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Ierofanga [76]
3 years ago
11

Find the smallest positive integer solution to the following system of congruences: x = 0 (mod 5) x = 8 (mod 11) The solution is

Mathematics
1 answer:
igomit [66]3 years ago
8 0

Answer:

The smallest positive integer solution to the given system of congruences is 30.

Step-by-step explanation:

The given system of congruences is

x=0(mod5)

x=8(mod11)

where, m and n are positive integers.

It means, if the number divided by 5, then remainder is 0 and if the same number is divided by 11, then the remainder is 8. It can be defined as

x=5m

x=11n+8

5m\cong 11n+8

Now, we can say that m>n because m and n are positive integers.

For n=1,

5m=11(1)+8=19

5m=19

19 is not divisible by 5 so m is not an integer for n=1.

For n=2,

5m=11(2)+8

5m=30

m=6

The value of m is 6 and the value of n is 2. So the smallest positive integer solution to the given system of congruences is

x=5(6)=30

Therefore the smallest positive integer solution to the given system of congruences is 30.

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204.6 is what percent of 125? Round to the nearest tenth.
Zina [86]

Answer:

255.8

Explanation:

To get the solution, you are looking for, you need to point out what we know.

1. We assume, that the number 125 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 125 is 100%, so we can write it down as 125=100%.

4. We know, that x is 204.6% of the output value, so we can write it down as x=204.6%.

5. Now we have two simple equations:

1) 125=100%

2) x=204.6%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

125/x=100%/204.6%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 204.6% of 125

125/x=100/204.6

(125/x)*x=(100/204.6)*x       - we multiply both sides of the equation by x

125=0.48875855327468*x       - we divide both sides of the equation by (0.48875855327468) to get x

125/0.48875855327468=x

255.75=x

x=255.75

now you  have:

204.6% of 125=255.75

If you round 255.75  to the nearest tenth, it would be 255.8 because rounding to the nearest tenth the number will be  7 because 7 is in the tenth place in 255.<u>7</u>5, so you would round up because  anything about the number 5 you will round up and anything below 5 you round down and  when you round up you will get 255.8 which is your answer.

Hope this helps :)

5 0
2 years ago
Mario invested $6,000 in an account that pays 5% annual interest compounded annually how much will be there after 2.5 years
Liono4ka [1.6K]

Answer:

$48,000

Step-by-step explanation:

i = \frac{p \times r \times t}{100 }  \\ 6000 =  \frac{p \times 5 \times 2.5}{100 }  \\ 600000 =  12.5 \\ 48000

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How does knowing the slope and y-intercept help you graph and write the equation of a line?
IgorLugansk [536]

Answer:

It allows to to know y-intercept formula which is used to graph a line.

Step-by-step explanation:

Y-intercept formula:

y=mx+b

  M: slope (keep in fraction if it is fraction, to help you graph)

  B: y-interecept

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3 years ago
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Allisa [31]

Answer:

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Step-by-step explanation:

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