When $R$ is the set of all real numbers,$\{x \in R: \frac{\sqrt{12-x-x^2}}{x+10} \leq \frac{\sqrt{12-x-x^2}}{2x+9}\} = $

$A$ solution is to be kept between $40^{\circ} C$ and $45^{\circ} C$. What is the range of temperature in degree Fahrenheit,if the conversion formula is $F = \frac{9}{5} C + 32$?

If $\frac{x^{2}-1}{x^{2}+1} \geq 0,$ then $x \in$

In a manufacturing company,the cost and revenue functions of a product are given by $C(x) = 500 + \frac{5}{2}x$ and $R(x) = 3x$,where $x$ is the number of items produced and sold. How many items must be sold to realize no profit or loss? Is there any profit?

$A$ man wants to cut three lengths from a single piece of board of length $91 \, cm$. The second length is to be $3 \, cm$ longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least $5 \, cm$ longer than the second?

The longest side of a triangle is twice the shortest side and the third side is $2 \text{ cm}$ longer than the shortest side. If the perimeter of the triangle is more than $166 \text{ cm}$, then find the minimum length of the shortest side. (in $\text{ cm}$)