}\right)\) and keeping the axes parallel, the new coordinates of the point \(\left(-\frac{1}{5}, \frac{1}{3}\right)\) will be: (1) \(\left(\frac{7}{10}, -\frac{2}{3}\right)\) (2) \(\left(-\frac{1}{10}, \frac{2}{3}\right)\) (3) \(\left(-\frac{7}{10}, \frac{2}{3}\right)\) (4) \(\left(-\frac{7}{10}, 0\right)\)