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3 years ago

What is an equation for the line that passes through the coordinates (4,5) and (8, 3)?

2 answers:

8 0

The equation to find the slope of a line is y2 - y1 / x2 - x1

So, what you do is take the y coordinate in your first point, which in this case is 5, and subtract it from your y coordinate in the second point, which is 3.

3 - 5 = -2
-2 / x2 - x1

Now take the x coordinate in your first point, which in this case is 4, and subtract it from the x coordinate in your second point, which is 8.

8 - 4 = 4

Now you're left with -2 / 4, which is the equation for the line that passes through the points (4,5) and (8,3)

Hope this helps!!

lapo4ka [179]3 years ago

4 0

-1/2x+7. Because x=(y2-y1)/(x2-x1)

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Talia is writing a coordinate proof to show that the diagonals of a square are perpendicular. Which sentence describes what Tali

AfilCa [17]

Answer:

Step-by-step explanation:

The slopes of perpendicular lines are negative reciprocals. That means that their product is -1.

In option D, since the slopes are 1 and -1, their product is -1, and the lines are perpendicular.

Answer: D.

3 0

1 year ago

An automobile manufacturer finds that 1 in every 2500 automobiles produced has a particular manufacturing defect. (a) Use a bin

Advocard [28]

Answer:

a) 0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

b) 0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

Step-by-step explanation:

Binomial 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.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

To use the Poisson approximation for the binomial, we have that:

$\mu = np$

1 in every 2500 automobiles produced has a particular manufacturing defect.

This means that $p = \frac{1}{2500} = 0.0004$

a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 7000 cars.

This is $P(X = 4)$ when $n = 7000$ . So

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

$P(X = 4) = C_{7000,4}.(0.0004)^{4}.(0.9996)^{6996} = 0.1558$

0.1558 = 15.58% probability of finding 4 cars with the defect in a random sample of 7000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p.

Using the approximation:

$\mu = np = 7000*0.0004 = 2.8$ . So

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 4) = \frac{e^{-2.8}*(2.8)^{4}}{(4)!} = 0.1557$

0.1557 = 15.57% probability of finding 4 cars with the defect in a random sample of 7000 cars. These probabilities are very close, which means that the approximation works.

6 0

3 years ago

Consider the expression (3x+7)(3x+2)

Nastasia [14]

Answer:

a. shown below

b. 9x+14

Step-by-step explanation:

a. (on the bottom)

b. (3x+7)(3x+2)

multiply the terms:

9x+14