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r-ruslan [8.4K]
3 years ago
11

(3x+2) and (5x-6) solve for x

Mathematics
1 answer:
HACTEHA [7]3 years ago
6 0

Answer:

x=3X 2 + 5x -6

Step-by-step explanation:

3X2 + 5X-6= 3X2 + 5X 6

X=3X2 +5X -6

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4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.
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4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.

Start with

x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 4, the last two terms vanish and we're left with

x\equiv63\equiv64-1\equiv-1\equiv3\pmod4

We have 3^2\equiv9\equiv1\pmod4, so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 7, the first and last terms vanish and we're left with

x\equiv72\equiv2\pmod7

which is what we want, so no adjustments needed here.

x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5

Taken mod 9, the first two terms vanish and we're left with

x\equiv140\equiv5\pmod9

so we don't need to make any adjustments here, and we end up with x=401.

By the Chinese remainder theorem, we find that any x such that

x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}

is a solution to this system, i.e. x=149+252n for any integer n, the smallest and positive of which is 149.

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3 years ago
Of the choices below, what is the best estimate of the speed of the milk van?
galben [10]

Answer:

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Step-by-step explanation:

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