Sarah cut off 1/8 of a 48 inch piece of ribbon. Jane cut off 1/9 of a 36 inch piece of ribbon. They compared their cut pieces. Whose piece is longer? How much longer?

Sarah's, 2 inches.

Step-by-step explanation:

Given:

Sarah cut off 1/8 of a 48 inch piece of ribbon.

Jane cut off 1/9 of a 36 inch piece of ribbon.

Question asked:

Whose piece is longer ?

How much longer ?

Solution:

As Sarah cut off 1/8 of a 48 inch piece of ribbon, means she has cut piece of size:

As Jane cut off 1/9 of a 36 inch piece of ribbon, means she has cut piece of size:

As Sarah has 6 inches piece of ribbon and Jane has 4 inches piece of ribbon so Sarah's piece longer.

Now, to find it is how much longer we will subtract Jane's piece of ribbon from Sarah's piece of ribbon,

6 inches - 4 inches = 2 inches.

And hence,  Sarah's piece of ribbon is 2 inches longer than Jane's  piece of ribbon .

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1