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crimeas [40]
4 years ago
5

If the points A, B and C have the coordinates A(5, 2), B(2, −3) and C(−8, 3), show that the triangle ABC is a right-angled trian

gle.
Mathematics
1 answer:
bixtya [17]4 years ago
6 0

Answer:

See below.

Step-by-step explanation:

Triangle ABC will be right-angled if 2 of its sides are perpendicular to each other. When sides are perpendicular the product of their slopes = -1.

Slope  of side AB = (-3-2)/(2-5) = -5/-3 = 5/3

Slope of side BC = (3- -3) / -8-2) = 6/-10 = -3/5

The product of the slopes = 5/3 * -3/5 = -15/15 = -1.

So AB is perpendicular to BC  and triangle ABC is right-angled .

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Mama's Italian Restaurant has collected data about customer sauce orders. It calculated that P(marinara) = 0.82, P(alfredo) = 0.
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Complete the table<br> Distance(ft)<br> Height(ft)
Bumek [7]

Answer:

a = 6, b = 7, c = 8, d = 7 and e = 6

Step-by-step explanation:

Let's remember that the complete revolution of the wheel is 360 degrees, and the distance traveled by a complete revolution is the length of the circumference: 2*pi*radius.

The inicial height of the point is 6 ft, and the radius of the wheel is 1 ft.

When the distance traveled is 0, the wheel turned 0 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be a = 6 + 0 = 6 ft

When the distance traveled is pi/2, the wheel turned 90 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be b = 6 + 1 = 7 ft

When the distance traveled is pi, the wheel turned 180 degrees, and the point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel.

So the height will be c = 6 + 2= 8 ft

When the distance traveled is 3pi/2, the wheel turned 270 degrees, and the point will be half the complete height of the wheel, which is 2 feet.

So the height will be d = 6 + 1 = 7 ft

When the distance traveled is 2pi, the wheel turned 360 degrees, and the point will be in its inicial position (the lower position of the wheel), which is 6 feet high.

So the height will be e = 6 + 0 = 6 ft

So the answers are:

a = 6, b = 7, c = 8, d = 7 and e = 6

4 0
4 years ago
The difference of the square of a number and 12 is equal to 4 times that number. find the negative solution.
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3 years ago
On the planet of Mercury, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas,
erastova [34]

Answer:

a

The distribution of  X is normal

b

P(X  <  1.4) = 0.12654

c

P(X  >  3.5) = 0.36051

Step-by-step explanation:

From the question we are told that

   The population mean is  \mu =  3 \  hours

   The standard deviation is  \sigma  =  1.4 \ hours

Generally given from the question that the amount of time spent alone by the population size is normally distributed then then the distribution of X (i.e the amount of time spent by the sample size (the one Mercurian)) will be normally distributed

  Generally the probability that the child spend less than one hour in a day is mathematically represented as

        P(X  <  1.4) =  P(\frac{X - \mu}{\sigma} < \frac{1.4 - \mu}{\sigma}   )

Here \frac{X - \mu}{\sigma }  =  Z (The\ standardized\ value\ of\  X)

So

      P(X  <  1.4) =  P(Z < \frac{1.4 - 3.0}{1.4}   )

     P(X  <  1.4) =  P(Z < -1.1429  )

From the z-table the value of  

        P(Z < -1.1429  )=0.12654

So     P(X  <  1.4) = 0.12654

Generally the percentage of children that spends over 3.5 hours unsupervised is mathematically represented as

        P(X  >  3.5) =  P(\frac{X - \mu}{\sigma} > \frac{3.5 - \mu}{\sigma}   )

        P(X >  3.5) =  P(Z > \frac{3.5 - 3.0}{1.4}   )

        P(X >  3.5) =  P(Z > 0.3571  )

From the z-table the value of  

        P(Z >0.3571  )=0.36051

So     P(X  >  3.5) = 0.36051

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3 years ago
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