08.12.2022 the following question

# QUESTION 1. 1A. Prove that GCD(a, a+2) = 1 if a is odd, and GCD(a, a+2) = 2 if a is even 1B. Show that if a≡b(mod n) and if b≡c(mod n), then a≡c(mod n) 1C. Simplify the following congruences: 15x≡9 (mod 25) 6x≡3 (mod 9) 14x≡42 (mod 50) 1D. Describe the general solution for x and y, if it exists: 35x+47y=1 Request clarification:Expert:We answer only one question at a time. You decide User: Hello, this is one question with 4 parts. If not possible to answer all please answer part C and D Expert:I can solve Only D.. do you want itUser: Okay then, is there another part you can also solve? If yes, please assist also 6

08.12.2022, solved by verified expert
1 students found this answer helpful

-4+47.k, 3-35.k

Step-by-step explanation:

A)

If a = 1, then gcd(1, 3) = 1.

If a > 1, then lets execute a single step of the Euclidean algorithm:

gcd (a+2, a) = gcd(a, (a + 2) mod a)

[Here, "x mod y" denotes the remainder of division of x by y.]

Now, clearly, (a + 2) mod a = 2, since a > 2. (a is

odd, and a 1, so a has to be at least 3.)

So, we have

gcd(a+2, a) = gcd (a, 2).

Continuing with the Euclidean algorithm, we get

gcd(a, 2)= gcd (2, a mod 2).

We know that a is odd, i.e., a mod 2 = 1, and clearly gcd (2, 1) = 1.

D) ### Faq

Mathematics

310%

310/100=3.10

(3.10)(72)

Mathematics

Change in price = \$84.50 - \$50.70 = \$33.80

% change in price = (change in price)/Orignal price * 100

= 33.80/50.70 * 100 = 40%

Decrease in price = 40%

Mathematics

The answer is in the image Mathematics

The answer is in the image Mathematics
Answer: y < −2x + 3.

Explanation:
See the graph below.
Process:
1.- Find the slope
m=y2-y1/x2-x1;
Substitution
m=-1-3/2-0;
m=-4/2;
m=-2.
2.- Find the equation of the line
y - y1 = m(x - x1);
Substitution
y - 3 = -2(x - 0).
Simplify and solve for y
y - 3 = -2x;
y = -2x + 3.
3.- Write the inequality
As the left area of the plane is shaded the inequality must be
y < -2x + 3. Mathematics The answer is in the image

Mathematics

The answer is in the image Mathematics

Origanal price of tv = \$600

30% of \$600 =(30/100)*600 = \$180

Price after discount = \$600 - \$180 = \$420

Price after discount = \$420 - \$35 =\$385

Final price = \$385

Mathematics