What is the value of x? Enter your answer in the box.

Mathematics

1 answer:

PIT_PIT [208]3 years ago

6 0

We will use the angle bisector theorem here for $\angle GEH$ . ED being the angle bisector.

Thus, from the diagram we will have:

$\frac{HD}{DG} =\frac{EH}{EG}$

We will now plug in the values given in the diagram.

$\frac{35}{x+4} =\frac{56}{44.8}$

$x+4=\frac{35\times 44.8}{56}$

$x+4=28$

$x=24$

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$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\to &\$4432.37\\
P=\textit{original amount deposited}\to &\$3000\\
r=rate\to r\%\to \frac{r}{100}\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &8
\end{cases}$

$\bf 4432.37=3000\left(1+\frac{r}{1}\right)^{1\cdot 8}\implies \cfrac{4432.37}{3000}=(1+r)^8
\\\\\\
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