Basic Maths: Test 8

$\displaystyle \begin{array}{l}Let\,\,\,?\,=p\\8\sqrt{p}\div 14\times 3+9=29\\\frac{24\sqrt{p}}{14}+9=29\\\frac{24\sqrt{p}}{14}=20\\24\sqrt{p}=280\\p=1225/9=136.11\end{array}$

$\displaystyle \begin{array}{l}\sqrt{p}+{{\left( 14 \right)}^{2}}\times 18\div 6-1029=-83\times \left( 12-7 \right)\\\sqrt{p}+196\times 3-1029=-83\times 5\\\sqrt{p}+588-1029=-415\\\sqrt{p}=1029-415-588\\\sqrt{p}=26\\\therefore \,\,p=676\end{array}$

$\displaystyle \begin{array}{l}{{\left( 83 \right)}^{27.3}}\div {{\left( 83 \right)}^{14}}\times {{\left( 83 \right)}^{46.8}}={{\left( 83 \right)}^{31.9+p}}\\\Rightarrow {{\left( 83 \right)}^{27.3-14+46.8}}={{\left( 83 \right)}^{31.9+p}}\\\Rightarrow {{\left( 83 \right)}^{60.1}}={{\left( 83 \right)}^{31.9+p}}\\\Rightarrow p+31.9=60.1\\\Rightarrow p=60.1-31.9=28.2\end{array}$

$\displaystyle \begin{array}{l}\frac{586\times 40}{100}=341.2-p\\\Rightarrow \text{234}\text{.4}=341.2-p\\\Rightarrow p=341.2-234.4=106.8\end{array}$

$\displaystyle p=\frac{504.14}{14\times 13}=2.77$