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3 years ago

Let a >= b. show that gcd(a,b) = gcd(a-b, b)

Mathematics

1 answer:

Deffense [45]3 years ago

5 0

let $\gcd(a,b)= G$ , $a\ge b$

$\therefore a=G\cdot m$ and $b=G\cdot n$

$a-b=Gm-Gn=G(m-n)$

Now, $\gcd(a-b,b)$ clearly is, $G$

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Is the association between x and y positive or negative?<br> A. none B.positive C, negative

Vinvika [58]

Answer:

A.non at all so, please choose the right answer

8 0

3 years ago

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What is the converse of the statement?<br> "If x - 2 = 5, then x = 7"

dlinn [17]

ANSWER

"If x=7, then x - 2 = 5"

EXPLANATION

Let

$p \to \: q$

be a propositional statement.

The converse of this statement is

$q \to \: p$

In other words, the converse of the statement,

"If p then q" is "If q, then p"

The given given conditional statement is

"If x - 2 = 5, then x = 7"

Therefore the converse is

"If x=7, then x - 2 = 5"

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3 years ago

How do I solve The sum of a number and 3 is subtracted from 10 the result is 5

meriva

State the given in the question

Given that the sum of a number and 3 is subtracted from, the result is 5

State what is to be found in the question

We are to find the number. In other to achieve this, we would follow the steps below:

Step 1: Represent the number with an unknown

Let x represent the number

Step 2: Interpret the given statement mathematically

If x is the number, then the sum of the number and 3 would be

$x+3$

Then the sum of a number and 3 subtracted from 10 would be

$10-(x+3)$

Finally, when the sum of a number and 3 subtracted from 10, the result is 5, would be

$10-(x+3)=5$

Step 3: Solve for x in the mathematical interpretation of the given statement

The value of x is as calculated as shown below:

$\begin{gathered} 10-(x+3)=5 \\ \text{Open the bracket or the parenthesis} \\ 10-x-3=5 \\ \text{collect like terms} \\ 10-3-5=x \\ 7-5=x \\ 2=x \\ \text{Therefore:} \\ x=2 \end{gathered}$

Hence, the number is 5

4 0

1 year ago

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC

jarptica [38.1K]

We are given

△ABC, m∠A=60° m∠C=45°, AB=8

Firstly, we will find all angles and sides

Calculation of angle B:

we know that sum of all angles is 180

m∠A+ m∠B+m∠C=180

we can plug values

60°+ m∠B+45°=180

m∠B=75°

Calculation of BC:

we can use law of sines

$\frac{AB}{sin(C)}=\frac{BC}{sin(A)}$

now, we can plug values

$\frac{8}{sin(45)}=\frac{BC}{sin(60)}$

$BC=\frac{8}{sin(45)} \times sin(60)$

$BC=9.798$

Calculation of AC:

$\frac{AB}{sin(C)}=\frac{AC}{sin(B)}$

now, we can plug values

$\frac{8}{sin(45)}=\frac{AC}{sin(75)}$

$AC=\frac{8}{sin(45)} \times sin(75)$

$AC=10.928$

Perimeter:

$p=AB+BC+AC$

we can plug values

$p=10.928+8+9.798$

$p=28.726$

Area:

we can use formula

$A=\frac{1}{2}AB \times AC \times sin(A)$

now, we can plug values

$A=\frac{1}{2}8 \times 10.928 \times sin(60)$

$A=37.85570$ ...............Answer

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4 years ago

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Which number is a multiple of 7? A 27 B 48 C 56 ET D 74

saul85 [17]

Answer:

C. 56

Step-by-step explanation:

7*8=56

7 0

3 years ago

Let a >= b. show that gcd(a,b) = gcd(a-b, b) ​

Let a >= b. show that gcd(a,b) = gcd(a-b, b)