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3 years ago

ΔABC ~ ΔDEC. ∠1 and ∠2 have the same measure. Find DC and DE. (Hint: Let DC=x and AC=x+3. Use the figure shown.)

Mathematics

1 answer:

Sveta_85 [38]3 years ago

8 0

DC/AC=EC/BC
x/(x+3)=10/16
10(x+3)=16x
10x+30=16x
30=6x
x=5
DC=x=5
DC=5 units long

10/16=DE/AB, DE=y

10/16=y/10
16*y=10*10
y=6.25≈6.3
DE≈6.3

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$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
~~
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$16010.32\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semi-annually, thus twice}
\end{array}\to &2\\
t=years\to &9
\end{cases}
\\\\\\
A=16010.32\left(1+\frac{0.05}{2}\right)^{2\cdot 9}\implies A=16010.32(1.025)^{18}
\\\\\\
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3 years ago

ΔABC ​~ ΔDEC. ∠1 and ∠2 have the same measure. Find DC and DE.​ (Hint: Let DC=x and AC=x+3. Use the figure shown.)

ΔABC ~ ΔDEC. ∠1 and ∠2 have the same measure. Find DC and DE. (Hint: Let DC=x and AC=x+3. Use the figure shown.)