Which of the following shows that ABCD is a parallelogram for x=6 and y =8? (20 points)

AB = CD = 44 and BC = AD = 31 ; so ABCD is a parallelogram

Step-by-step explanation:

A parallelogram should have two pairs of parallel sides meaning the length of side AB should be the same as the length of side CD and the length of side AD should be the same as the length of side BC.

First, lets see if line AB is parallel to line CD.

Let's start by finding out the length of line AB.

Since we know x = 6 we will replace x with 6 in the expression:

7(6) + 2 = 42 + 2 = 44

Now that we know the length of line AB is 44, lets find the length of line CD by replacing x with its value of 6:

9(6) - 10 = 54 - 10 = 44

Now that we know the length of line CD is 44, we can see that line AB is parallel to line CD since they both have the same length of 44.

Now, lets see if line BC is parallel to line AD.

Let's start by finding out the length of line BC.

Since we know y = 8 we will replace y with 8 in the expression:

3(8) + 7 = 24 + 7 = 31

Now that we know the length of line BC is 31, lets find the length of line AD by replacing y with its value of 8:

5(8) - 9 = 40 - 9 = 31

Now that we know the length of line AD is 31, we can see that line BC is parallel to line AD since they both have the same length of 31.

Conclusion

ABCD is a parallelogram because it contains two parallel sides.

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step-by-step explanation:

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.