Point H is the circumcenter of triangle DEF.

Mathematics

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Which function increases at a faster rate on 0 to infinity, f(x) = x2 or g(x) = 2x? Explain your reasoning.

lawyer [12517]

Based on a table of values, the outputs of f(x) for whole numbers are 0, 1, 4, 9, 16, 25, 36, and further. Meanwhile, for the same inputs, g(x) generates outputs of 1, 2, 4, 8, 16, 32, and 64. It is evident that g(x) consistently doubles its outputs, leading to numbers that surpass those produced by f(x). The exponential function, g(x), experiences a constant multiplicative change rate, allowing it to accelerate more quickly compared to the quadratic function.

(ed. just click all of them)

9 0

2 months ago

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The savings account offering which of these APRs and compounding periods offers the best APY?

zzz [12365]

$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
~~~~~~~~~~~~\textit{4.0784\% compounded monthly}\\\\
~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0784\%\to \frac{4.0784}{100}\to &0.040784\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{monthly, thus twelve}
\end{array}\to &12
\end{cases}
\\\\\\
\left(1+\frac{0.040784}{12}\right)^{12}-1\\\\
-------------------------------\\\\
~~~~~~~~~~~~\textit{4.0798\% compounded semiannually}\\\\
$

$\bf ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0798\%\to \frac{4.0798}{100}\to &0.040798\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semi-annually, thus twice}
\end{array}\to &2
\end{cases}
\\\\\\
\left(1+\frac{0.040798}{2}\right)^{2}-1\\\\
-------------------------------\\\\
$

$\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\
~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0730\%\to \frac{4.0730}{100}\to &0.040730\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{daily, thus 365}
\end{array}\to &365
\end{cases}
\\\\\\
\left(1+\frac{0.040730}{365}\right)^{365}-1$

7 0

2 months ago

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A certain food has a gluten ratio of 13\,\text{mg}13mg13, start text, m, g, end text of gluten per \text{L}Lstart text, L, end t

tester [12383]

Answer:

The gluten content expressed in micrograms per milliliter is 13 µg/mL.

Step-by-step explanation:

Take into account the details given.

The gluten content of the product is specified as $13 \frac{mg}{L}$ .

We now need to convert the gluten content to micrograms per milliliter.

For conversion from mg to micrograms, refer to the following facts:

1 mg equals 1000 micrograms.

1 L corresponds to 1000 milliliters.

Next, replace 1 mg = 1000 micrograms and 1 L = 1000 milliliters into the ratio provided above.

$13( \frac{1000 \ micro-grams}{1000 \ milliliter} )= 13( \frac{micro-grams}{milliliter})$

Consequently, the gluten ratio in micrograms per milliliter is 13 µg/mL.

5 0

3 months ago

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Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2 and the profit

zzz [12365]

This question is quite lengthy, so I will offer a brief overview. To find your x-value, set y to 0 in the given equation.

2x + 3y = 1470

2x + 3(0) = 1470

2x = 1470

x = 735

Thus, your farthest point on the x-axis is (735,0).

Now, repeat for y.

2x + 3y = 1470.

2(0) + 3y = 1470

3y= 1470

y= 490

Your highest point thus is (0,490).

After plotting both points, connect them with a straight line to illustrate your graph.

Check

8 0

1 month ago

Translate to an algebraic expression n−1 increased by 110%

tester [12383]

Answer:

Part 1) The algebraic expression can be represented as $1.10(n-1)$ or $1.10n-1.10$