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Novay_Z [31]
3 years ago
7

On a coordinate plane, the segment with endpoints (10, 40) and (70, 120) is

Mathematics
1 answer:
OlgaM077 [116]3 years ago
3 0

Answer:

The length of the resulting segment is 500.

Step-by-step explanation:

Vectorially speaking, the dilation is defined by following operation:

P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)] (1)

Where:

O(x,y) - Center of dilation.

P(x,y) - Original point.

k - Scale factor.

P'(x,y) - Dilated point.

First, we proceed to determine the coordinates of the dilated segment:

(P(x,y) = (10, 40), Q(x,y) = (70, 120), O(x,y) = (0,0), k = 5)

P'(x,y) = O(x,y) + k\cdot [P(x,y)-O(x,y)]

P(x,y) = (0,0) +5\cdot [(10,40)-(0,0)]

P'(x,y) = (50,200)

Q'(x,y) = O(x,y) + k\cdot [Q(x,y)-O(x,y)]

Q' (x,y) = (0,0) +5\cdot [(70,120)-(0,0)]

Q'(x,y) = (350, 600)

Then, the length of the resulting segment is determined by following Pythagorean identity:

l_{P'Q'} = \sqrt{(350-50)^{2}+(600-200)^{2}}

l_{P'Q'} = 500

The length of the resulting segment is 500.

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HELP PLZ WILL GIVE BRAINLIEST! find the arrithmetic means in the given sequence<br> -3,?,?,?,93
pav-90 [236]

Answer:

Step-by-step explanation:

The standard form of an arithmetic sequence is

aₙ = a₁ + d(n - 1)

where aₙ is the number of the term in the sequence (in order from first term where n = 1, to second term where n = 2, to third term where n = 3, etc) a₁ is the the first term in the sequence, and d is the arithmetic difference or means.  This is what we are looking to solve for.  

In our sequence we have the first term, -3 (where n = 1) and the fifth term, 93 (where n = 5).  If we fill in what we have, the only unknown is d, our arithmetic difference (means) between each number in the sequence.

Because we have the fifth term, we can write our standard form to fit our needs:

a₅ = a₁ + d(n-1).  Therefore,

93 = -3 + d(5 - 1) and

93 = -3 + d(4) so

96 = 4d and

d = 24

Our arithmetic difference (means) is 24.  Let's test it on a few values of n.  Let's look for the second, third, and 4th terms, and then try it out for n = 5 to make sure the 5th term, using our arithmetic sequence with d = 24 works and we do, in fact, find the fifth term to be 93.

Testing n = 2

a₂ = -3 + 24(2 - 1) so

a₂ = -3 + 24(1)  and

a₂ = 21.  Second term is 21 (Notice that difference between -3 and 21 is 24)

Testing n = 3

a₃ = -3 + 24(3 - 1) so

a₃ = -3 + 24(2) and

a₃ = 48 - 3 and

a₃ = 45 (Notice the difference between 21 and 45 is 24)

Testing n = 4

a₄ = -3 + 24(4 - 1) so

a₄ = -3 + 24(3) and

a₄ = 72 - 3 and

a₄ = 69 (Notice the difference between 45 and 69 is 24)

Testing n = 5 (and it better come out as 93 or we did something wrong!)

a₅ = -3 + 24(5 - 1) and

a₅ = -3 + 24(4) so

a₅ = 96 - 3 so

a₅ = 93 (Phew!)  ; )

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Answer:

Your answer should be 1,200 because 120 x 10 is 1,200

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