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2 years ago

Find the exact solution of the following quadratic equation by using the Quadratic Formula. x^2-9x=36

Mathematics

1 answer:

natita [175]2 years ago

4 0

Answer:

x = 12 or x = -3

Step-by-step explanation:

Solve for x over the real numbers:

x^2 - 9 x = 36

Subtract 36 from both sides:

x^2 - 9 x - 36 = 0

x = (9 ± sqrt((-9)^2 - 4 (-36)))/2 = (9 ± sqrt(81 + 144))/2 = (9 ± sqrt(225))/2:

x = (9 + sqrt(225))/2 or x = (9 - sqrt(225))/2

sqrt(225) = sqrt(9×25) = sqrt(3^2×5^2) = 3×5 = 15:

x = (9 + 15)/2 or x = (9 - 15)/2

(9 + 15)/2 = 24/2 = 12:

x = 12 or x = (9 - 15)/2

(9 - 15)/2 = -6/2 = -3:

Answer: x = 12 or x = -3

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2 years ago

The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had los

Gnesinka [82]

The bones at the time they were discovered when the radioactive element carbon-14 has a half-life of total 5750 years are 10062.5-year-old.

<h3>What is half-lives?</h3>

Half lives is the time interval which is need to decay the atomic nuclei of a radioactive sample.

There is a scientist who determined that the bones from a mastodon had lost 70.3% of their carbon-14. Thus, the fraction remaining is,

f=1-(70.3/100)=1-0.703

f=1-(70.3/100)=0.297

Now the fraction remaining can be given as,

f=(1/2)ⁿ

Here, n is the half life elapsed. Put the value of fraction remaining.

0.297=(1/2)ⁿ

n=1.75

The radioactive element carbon-14 has a half-life of total 5750 years. Thus,

Years=1.75*5750

Years=10062.5

Thus, the bones at the time they were discovered when the radioactive element carbon-14 has a half-life of total 5750 years are 10062.5-year-old.

Learn more about the half lives here;

brainly.com/question/2320811

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1 year ago

If 9 out of 10 doctors in a small city recommend afternoon naps, and there are 8 doctors in the city who don’t recommend naps, h

Hitman42 [59]

Answer:

Step-by-step explanation:

1 out of 10 do not recommend naps, so 9 times as many do recommend naps.

9 × (8 doctors) = 72 doctors . . . . . recommend naps

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