Two workers in a holiday boutique are filling stockings with small gifts and candy. kate had already filled 5 stockings and will continue to fill them st a rate of 4 stockings per hour. todd, who just arrived to , can fill 5 stockings per hour. at some pint, todd will catch up with kate and they will have completed the same number of stockings. how long will it take for todd to catch up?

After 5 hours they both catch up.

Step-by-step explanation:

Given : Two workers in a holiday boutique are filling stockings with small gifts and candy.

Kate had already filled 5 stockings and will continue to fill them st a rate of 4 stockings per hour.

Todd, who just arrived to help, can fill 5 stockings per hour. At some pint, Todd will catch up with Kate and they will have completed the same number of stockings.

To find : How long will it take for Todd to catch up?

Solution :

We know, Kate has already filled 5 stocking.

She fills 4 stockings every hour.

Let after x hours Kate filled stockings

Total stoking Kate has made is =

Now, Todd started out with none done.  He fills 5 stockings per hour.

So, after x hours he fill stockings.

Total stockings Todd has made is =  

We have to find when they catch up

We equate the equations,

Therefore, After 5 hours they both catch up.

answer: h

step-by-step explanation:

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