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4 years ago

The endpoints of DE are D(-4,11) and E(-4,-13). The endpoints of GH are G(-14,5) and H(-9,5). Are DE and GH congruent? Explain.

Mathematics

1 answer:

Iteru [2.4K]4 years ago

8 0

DE and GH are perpendicular to each other so they cant be congruent lines

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Phil is standing x+5 feet from the base of a building. The height of the building is 6x−1 feet. Find the function that the strai

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Answer:

$f(x)=\sqrt{37x^{2}-2x+26}$

Step-by-step explanation:

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Applying the Pythagoras Theorem

see the attached figure to better understand the problem

$PT^{2}=(6x-1)^{2}+(x+5)^{2}$

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4 years ago

Every two years, a manufacturer's total yearly sales decline 20%. She sells 400 total units in her first year. Rounded to the ne

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$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1 - r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
p=period
\end{cases}$

we know, the first year she sold 400 units, thus year 0, 400 units, t = 0, A = 400.

$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1 - r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &400\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &0\\
p=period
\end{cases}
\\\\\\
400=I(1-r)^{\frac{0}{p}}\implies 400=I\cdot 1\implies 400=I$

therefore then

$\bf \textit{Periodic Exponential Decay}\\\\
A=I(1 - r)^{\frac{t}{p}}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &400\\
r=rate\to 20\%\to \frac{20}{100}\to &0.20\\
t=\textit{elapsed time}\\
p=period\to &2
\end{cases}
\\\\\\
A=400(1-0.2)^{\frac{t}{2}}$

now, how many units will it had decreased by the 9th year? t = 9

$\bf A=400(1-0.2)^{\frac{9}{2}}$

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