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sveticcg [70]
2 years ago
6

Please help need asap

Mathematics
1 answer:
larisa86 [58]2 years ago
4 0
Answer to the nearest tenth is 20.8
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Solve the following simultaneous linear congruences.
Anastaziya [24]

a. The moduli are coprime, so you can apply the Chinese remainder theorem directly. Let

x=4\cdot5+3\cdot5+3\cdot4

  • Taken mod 3, the last two terms vanish, and 20\equiv2\pmod3 so we need to multiply by the inverse of 2 modulo 3 to end up with a remainder of 1. Since 2\cdot2\equiv4\equiv1\pmod3, we multiply the first term by 2.

x=4\cdot5\cdot2+3\cdot5+3\cdot4

  • Taken mod 4, the first and last terms vanish, and 15\equiv3\pmod4. Multiply by the inverse of 3 modulo 4 (which is 3 because 3\cdot3\equiv9\equiv1\pmod4), then by 2 to ensure the proper remainder is left.

x=4\cdot5\cdot2+3\cdot5\cdot3\cdot2+3\cdot4

  • Taken mod 5, the first two terms vanish, and 12\equiv2\pmod5. Multiply by the inverse of 2 modulo 5 (3, since 3\cdot2\equiv6\equiv1\pmod5) and again by 3.

x=4\cdot5\cdot2+3\cdot5\cdot3\cdot2+3\cdot4\cdot3\cdot3

\implies x=238

By the CRT, we have

x\equiv238\pmod{3\cdot4\cdot5}\implies x\equiv-2\pmod{60}\implies\boxed{x\equiv58\pmod{60}}

i.e. any number 58+60n (where n is an integer) satisifes the system.

b. The moduli are not coprime, so we need to check for possible contradictions. If x\equiv a\pmod m and x\equiv b\pmod n, then we need to have a\equiv b\pmod{\mathrm{gcd}(m,n)}. This basically amounts to checking that if x\equiv a\pmod m, then we should also have x\equiv a\pmod{\text{any divisor of }m}.

x\equiv4\pmod{10}\implies\begin{cases}x\equiv4\equiv0\pmod2\\x\equiv4\pmod5\end{cases}

x\equiv8\pmod{12}\implies\begin{cases}x\equiv0\pmod2\\x\equiv2\pmod3\end{cases}

x\equiv6\pmod{18}\implies\begin{cases}x\equiv0\pmod2\\x\equiv0\pmod3\end{cases}

The last congruence conflicts with the previous one modulo 3, so there is no solution to this system.

5 0
3 years ago
Write an inequality for the following statement.<br> 9 is greater than a
KIM [24]

Answer:

9>a

Step-by-step explanation:

The greater than symbol is >

The less than symbol is <

It can be helpful to imagine the signs as little crocodile mouths. They will turn their heads to the biggest catch, or in this case, the greater number. So the open end of the sign will be towards the greater number.

6 0
3 years ago
Read 2 more answers
Guys please which one is the correct answer I need help!
Anika [276]

Answer:

D is your answer

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Reduce the following fraction: . -32abc/64 a to the 2nd power bc to the 3rd power
Ksenya-84 [330]
-1/2ac^2 flip to make it positive which makes it a whole number = 2ac^2
5 0
3 years ago
Is y=3x+4 a function?
Oxana [17]

Answer:

Yes, it is a function

Step-by-step explanation:

Every possible input x value is paired with a unique output y value.

Another approach is to graph the function then conduct the VLT (vertical line test) at which point you will realize that any vertical line will intersect the graph at one point only meaning it is a function.

Hope this helps.

5 0
1 year ago
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