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Allushta [10]
3 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]3 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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Renee is simplifying the expression (7) (StartFraction 13 over 29 EndFraction) (StartFraction 1 over 7 EndFraction). She recogni
dsp73

Answer:

The correct option is commutative property.

Step-by-step explanation:

The expression that Renee is simplifying is:

(7)\cdot(\frac{13}{29})\cdot(\frac{1}{7})

It is provided that, Renee recognizes that 7 and \frac{1}{7} are reciprocals, so she would like to find their product before she multiplies by \frac{13}{29}.

The associative property of multiplication states that:

a\times b\times c=(a\times b)\times c=a\times (b\times c)

The commutative property of multiplication states that:

a\times b\times c=a\times c\times b=c\times a\times b

The distributive property of multiplication states that:

a\cdot (b+c)=a\cdot b+a\cdot c

The identity property of multiplication states that:

a\times 1=a\\b\times 1=b

So, Renee should use the commutative property of multiplication to find the product of 7 and \frac{1}{7},

(7)\cdot(\frac{13}{29})\cdot(\frac{1}{7})=(7\times\frac{1}{7})\times\frac{13}{29}=\frac{13}{29}

Thus, the correct option is commutative property.

5 0
3 years ago
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Given that EF is a diameter of circle D, which of the following arcs must be a major arc?
Rainbow [258]

Answer:

Arc ECG is the major arc

Step-by-step explanation:

Arc ECG is made by an angle which is greater than 180°.

All the other arcs listed are made by angles which are 180° or less than.

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Answer:

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Explanation:

"A geometric series is a series with a constant ratio between successive terms".

Here, we can observe that the first term 'a' is '2'.

And the common ratio 'r' =

Therefore, the first term 'a' is 2 and common ratio 'r' is '-1'.

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A caterer is planning a large dinner party for 1001 guests. Each table must seat an equal number of​ guests, more than 1 guest a
MArishka [77]

Answer:

The prime factorization of 1001 is 7*11*13, so with the constraint that the tables seat between 2 and 19 guests, we can use tables that seat either 7, 11, or 13 guests.

For tables that seat 7, the caterer would need 11*13 = 143 tables.

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Step-by-step explanation:

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