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Orlov [11]
3 years ago
6

Ken paid $12 for two magazines the cost of each magazine was a multiple of $3 what are the possible prices of the magazines

Mathematics
1 answer:
defon3 years ago
8 0
The price could have been 6 each or 9 for one and 3 for the other
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Use the Euclidean Algorithm to compute the greatest common divisors indicated. (a) gcd(20, 12) (b) gcd(100, 36) (c) gcd(207, 496
coldgirl [10]

Answer:

(a) gcd(20, 12)=4

(b) gcd(100, 36)=4

(c) gcd(496,207 )=1

Step-by-step explanation:

The Euclidean algorithm is an efficient method for computing the greatest common divisor of two integers, without explicitly factoring the two integers.

The Euclidean algorithm solves the problem:

<em>                                   Given integers </em>a, b<em>, find </em>d=gcd(a,b)<em />

Here is an outline of the steps:

  1. Let a=x, b=y.
  2. Given x, y, use the division algorithm to write x=yq+r.
  3. If r=0, stop and output y; this is the gcd of a, b.
  4. If r\neq 0, replace (x,y) by (y,r). Go to step 2.

The division algorithm is an algorithm in which given 2 integers N and D, it computes their quotient Q and remainder R.

Let's say we have to divide N (dividend) by D (divisor). We will take the following steps:

Step 1: Subtract D from N repeatedly.

Step 2: The resulting number is known as the remainder R, and the number of times that D is subtracted is called the quotient Q.

(a) To find gcd(20, 12) we apply the Euclidean algorithm:

20 = 12\cdot 1 + 8\\ 12 = 8\cdot 1 + 4\\ 8 = 4\cdot 2 + 0

The process stops since we reached 0, and we obtain gcd(20, 12)=4.

(b) To find gcd(100, 36) we apply the Euclidean algorithm:

100 = 36\cdot 2 + 28\\ 36 = 28\cdot1 + 8\\ 28 = 8\cdot 3 + 4\\ 8 = 4\cdot 2 + 0

The process stops since we reached 0, and we obtain gcd(100, 36)=4.

(c) To find gcd(496,207 ) we apply the Euclidean algorithm:

496 = 207\cdot 2 + 82\\ 207 = 82\cdot 2 + 43\\ 82 = 43\cdot 1 + 39\\ 43 = 39\cdot 1 + 4\\ 39 = 4\cdot 9 + 3\\ 4 = 3\cdot 1 + 1\\ 3 = 1\cdot 3 + 0

The process stops since we reached 0, and we obtain gcd(496,207 )=1.

3 0
3 years ago
Jamie spent
atroni [7]
That’s how you do it ☺︎︎

7 0
3 years ago
Which expression is equivalent to -16 - 7?
lakkis [162]

Step-by-step explanation:

B. -16 + (-7) ...this is the same as -16-7

3 0
2 years ago
TEMA: Propriedade de Potência e Multiplicação de Números Negativos e Positivos.
GalinKa [24]
The correct answer is 34
7 0
3 years ago
What is the value of x?
Lunna [17]

Answer:

x = 23 degrees

Step-by-step explanation:

sin theta = opposite side/ hypotenuse

sin x= 9/23

Take the arcsin of each side

arcsin( sinx) = arcsin (9/23)

x = arcsin (9/23)

x=23.03568411

Rounding to the nearest degree

x = 23 degrees

4 0
3 years ago
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