For each of the following pairs of numbers, find the gcd of the two numbers, and express the gcd as a linear combination of the two numbers. (a) 56 and 42 (b) 81 and 60

a. 14 and 14= (-1)56+1(44)

b. 3 and 3= (-4)60+3(81)

Step-by-step explanation:

Case 1: GCD is the highest common divisor for both numbers without reminder

a. GCD of 56 and 42 = 14

b GCD of 81 and 60 = 3

Case 2: Express GCD as a Linear combination.

a. GCD = 14 which is also the difference between 56 and 42

Therefore

14= (-1)56+1(44) expresses 14 as a linear combination of 56 and 44.

b. GCD=3, we need to look for a multiple of 60 and 81 that their differences would be 3

Therefore the multiples are:

For 60 = 240 (60×4)

For 81 = 243 (81×3)

3= (-4)60+3(81) expresses 3 as a linear combination of 81 and 60

1/3 + 1/5 = 8/15.

step-by-step explanation:

hope it

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180