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2 years ago

Using the quadratic formula, what are the solutions to x2 – 3x = -2?

Mathematics

2 answers:

Kryger [21]2 years ago

6 0

Step-by-step explanation:

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Mazyrski [523]2 years ago

6 0

Answer:

$x=1,\: x=2$

Step-by-step explanation:

To be honest, you don't need the quadratic formula as you can just factor the polynomial after setting it equal to 0:

$x^2-3x=-2\\\\x^2-3x+2=0\\\\(x-1)(x-2)=0\\\\x=1,\: x=2$

If you really need to use the quadratic formula, here's the process:

$ax^2+bx+c=0\\\\x^2-3x+2=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(2)}}{2(1)}\\\\x=\frac{3\pm\sqrt{9-8}}{2}\\\\x=\frac{3\pm\sqrt{1}}{2}\\\\x=\frac{3\pm1}{2}\\x_1=\frac{3-1}{2}\\ \\x_1=\frac{2}{2}\\\\x_1=1\\\\x_2=\frac{3+1}{2}\\\\x_2=\frac{4}{2}\\ \\x_2=2$

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A tattoo enthusiast website claims that :

KATRIN_1 [288]

Answer:

The probability that a person is a Millennial given that they have tattoos is 0.5069 (50.69%) or about 0.51 (51%).

Step-by-step explanation:

We have here a case where we need to use Bayes' Theorem and all conditional probabilities related. Roughly speaking, a conditional probability is a kind of probability where an event determines the occurrence of another event. Mathematically:

$\\ P(A|B) = \frac{P(A \cap B)}{P(B)}$

In the case of the Bayes' Theorem, we have also a conditional probability where one event is the sum of different probabilities.

We have a series of different probabilities that we have to distinguish one from the others:

The probability that a person has a tattoo assuming that is a Millennial is:

$\\ P(T|M) = 0.47$

The probability that a person has a tattoo assuming that is of Generation X is:

$\\ P(T|X) = 0.36$

The probability that a person has a tattoo assuming that is of Boomers is:

$\\ P(T|B) = 0.13$

The probability of being of Millennials is:

$\\ P(M) = 0.22$

The probability of being of Generation X is:

$\\ P(X) = 0.20$

The probability of being of Boomers is:

$\\ P(B) = 0.22$

Therefore, the probability of the event of having a tattoo P(T) is:

$\\ P(T) = P(T|M)*P(M) + P(T|X)*P(X) + P(T|B)*P(B)$

$\\ P(T) = 0.47*0.22 + 0.36*0.20 + 0.13*0.22$

$\\ P(T) = 0.204$

For non-independent events that happen at the same time, we can say that the probability of occurring simultaneously is:

$\\ P(M \cap T) = P(M|T)*P(T)$

$\\ P(T \cap M) = P(T|M)*P(M)$

But

$\\ P(M \cap T) = P(T \cap M)$

Then

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

We are asked for the probability that a person is a Millennial given or assuming that they have tattoos or P(M | T). Solving the previous formula for the latter:

$\\ P(M|T)*P(T) = P(T|M)*P(M)$

$\\ P(M|T) = \frac{P(T|M)*P(M)}{P(T)}$