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Anarel [89]
3 years ago
5

Let ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication. Which of the followin

g are generators of ℤ×17? I.5 II.8 III.16
(I) 5.
(II) 8.
(III) 16.

(A) None.
(B) I only.
(C) II only.
(D) III only.
(E) I, II, and III
Mathematics
1 answer:
joja [24]3 years ago
7 0

Answer:  The correct option is (E) I, II and III.

Step-by-step explanation:  Given that ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication.

We are to select the correct generators of ℤ×17.

According to the given information, we can write

ℤ17 = {0, 1, 2, 3, . . . , 16}

and

ℤ×17 = {1, 2 , 3 , . . . 16}.

The generators of ℤ×17 are those elements which are co prime to 17.

Since all the elements from 1 to 16 are co prime to 17, so all the elements of the set  ℤ×17 are its generators.

Therefore, 5, 8 and 16, all are generators. So, i, ii and iii are generators.

Thus, (E) is the correct option.

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A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Aven
Advocard [28]

Answer:

72°

Step-by-step explanation:

From the information given:

A town planner wants to build two new streets, Elm Street and Garden Road, to connect parallel streets Maple Drive and Pine Avenue.

We are also told that there is a  Trapezoid EFGH with EH as the Pine avenue and EF as the Elm street.

However, side FG and EH are parallel.

∠G = 108°

From the property of parallel lines :

since FG || EH

Then  ∠G = ∠H  = 108°  (i.e corresponding angle will also be equal)

The required angle between Elm Street and Pine Avenue would be interior angles +  180°  given that  alternate angles are also equal.

The required angle between Elm Street and Pine Avenue = 180° - 108°

The required angle between Elm Street and Pine Avenue = 72°

3 0
3 years ago
What is the slope of the line that goes through (-5,5) and (5,-7)
ludmilkaskok [199]

Answer:

A. -1/5

Step-by-step explanation:

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-1/5 option A

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3 years ago
How do you work out "2(c+4)="
Nonamiya [84]

First you do distributive property.

2c + 8 = 0

Then subtract 8 with 0

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3 years ago
Convert the fraction 5/8 to decimal using long division method
erma4kov [3.2K]
1/8=0.125
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