Which two ratios form a proportion a) 1:2 and 4:2 b) 1:2 and 2:4 c) 2:1 and 2:4 d) 2:1 and 6:3

Mathematics

1 answer:

algol133 years ago

6 0

Answer:

The ratios in option b and d form a proportion.

Step-by-step explanation:

Option a)

1:2 and 4:2 or 1/2 and 4/2

1:2 or 1/2 is already in the simple form

Let us reduce 4:2 or 4/2 to check whether it is equal to 1/2 or not

as 4/2 = 2/1 which is NOT equal to 1/2

Thus, 1:2 and 4:2 are NOT in proportions

Option b)

1:2 and 2:4 or 1/2 and 2/4

1:2 or 1/2 is already in the simple form

Let us reduce 2:4 or 2/4 to check whether it is equal to 1/2 or not

as 2/4 = 1/2 which is EQUAL to 1/2

Thus, 1:2 and 2:4 are in proportions

Option c)

2:1 and 2:4 or 2/1 and 2/4

2:1 or 2/1 is already in the simple form

Let us reduce 2:4 or 2/4 to check whether it is equal to 2/1 or not

as 2/4 = 1/2 which is NOT equal to 2/1

Thus, 2:1 and 2:4 are NOT in proportions

Option d)

2:1 and 6:3 or 2/1 and 6/3

2:1 or 2/1 is already in the simple form

Let us reduce 6:3 or 6/3 to check whether it is equal to 2/1 or not

as 6/3 = 2/1 which is equal to 2/1

Thus, 2:1 and 6:3 are in proportions

Therefore, the ratios in option b and d form a proportion.

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Answer:

k=45

Step-by-step explanation:

Since the sum of the measures are 180 and the measures are 45 degrees, k degrees, and 2k degrees, we can conclude that $45+2k+k=180$ . 2k and k are like terms, so you can add 2k and k to get 3k.Then, you would have $45+3k=180$ . Since you are finding k, you want to isolate k as best you can. To do this, you subtract 45 on both sides $45-45+3k=180 -45 \\3k=135$ as shown by the equation, 180-45 is 135. Then, you divide 3 on both sides to get k=45.