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grin007 [14]
3 years ago
6

Which reason justifies Statement 5?

Mathematics
2 answers:
zloy xaker [14]3 years ago
6 0

Answer:

The answer is A. Substitution

Step-by-step explanation:

Looking at the previous proofs, you can see that:

∠Y≅∠4

∠Z≅∠6

∠X + ∠4 + ∠6 = 180°

Statement 5 then replaces ∠4 and ∠6 with ∠Y and ∠Z, respectively. Replacing it means that it was substituted with the GIVEN values by the previous statements.

The best answer is the Substitution.  

ser-zykov [4K]3 years ago
6 0

Answer:

My other answer was deleted, but yes, it should be A, substitution.

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he radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost
elena-s [515]

Answer:

The bones were 12,485 years old at the time they were​ discovered.

Step-by-step explanation:

Amount of the element:

The amount of the element after t years is given by the following equation, considering the decay rate proportional to the amount present:

A(t) = A(0)e^{-kt}

In which A(0) is the initial amount and k is the decay rate, as a decimal.

The radioactive element​ carbon-14 has a​ half-life of 5750 years.

This means that A(5750) = 0.5A(0), and we use this to find k. So

A(t) = A(0)e^{-kt}

0.5A(0) = A(0)e^{-5750k}

e^{-5750k} = 0.5

\ln{e^{-5750k}} = \ln{0.5}

-5750k = \ln{0.5}

k = -\frac{\ln{0.5}}{5750}

k = 0.00012054733

So

A(t) = A(0)e^{-0.00012054733t}

A scientist determined that the bones from a mastodon had lost 77.8 ​% of their​ carbon-14. How old were the bones at the time they were​ discovered?

Had 100 - 77.8 = 22.2% remaining, so this is t for which:

A(t) = 0.222A(0)

Then

0.222A(0) = A(0)e^{-0.00012054733t}

e^{-0.00012054733t} = 0.222

\ln{e^{-0.00012054733t}} = \ln{0.222}

-0.00012054733t = \ln{0.222}

t = -\frac{\ln{0.222}}{0.00012054733}

t = 12485

The bones were 12,485 years old at the time they were​ discovered.

8 0
3 years ago
PLZ HELP, GIVING BRAINLIEST!
mote1985 [20]

Answer:

  d)  (-3/2, -1/2)

Step-by-step explanation:

The midpoint (M) between two given points is the average of their coordinate values:

  M = (A + B)/2 = ((-8, 1) +(5, -2))/2 = (-3, -1)/2

  M = (-3/2, -1/2) . . . . . matches choice D

4 0
3 years ago
What is 9c-c equal when u combined like terms
vodka [1.7K]

What is 9c-c equal when u combined like terms?

8c

4 0
3 years ago
Over the next week you want to watch a movie a day. In how many ways can this be done if you have 8 movies
Leto [7]
<span>You can select from any of the 8 on the first day, leaving 7 to choose from on the second day, leaving 6 for the third. So, 8 x 7 x 6 x 5 x 4 x 3 x 2 or 8! That's 8factorial, so multiply those out or use a calculator to get 8! and that is your answer.</span>
7 0
3 years ago
Read 2 more answers
Can someone please teach me how to to this<br> Item: $30 Discount: 15%
seraphim [82]

Answer:

$25.5

Step-by-step explanation:

Sure, so the total of the

Item:

30 Dollars ($)

and the discount price is

15 percent (%)

So 30 times 0.15 because 30 is the price in total and 0.15 is the percentage but in a decimal form.

30 times 0.15 equals 4.5

4.5 is the amount that 15 % equals.

30 minus (-) 4.5 because once again the total is 30 and since we have a discount price then we minus (-) the discount price by the total and you get

A total with the discount price as 25.5 Dollars or $25.5

Hope this helps ;)

5 0
2 years ago
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