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Arte-miy333 [17]
3 years ago
7

Prove that for a,b,c E ℤ, if a ❘ ( ab + c ), then a I c.

Mathematics
1 answer:
zhenek [66]3 years ago
3 0

Answer:

True.

Step-by-step explanation:

Let a,b,c integers  and a | (ab+c), that is to say that there exist a integer k such that ab+c = ka. Then:

ab+c = ka

c = ka-ab

c = a(k-b). So, c is a multiple of a, that is a | c.

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Which of the following has no solution?
Softa [21]

Answer:

(x + 1 s 1) n (x + 12 1)

(x +1<1) n (x + 1 > 1)

Step-by-step explanation:

Just simplify each the statements.

Then compare and and see if the statements are contradictory and therefore FALSE, if so, then there is no solution.

(x + 1<-1) n (x + 1< 1)

(x <-2) n (x < 0) which is true, so there is a solution.

(x + 1 s 1) n (x + 12 1)

this doesn't make sense so there is no solution.

(x +1<1) n (x + 1 > 1)

(x < 0) n (x > 0)

This is not possible, the statements are contradictory and therefore FALSE, so there is no solution.

5 0
3 years ago
Elena packed 48 cubes into this box.Each cube has edges that are 1 centimeter.How many layers of cubes did Elena make
solniwko [45]
Elena packed 48 cubes.
Each cube has an edge of 1 centimeter.
The number of layers that Elena can make depends on how each layer is arranged and depends on how many cubes are there in a layer.
Assume that each layer has  only 1 cube, then there are 48 layers.
4 0
3 years ago
The distance between City A and City B is 250 miles. A length of 2.1 feet represents this distance on a certain wall map. City C
tigry1 [53]

Answer:

650 miles

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

5 0
3 years ago
Read 2 more answers
Use set notation to write the members of the following set, or state that the set has no members. Odd numbers between 2 and 82 t
adell [148]

Let the set of all Odd multiples of 9 between 2 and 82 be denoted by D, then, using set-builder notation,

D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}

The odd multiples of 9, m, in the range 2\le m \le 82 form the set

\{9,27,45,63,81\}

Each member of the set is a term of the arithmetic progression

U_n=18n+9

where the values of n range from 0 to 4, or 0\le n\le 4

Putting these facts together, we get the result

D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}

Learn more about set-builder notation here: brainly.com/question/17238769

3 0
3 years ago
The measure of angle 3 is 42°.<br><br> What is the measure of angle 1 in degrees?
polet [3.4K]

Answer:

<1 = 48

Step-by-step explanation:

<1 + <2 + <3 = 180 since they form a line

<1 + 90+ 42 =180

Combine like terms

<1 + 132 =180

Subtract 132 from each side

<1 +132-132 =180-132

<1 = 48

4 0
3 years ago
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