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4 years ago

The line x+ 2y = 9 intersects the curve xy + 18 = 0 at the points A and B. Find the coordinates of A and B.

Mathematics

1 answer:

victus00 [196]4 years ago

6 0

Subtracting the second equation by 18 on both sides, we have xy=-18. Next, we divide both sides by x to get y=-18/x Plugging that into the first equation, we have x+2(-18/x)=9. Multiplying both sides by x, we get x^2-36=9x. After that, we subtract both sides by 9x to get x^2-9x-36=0. Finding 2 numbers that add up to -9 but multiply to -36, we do a bit of guess and check to find the answers to be -12 and 3. Factoring it, we get
x^2-12x+3x-36=x(x-12)+3(x-12)=(x+3)(x-12). To find the x values, we have to find out when 0=(x+3)(x-12). This is simple as when you multiply 0 with anything, it is 0. Therefore, x=-3 and 12. Plugging those into x=-18/y, we get x=-18/y and by multiplying y to both sides, we get xy=-18 and then we can divide both sides by x to get -18/x=y. Plugging -3 in, we get -18/-3=6 and by plugging 12 in we get -18/12=-1.5. Therefore, our points are (-3,6) and (12, -1.5)

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According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5.1% of burglaries are cleared with arrests.

This means that $p = 0.051$

A new detective is assigned to six different burglaries.

This means that $n = 6$

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695$

26.95% probability that at least one of them is cleared with an arrest

8 0

3 years ago

How do I do this I don’t know where to start

seropon [69]

This is simple pythagoras, its just a²+b²=c². First you find the hypotenuse, which is 97; now you have the equation: x²+72²=97²
x²=9409-5184
x= √4225
x=65
the answer is 65m

8 0

3 years ago

Read 2 more answers

Draw and write to solve. Explain

Luda [366]

Answer:

Step-by-step explanation:

she has 10

she gets 4 more

10+4=14

8 0

2 years ago

Refer to the following information on full-term births in the United States over a given period of time.Type of Birth Number of

Anestetic [448]

Answer:

Refer to the following information on full-term births in the United States over a given period of time.

Type of Birth Number of Births

Single birth 47,200,000

Twins 600,000

Triplets 3000

Quadruplets 200

Use this information to estimate the probabilities of the following events.

(a) A randomly selected pregnant woman who reaches full term delivers twins. (Give the answer to three significant figures.)

(b) A randomly selected pregnant woman who reaches full term delivers quadruplets. (Give the answer to three significant figures.)

(c) A randomly selected pregnant woman who reaches full term gives birth to more than a single child. (Give the answer to three significant figures

7 0

3 years ago

There is 6/8 of a cake left over after a birthday party how many 1/4 peices can be made from the left over cake?

Marrrta [24]

=6/8 / 1/4
=6/8 x 4/1
=3 pieces

4 0

3 years ago