The lines y=x+1 and y=-x-3 are graphed. What is the solution to the system? Please help

Mathematics

1 answer:

Fed [463]3 years ago

7 0

Answer: (-2, -1)

Step-by-step explanation: Since these lines are already graphed, we are looking for their point of intersection. This point where the two lines intersect will represent the x and y that is the solution to this system of equations.

The two lines intersect in quadrant III

where x and y are both negative.

When finding the coordinates of a given point,

be very careful with your signs.

Let's just do a quick review on the coordinate system. On the x-axis, left means negative and right means positive and on the y-axis, down means negative and up means positive.

So to find the coordinates for this point, we start at the origin.

Then we move to the left 2 and down 1 so that's (-2, -1).

So the solution to this system is (-2, -1).

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Karolina [17]

Answer:

The second answer is correct.

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2 years ago

The number and frequency of Atlantic hurricanes annually from 1940 through 2007 is shown here:

klio [65]

Answer:

The probability table is shown below.

A Poisson distribution can be used to approximate the model of the number of hurricanes each season.

Step-by-step explanation:

(a)

The formula to compute the probability of an event E is:

$P(E)=\frac{Favorable\ no.\ of\ frequencies}{Total\ NO.\ of\ frequencies}$

Use this formula to compute the probabilities of 0 - 8 hurricanes each season.

The table for the probabilities is shown below.

(b)

Compute the mean number of hurricanes per season as follows:

$E(X)=\frac{\sum x f_{x}}{\sum f_{x}}=\frac{176}{68}= 2.5882\approx2.59$

If the variable X follows a Poisson distribution with parameter λ = 7.56 then the probability function is:

$P(X=x)=\frac{e^{-2.59}(2.59)^{x}}{x!} ;\ x=0, 1, 2,...$

Compute the probability of X = 0 as follows:

$P(X=0)=\frac{e^{-2.59}(2.59)^{0}}{0!} =\frac{0.075\times1}{1}=0.075$

Compute the probability of X = 1 as follows:

$\neq P(X=1)=\frac{e^{-2.59}(2.59)^{1}}{1!} =\frac{0.075\times7.56}{1}=0.1943$

Compute the probabilities for the rest of the values of X in the similar way.

The probabilities are shown in the table.

On comparing the two probability tables, it can be seen that the Poisson distribution can be used to approximate the distribution of the number of hurricanes each season. This is because for every value of X the Poisson probability is approximately equal to the empirical probability.