$5x + 7 - 2( - 8x - 1) = 7(x - 1) \\ 5x + 7 + 16x + 2 = 7x - 7 \\ collecting \: like \: \: terms \: \\ 5x + 16x - 7x = - 7 - 2 - 7 \\ 14x = - 16 \\ divide \: both \: side \: by \: 14 \\ \frac{14x}{14} = \frac{ - 16}{14} \\ x = - \frac{ 8}{7}$

8 0

3 years ago

The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio i

kati45 [8]

$\bf \begin{array}{ccll}
n&term&value\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
2&a_2&20\\
3&a_3&20r\\
4&a_4&20rr\\
&&20r^2\\\\
&&\frac{45}{4}
\end{array}\implies \stackrel{4^{th}~term}{20r^2=\cfrac{45}{4}}\implies r^2=\cfrac{45}{80}
\\\\\\
r^2=\stackrel{simplified}{\cfrac{9}{16}}\implies r=\sqrt{\cfrac{9}{16}}\implies r=\cfrac{\sqrt{9}}{\sqrt{16}}\implies r=\cfrac{3}{4}$

4 0

3 years ago