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Allushta [10]
4 years ago
14

Let F be a field, and suppose a EF, a *0. Prove that a has a unique multiplicative inverse.

Mathematics
1 answer:
bezimeni [28]4 years ago
6 0

Answer with Step-by-step explanation:

Let F be a field .Suppose a\in F and a\neq 0

We have to prove that a has unique multiplicative inverse.

Suppose a has two inverses b and c

Then, ac=1,ab=1 where 1 =Multiplicative identity

ac=ab

c=b (cancel a on both sides)

Hence, a has unique multiplicative inverse.

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What is 9% sales tax on a $15.00 shirt
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5 (2x – 1) –7 = 2 (x – 3)
Sladkaya [172]

Answer:

x−3=x−3

Step-by-step explanation:

Evaluate (2x−1)−7, then set it equal to 2.

Subtract 7 from −1 = 2x−8

Solve 2x−8=2.

Move all terms not containing x to the right side of the equation.

Add 8 to both sides of the equation=2x=2+8

Add 2 and 8=2x=10

Divide each term by 2 and simplify.

Divide each term in 2x=10 by 2=2x/2=10/2

Cancel the common factor of 2

Cancel the common factor=10/2

Divide x by 1=x=10/2

Divide 10 by 2=x=5

Remove parentheses=x−3

List all of the solutions.

5=

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x−3=x−3

7 0
3 years ago
At a lunch buffet, the price for an adult plate is $19, and the price for a child plate is $8. On Tuesday, a total of 32 plates
mestny [16]

Answer:

Adult plate = 21 , child plate = 11

Step-by-step explanation:

number of adult plate = a , no of child plate = c

$487 = $19a + $8c (equation 1)

32 = a + c (equation 2)

Multiply equation 2 by 8 gets you:

256 = 8a + 8c (equation 3)

Solve equation 1 and equation 3 simultaneously:

487 = 19a + 8c (equation 1) minus

256 = 8a + 8c (equation 3) :

231 = 11a

a = 231/11

a= 21

Substitute a = 21 into equation 2 :

32 = 21 + c

c = 32 - 21

c = 11

So 21 adult plates and 11 child plates were sold.

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3 years ago
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You’re piloting an airplane to prepare for landing you change the planes altitude from a meters to c meters.
soldier1979 [14.2K]

Answer:

|a-c| meters

Step-by-step explanation:

If I am piloting an airplane to prepare for landing, I change the plane's altitude from a meters to c meters, then the expression that represents the distance between two altitudes is given by |a-c| meters, not by |a+c|.

For, example if the altitude of the plane changes from 1000 meters to 500 meters for preparing for landing then the distance between those two altitudes is |1000 - 500| = 500 meters. (Answer)

But using the expression |a+c|, I will get the wrong answer as |1000 + 500| = 1500 meters.

8 0
4 years ago
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