3 years ago

Triangle ABC is congruent to triangle DFE. Find x

Mathematics

1 answer:

ale4655 [162]3 years ago

5 0

ΔABC ≡ ΔDFE

⇒ ∠DEF = ∠36°

<u>Solve x:</u>

3x - 6 = 36

3x = 42

x = 14

Answer: x = 14

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We use the identity sin (A - B) = sin A cos B - cos B sin A

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The sum of three consecutive even numbers is 558. What is the 1st number

Zanzabum

Answer:

The first number is 184

Step-by-step explanation:

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2 years ago

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2 years ago

Read 2 more answers

What is the T.A. = and V =

chubhunter [2.5K]

The formula of the area of the equilateral triangle:
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The formula of the area of the rectangle:
$A=width\times length=wl\\\\w=3;\ l=6\\\\A=3\cdot6=18$

$T.A.=2A_\Delta+3A\\\\T.A.=2\cdot\dfrac{9\sqrt3}{4}+3\cdot18=\dfrac{9\sqrt3}{2}+54=(54+4.5\sqrt3)\ in^2$
The formula of the volume of the triangular prism:
$V=A_\Delta\cdot l\\\\V=\dfrac{9\sqrt3}{4}\cdot6=\dfrac{9\sqrt3}{2}\cdot3=\dfrac{27\sqrt3}{2}=13.5\sqrt3\ in^3$

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2 years ago

find the value of an investment of $3500 for 3 years at an interest rate of 5.6% if the money is compounded weekly

sergeinik [125]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$3500\\
r=rate\to 5.6\%\to \frac{5.6}{100}\to &0.056\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{weekly, thus fifty two}
\end{array}\to &52\\
t=years\to &3
\end{cases}$

$\bf A=3500\left(1+\frac{0.056}{52}\right)^{52\cdot 3}\implies A=3500\left( \frac{6507}{6500} \right)^{156}
\\\\\\
A\approx 4139.9038869337$

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3 years ago