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A quadrilateral ABCD is inscribed in a circle such that AB is a diameter and $\angle\text{ADC}=130^\circ.$ Find $\angle\text{BAC}.$
→In the given figure, if $\text{AB }||\text{ DE}$ and $\text{BD }||\text{ FG}$ such that $\angle\text{FGH}=125^\circ$ and $\angle\text{B}=55^\circ,$ find $x$ and $y.$
→Draw the graph of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes: $3x + 2y + 6 = 0$
→Find the values of $n$ and $\overline{\text{X}}$ in the following case:$\sum\limits^\text{n}_{\text{i}=1}(\text{x}_\text{i}-12)=-10$ and $\sum\limits^\text{n}_{\text{i}=1}(\text{x}_\text{i}-3)=62$
→For any positive real number $x$, find the value of $\Big(\frac{\text{x}^{\text{a}}}{\text{x}^{\text{b}}}\Big)^{\text{a}+\text{b}}\times\Big(\frac{\text{x}^{\text{b}}}{\text{x}^{\text{c}}}\Big)^{\text{b}+\text{c}}\times\Big(\frac{\text{x}^{\text{c}}}{\text{x}^{\text{a}}}\Big)^{\text{c}+\text{a}}$
→Prove that the bisectors of two adjacent supplementary angles include a right angle.
A patient in a hospital is given soup daily in a cylindrical bowl of diameter $7\ cm$. If the bowl is filled with soup to a height of $4\ cm$, how much soup the hospital has to prepare daily to serve $250$ patients?
→ Factorize the following polynomials: $x^3 + 13x^2 + 31x - 45$ given that $x + 9$ is a factor.
→Simplify the following expressions: $(x^2 - x + 1)^2 - (x^2 + x + 1)^2$
→$ABCD$ is quadrilateral such that $AB = AD$ and $CB = CD.$ Prove that $AC$ is the perpendicular bisector of $BD.$
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