Lorena has
3 meters=300 cm
1st piece=314 cm
8 meters=800 cm
2nd piece=824 cm
together=824+314=1138 cm or 11 meters and 38 cm
1m=100 cm
a.

By Fermat's little theorem, we have


5 and 7 are both prime, so
and
. By Euler's theorem, we get


Now we can use the Chinese remainder theorem to solve for
. Start with

- Taken mod 5, the second term vanishes and
. Multiply by the inverse of 4 mod 5 (4), then by 2.

- Taken mod 7, the first term vanishes and
. Multiply by the inverse of 2 mod 7 (4), then by 6.


b.

We have
, so by Euler's theorem,

Now, raising both sides of the original congruence to the power of 6 gives

Then multiplying both sides by
gives

so that
is the inverse of 25 mod 64. To find this inverse, solve for
in
. Using the Euclidean algorithm, we have
64 = 2*25 + 14
25 = 1*14 + 11
14 = 1*11 + 3
11 = 3*3 + 2
3 = 1*2 + 1
=> 1 = 9*64 - 23*25
so that
.
So we know

Squaring both sides of this gives

and multiplying both sides by
tells us

Use the Euclidean algorithm to solve for
.
64 = 3*17 + 13
17 = 1*13 + 4
13 = 3*4 + 1
=> 1 = 4*64 - 15*17
so that
, and so 
The answer to the given question is as below:-
Polynomials:-
x³-7x²+9x-5x⁴-20
x⁵-5x⁴+4x³+2x-1
3x²-5x⁴+2x-12
Non-polynomial:-
x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1

![\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%7D%20-%5Csqrt%5B3%5D%7Bx%7D%204%2B%5Csqrt%7Bx%7D-8x%2B16)
<h3>What are polynomials?</h3>
A polynomial is a mathematical equation made up of indeterminates and coefficients and involves only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. The exponents of the polynomials can not be irrational.
So the table will be formed as:-
Polynomials:- Non-polynomial:-
x³-7x²+9x-5x⁴-20 x⁻5-5x⁻⁴+4x⁻³+2x⁻1-1
x⁵-5x⁴+4x³+2x-1 
3x²-5x⁴+2x-12 ![\sqrt[4]{x} -\sqrt[3]{x} 4+\sqrt{x}-8x+16](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%7D%20-%5Csqrt%5B3%5D%7Bx%7D%204%2B%5Csqrt%7Bx%7D-8x%2B16)
Therefore the polynomials and non-polynomials are shown in the table above.
To know more about polynomials follow
brainly.com/question/2833285
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Answer:
First answer is 1200
Second answer is 900 for each new employee
Step-by-step explanation:
First answer:
2200+1300+800+940+560+x = 7000
5800+x = 7000 subtract 5800 from both sides and you get your answer
x = 1200
Second answer:
x = 900. Each of the two employees made 900 a month or 1800 a month for both of them.
To find the average we take the total salaries and divide by the number of people to find the average salary. In this case, we know the average and we know all of the salaries, but two. We can figure this out.
(7000 + 2x)/8 = 1100 multiple both sides by 8 to clear the fraction/
7000 +2x = 8800 Subtract both sides by 7000
2x = 1800 Divide both sides by 2
x = 900