An average person in the United States throws away 4.5 × 10² grams of trash per day. In 2013, there were about 3.2×106 people in
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A used book store buys a hardback book for $1.50 and then sells it for $5. Over time, the store sells the same number of books it buys. The store manager can use the equation P(x)=5x−1.5x to determine the store's profit, P(x), where x is the number of books that the store sells. Which statement about the book store is true based on the profit equation?
Cost Price of book, C.P.=$1.50
Selling Price of book, S.P.=$5
PROFIT=S.P. -C.P.
So, Profit=$5-$1.50=$3.50
So, Profit=$3.50 on each book
Or, we are given P(x)= 5x-1.50x
Or, P(x)=3.50x
For each book, we must divide the profit P(x) by x, that is, number of books
So, Profit for each book sold is $3.50
Answer:Option C
Keywords:
<em>Quadratic equation, vertex shape, parabola </em>
For this case we have to rewrite the given quadratic equation, in the form of vertex, for this, we must take into account that a quadratic equation of the form , can be rewritten in the form of vertex as:
Vertice is the lowest or highest point of the parabola. The vertex is given by:
. So, let:
, to find the equation in the form of vertex, we follow the steps below:
Step 1:
We take the common factor to the first two terms of the equation:
Step 2:
We work square:
We divide the coefficient of the term by 2 and its result is squared, that is:
So, we have:
Step 3:
We simplify:
Step 4:
We factor:
Thus,
Answer:
The equation in the form of vertex is: , and the vertex is