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3 years ago

X = a.) 82 b.) 98 c.) 262

Mathematics

1 answer:

Katarina [22]3 years ago

5 0

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

There is a cyclic quadrilateral .

As we know that Sum of opposite angles of a cyclic quadrilateral is supplementary.

So, it becomes,

$98^\circ+x=180^\circ\\\\x=180^\circ-98^\circ\\\\x=82^\circ$

Hence, the value of x is 82°.

Therefore, Option 'a' is correct.

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Using an exponential function, it is found that the Tequesta settlement is 1845 years old.

<h3>What is an exponential function?</h3>

The exponential equation for a decaying amount of a substance is given by:

$A(t) = A(0)e^{-rt}$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.

$A(t) = A(0)e^{-rt}$

$0.5A(0) = A(0)e^{-5730r}$

$e^{-5730r} = 0.5$

$\ln{e^{-5730r}} = \ln{0.5}$

$5730r = -\ln{0.5}$

$r = -\frac{\ln{0.5}}{5730}$

$r = 0.00012096809$

Hence, the equation is:

$A(t) = A(0)e^{-0.00012096809t}$

The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).

$A(t) = A(0)e^{-0.00012096809t}$

$0.8A(0) = A(0)e^{-0.00012096809t}$

$e^{-0.00012096809t} = 0.8$

$\ln{e^{-0.00012096809t}} = \ln{0.8}$

$-0.00012096809t = \ln{0.8}$

$t = -\frac{\ln{0.8}}{0.00012096809}$

$t = 1845$

The Tequesta settlement is 1845 years old.

You can learn more about exponential functions at brainly.com/question/25537936

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1 year ago

Which number makes the equation true?

MrRa [10]

Answer:

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2 years ago

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How do I find the measure of these two supplementary angles using algebra?

nikdorinn [45]

Answer:

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Step-by-step explanation:

The two angles add to 180 degrees since they form a straight line

2x+10 +3x+20 =180

5x+30 = 180

Subtract 30 from each side

5x+30-30 =180-30

5x = 150

Divide by 5

5x/5 =180/5

x = 30

The left angle is 2x+10 = 2*30+10 = 60+10 =70

The right angle is 3x+20 = 3*30 +20 = 90+20 = 110

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Step-by-step explanation:

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