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3 years ago

Two numbers are between 10 and 20. Their greatest common factor is 3. Which two numbers could they be?

Mathematics

1 answer:

alina1380 [7]3 years ago

4 0

Answer:

12 and 15 or

12 and 18 or

15 or 18

Step-by-step explanation:

The two numbers have to both be divisible by 3, since their greatest common factor is 3. This only leaves..

12, 15, or 18 (no other numbers between 10 and 20 are divisible by 3)

The factors of 12 are: 2, 3, 4, 6, and 12

The factors of 15 are: 3, 5, and 15

The factors of 18 are: 2, 3, 6, 9, and 18

All three numbers have 3 as a greatest common factor, so we have 3 pairs of numbers they could be...

12 and 15 or

12 and 18 or

15 or 18

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Find thhe remainder when 7^203 is divided by 4

Aleksandr [31]

Using the square-and-multiply approach, we have

$7^{203}=7\times(7^{101})^2$
$7^{101}=7\times(7^{50})^2$
$7^{50}=(7^{25})^2$
$7^{25}=7\times(7^{12})^2$
$7^{12}=(7^6)^2$
$7^6=(7^3)^2$
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and so, using the property that, if $a_1\equiv b_1\mod n$ and $a_2\equiv b_2\mod n$ , then $a_1a_2\equiv b_1b_2\mod n$ , we get

$7\equiv3\mod4$
$7^2\equiv9\equiv1\mod4$
$7^3\equiv7\times1\equiv7\equiv3\mod4$
$7^6\equiv9\equiv1\mod4$
$7^{12}\equiv1\mod4$
$7^{25}\equiv7\times1\equiv7\equiv3\mod4$
$7^{50}\equiv9\equiv1\mod4$
$7^{101}\equiv7\times1\equiv7\equiv3\mod4$
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4 0

3 years ago

What is the domain of the function

kati45 [8]

Answer:

it will be the first one

Step-by-step explanation:

3 0

3 years ago

Please help me,please and thank you :)

nika2105 [10]

Answer: 4

36.87 degrees

Step-by-step explanation:

The figure shown is a right angled triangle. It has three sides, one of which is the longest. The longest side is called the hypotenuse. Either of the shorter sides is called the opposite and the adjacent side(always the side carrying both the 90 degrees angle and the given angle).

Since the triangle is a right angled triangle,

We can apply Pythagoras theorem to get the opposite side.

Hypothenuse ^2 = opposite ^2 + adjacent ^2

5^2 = 4 ^2 + opposite ^2

opposite = √ 25 - 16

opposite = √9 = 3

Let the angle be # degrees,

Cos # = adjacent / hypothenuse

= 4/5 = 0.8

# = cos^-1 (0.8) = 36.87 degrees

7 0

3 years ago