Question

Use the set of ordered pairs below to answer each question.

{(4, 20), (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}
a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3.
b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.
c. Write the ordered pair(s) whose second coordinate is a prime number.

Answer 1

The ordered pairs with a GCF of 3 are (6, 15), (6, 30), and (6, 18). Pairs where the first coordinate is a factor of the second are (1, 5) and (8, 4). Pairs with a prime number as the second coordinate are (2, 3), (15, 3), and (0, 3).

Step-by-step explanation:

To solve the student's question, we need to analyze the given set of ordered pairs, which are: {(4, 20), (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}.

a. The ordered pairs whose first and second coordinate have a greatest common factor (GCF) of 3 are (6, 15), (6, 30), and (6, 18), as the numbers in each pair share 3 as their common factor.

b. The ordered pair(s) whose first coordinate is a factor of its second coordinate are (1, 5) and (8, 4), since 1 is a factor of 5, and 8 is a factor of 4.

c. The ordered pair(s) whose second coordinate is a prime number are (2, 3), (15, 3), and (0, 3), as 3 is the only prime number in the second coordinates.

Answer 2

a) {(15,3)}

b) {(4,20), (6,30), (6,18)}

c) {(2,3), (15,3), (1,5), (0,3)}

Step-by-step explanation:

We are given the following ordered pair:

{(4, 20), (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}

a)Ordered pair whose first and second pair has a greatest common factor of 3. Since GCD of 15 and 3 is 3.

{(15,3)}

b)First coordinate is a factor of second coordinate

{(4,20), (6,30), (6,18)}

Since 4 is a factor of 20, 6 is a factor of 30 and 6 is a factor of 18.

c) Second coordinate is a prime number.

{(2,3), (15,3), (1,5), (0,3)}

Since 3 and 5 are prime numbers.