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kenny6666 [7]
2 years ago
9

Carbon-14 has a half-life of approximately 5,730 years. This exponential decay can be modeled with the function N(t) = N0.

Mathematics
1 answer:
kvasek [131]2 years ago
4 0

\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200\\ t=\textit{elapsed time}\dotfill &14325\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A=200\left( \frac{1}{2} \right)^{\frac{14325}{5730}}\implies A=200\left( \frac{1}{2} \right)^{\frac{5}{2}}\implies A\approx 35.36

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50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle
aalyn [17]

Answer:

EF=4\sqrt{3}

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

A_{\text{rect}}=8(6)=48\text{ cm}^2

The area of the triangle is 1/4 of this. Therefore:

\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

\displaystyle 12=\frac{1}{2}(DE)(DF)

Since DE = DF:

24=DF^2

Thus:

DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

(DE)^2+(DF)^2=(EF)^2

Therefore:

(2\sqrt6)^2+(2\sqrt6)^2=EF^2

Square:

24+24=EF^2

Add:

EF^2=48

And finally, we can take the square root of both sides:

EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}

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ryzh [129]

Answer

so there are 7 singing acts and 5 comedy acts.

Step-by-step explanation:

Let x= number of singing acts.

Let y= number of comedy acts.

We will take x+y=12 as our first equation, as there are 12 shows in total. We will take 5x+3y=50 as our second equation as there are 50 total minutes, and singing acts are 5 mins and comedy acts are 3 mins.

We solve x+y=12

Y=-x+12

We know y=-x+12, so we will substitute that for the y in the second equation.

1. Substitute 5x+3(-x+12)=50

2. Distribute 5x-3x+36=50

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Now that we have found x, we will find y by substitute the x in 5x+3y=50 with the value, 7, that we found for x.

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malfutka [58]
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Answer:

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2) quadrilaterals

3) parallelograms

4) rectangles.

mark brainliest  :)

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