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Vitek1552 [10]
3 years ago
9

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

Mathematics
2 answers:
horsena [70]3 years ago
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:

D.

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

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Step-by-step explanation:

a. (on the bottom)

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

multiply the terms:

9x+14

thats the area

6 0
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Consider the reduction of the complex figure with a scale factor of 1
BlackZzzverrR [31]

Answer:

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Step-by-step explanation:

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2 years ago
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kolezko [41]

Answer:

-6

Step-by-step explanation:

(2(4)+4) - (3(4)+6) = 12-18 = -6.

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1 year ago
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