If BD = 7x - 10, BC = 4x – 29, and CD = 5x – 9, find each value.

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10-09-2019
Mathematics

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If BD = 7x - 10, BC = 4x – 29, and CD = 5x – 9, find each value.

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jdoe0001 jdoe0001 · Answer 1 · 2019-09-10T02:01:41+02:00

[tex]\bf \underset{\leftarrow \qquad \textit{\large 7x-10}\qquad \to }{\stackrel{4x-29}{\boxed{B}\rule[0.35em]{10em}{0.25pt}} C\stackrel{5x-9}{\rule[0.35em]{17em}{0.25pt}\boxed{D}}} \\\\\\ BD=BC+CD\implies 7x-10=(4x-29)+(5x-9) \\\\\\ 7x-10=9x-38\implies 7x+28=9x\implies 28=2x \\\\\\ \cfrac{28}{2}=x\implies 14=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{BC}{4(14)-29\implies 27}~\hfill \stackrel{CD}{5(14)-9\implies 61}~\hfill \stackrel{BD}{7(14)-10\implies 88}[/tex]