Lucy bought a doormat for $7 and some placemats for $2 each. her total average cost per item was $3. create a rational equation, and determine how many placemats she bought.
she bought
placemats.

(2x+7)/(x+1) = 3; Relation

Lucy bought 4 place-mats

Step-by-step explanation:

Let the number of place-mats bought by Lucy be equal to x. The total cost of these x place-mats, at $2 each, would be;

2x

Her total cost will then be;

2x + 7; since she bought one doormat at $7.

The total items bought by her is then equal to;

x + 1

Her total average cost can thus be given as;

total cost / total number of items

(2x+7)/(x+1)

Therefore, we can formulate the following relation;

(2x+7)/(x+1) = 3; since the average cost per item was $3

2x+7 = 3(x+1)

2x+7 = 3x + 3

7-3 = 3x-2x

4 = x

Therefore, Lucy bought 4 place-mats

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

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step-by-step explanation: