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7nadin3 [17]
3 years ago
14

given the points A(0,0) and B(8,4), show that P(2,6) is on the perpendicular bisector of the segment AB.

Mathematics
1 answer:
Serggg [28]3 years ago
7 0

Answer:

Lil Nas X - THAT’S WHAT I WANT..................

Step-by-step explanation:

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One hundred twenty million five hundred forty thousand<span />
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Find the smallest positive $n$ such that \begin{align*} n &amp;\equiv 3 \pmod{4}, \\ n &amp;\equiv 2 \pmod{5}, \\ n &amp;\equiv
Alex777 [14]

4, 5, and 7 are mutually coprime, so you can use the Chinese remainder theorem right away.

We construct a number x such that taking it mod 4, 5, and 7 leaves the desired remainders:

x=3\cdot5\cdot7+4\cdot2\cdot7+4\cdot5\cdot6

  • Taken mod 4, the last two terms vanish and we have

x\equiv3\cdot5\cdot7\equiv105\equiv1\pmod4

so we multiply the first term by 3.

  • Taken mod 5, the first and last terms vanish and we have

x\equiv4\cdot2\cdot7\equiv51\equiv1\pmod5

so we multiply the second term by 2.

  • Taken mod 7, the first two terms vanish and we have

x\equiv4\cdot5\cdot6\equiv120\equiv1\pmod7

so we multiply the last term by 7.

Now,

x=3^2\cdot5\cdot7+4\cdot2^2\cdot7+4\cdot5\cdot6^2=1147

By the CRT, the system of congruences has a general solution

n\equiv1147\pmod{4\cdot5\cdot7}\implies\boxed{n\equiv27\pmod{140}}

or all integers 27+140k, k\in\mathbb Z, the least (and positive) of which is 27.

3 0
3 years ago
The life expectancy of a circulating coin is 30 years. The life expectancy of a circulating dollar bill is only
Afina-wow [57]
Life expectancy of dollar bill = d
life expectancy of coin = c

d = 1/20 c

substitute value in for c (30)

d = 1/20 * 30
d = 30/20
d = 1.5

life expectancy of a dollar bill = 1.5 years
3 0
3 years ago
What is the answer to 3z &gt; - 4.5
Stella [2.4K]

Answer:

z

Step-by-step explanation:

3z  > -4.5

z > - \frac{4.5}{3}

z > -1.5

z  <  1.5

3 0
3 years ago
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