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katrin2010 [14]
1 year ago
6

Line segment AB has endpoints A(1,8) and B(7,−4). What are the coordinates of the point located 5/6 of the way from A to B?

Mathematics
1 answer:
const2013 [10]1 year ago
6 0

The coordinate of the point is (6,-2)

<h3>How to determine the coordinate of the point?</h3>

The given parameters are:

A = (1,8)

B = (7,-4)

The location of the point (i.e 5/6) means that the ratio is:

m :n = 5 : (6 - 5)

m : n = 5 : 1

The coordinate of the point is then calculated as:

(x,y) = \frac{1}{m + n}* (mx_2 + nx_1,my_2 + ny_1)

So, we have:

(x,y) = \frac{1}{5 + 1}* (5 * 7 + 1 * 1 , 5 * -4 + 1 * 8)

Evaluate

(x,y) = \frac{1}{6}* (36 , -12)

Evaluate the product

(x,y) = (6,-2)

Hence, the coordinate of the point is (6,-2)

Read more abut line segment ratio at:

brainly.com/question/12959377

#SPJ1

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Nikolay [14]

Answer:

probability that the other side is colored black if the upper side of the chosen card is colored red = 1/3

Step-by-step explanation:

First of all;

Let B1 be the event that the card with two red sides is selected

Let B2 be the event that the

card with two black sides is selected

Let B3 be the event that the card with one red side and one black side is

selected

Let A be the event that the upper side of the selected card (when put down on the ground)

is red.

Now, from the question;

P(B3) = ⅓

P(A|B3) = ½

P(B1) = ⅓

P(A|B1) = 1

P(B2) = ⅓

P(A|B2)) = 0

(P(B3) = ⅓

P(A|B3) = ½

Now, we want to find the probability that the other side is colored black if the upper side of the chosen card is colored red. This probability is; P(B3|A). Thus, from the Bayes’ formula, it follows that;

P(B3|A) = [P(B3)•P(A|B3)]/[(P(B1)•P(A|B1)) + (P(B2)•P(A|B2)) + (P(B3)•P(A|B3))]

Thus;

P(B3|A) = [⅓×½]/[(⅓×1) + (⅓•0) + (⅓×½)]

P(B3|A) = (1/6)/(⅓ + 0 + 1/6)

P(B3|A) = (1/6)/(1/2)

P(B3|A) = 1/3

5 0
3 years ago
What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?
kompoz [17]

Answer:

K(-4,8) is the ortho center.

Step-by-step explanation:

In a right angled triangle, The vertex of the right angle is the ortho center.

Here we are given

J(-4,-1), K(-4,8) & L(2,8)

Using distance formula we get

JK^{2}= (-4+4)^{2}+ (8+1)^{2}=0+81=81

KL^{2}= (-4-2)^{2}+ (8+-8)^{2}=36+0=36

JL^{2}= (-4-2)^{2}+ (8+1)^{2}=36+81=117

So we can say that

JK^2 + KL^2=JL^2

By converse of pythagorean theorem we get

Hence the Vertex of the right angle is K(-4,8)

K(-4,8) is the ortho center.

7 0
3 years ago
Brad and Angelina can mow their yard together with two lawn mowers in 30 min. When brad works alone it takes him 45 min. How lon
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Answer:

Wouldn't it be 45 minutes as well?

Step-by-step explanation:

If you think about it in a real life scenario, if one person does the job and then another person does the same job at the same speed wouldn't it be the same time? But if its not i think it would be 15 minutes because 45-30 = 15

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Svetradugi [14.3K]

Answer:

80

Step-by-step explanation:

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2 years ago
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