Six students collect buttons for a project. the students have 10, 14, 15, 12, 13, and 14 buttons. they divide the buttons evenly so that each student receives the same number of buttons. how many buttons does each student receive?

There are 13 buttons each student receives.

Step-by-step explanation:

Since we have given that

Number of students collect buttons for a project = 6

Number of buttons collected by 6 students is given as

So, Total number of buttons they  collect altogether,

Now, according to question, they divide the buttons evenly so  that each student receives the same number of buttons,

Hence, there are 13 buttons each student receives.

"a" determine whether sage found the correct quotient. show your work

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