First, set the quadratic function equal to :

Then, separate the function into its two component factors:

It follows from this equation that either  or , 

The area of a rectangle is the product of its length by its width, which we know to be equal to  in our problem. We also know that the length is equal to , where  represents the width of the land. Therefore, we can write the following equation:

Distributing the  outside the parentheses, we get:

Subtracting  from each side of the equation, we get:

We get a quadratic equation, and since there is no factor of  and  that adds up to , we use the quadratic formula to solve this equation.

We can first calculate the discriminant (i.e. the part under the square root)

We replace that value in the quadratic formula, solving both the positive version of the formula (on the left) and the negative version of the formula (on the right):

Breaking down the square root:

We can pull two of the twos out of the square root and place a  outside of it:

We can then multiply the  and the :

At this point, we can reduce the equations, since each of the component parts of their right sides has a factor of :

Since width is a positive value, the answer is:

 The width of the piece of land is approximately .

The focus is solved by using the following formula , where  are the coordinates of the vertex, and  is the distance from the vertex. To solve for , we use

, where  is the coefficient in front of the  term and  is the focus.

Since , we can substitute in to get,

Now we need to find the vertex of the equation.

Since our equation is in vertex form, we can deduce that the vertex is at 

So the focus is at 

In order to find all the solutions, we need to set the equations equal to each other.

Now subtract  and  from each side.

Factor the left hand side to get

Factor the quadratic function inside the parenthesis to get

The solutions to this equation are

To figure out how many x-intercepts there are, we need to set out equation equal to zero.

Factor an x out

Factor inside of the parenthesis.  

We can see there are 3 x-intercepts at .

If the equation 

were graphed, the result would be a line with a slope of 0.5 and a y-intercept of 1.2. 0.5 represents the amount Tonya pays per hour to work at a computer, because we know that the rate is $0.50, and C represents the total amount she pays. Because we must add 1.2 (or $1.20) to the total amount of hours multiplied by the hourly rate in order to get the total amount Tonya paid, we can assume there is another charge for renting a computer, in addition to the hourly rate, and that that charge is $1.20. Therefore, the y-intercept of the graph of the equation represents the initial cost of using a computer. 

We start by cross multiplying to get the equation 26t=19t-95. We then subtract 19t from 26t giving us 7t= -95. We then divide by 7, giving us t= (-95)/7.

1. Solve for x in x/3 = 50

2. x = 150

3.Substitute 150 for x in x/10

4. x = 15

There are only x * 10 liters of water on the island. n * m equals how many liters are consumed per day. Divide x * 10 liters by n * m. Note the units (days) are correct in the answer.

The amount of money that Lauren can make depends on the number of sweaters that she can make. If she makes at most s sweaters a day, then we can multiply the number of days that she works by s to determine the total number of sweaters she makes.

total number of sweaters = (s)(number of days)

We are told to consider a time interval of three weeks. Because there are seven days in one week, the number of days over this period of time would equal 3(7), or 21 days. In other words, there are 21 days in three weeks Thus, the number of sweaters is equal to the product of s and 21.

total number of sweaters = (s)(21)

Now that we have the number of sweaters Lauren can make, we can multiply this by the cost of each sweater, which is equal to c cents, in order to obtain the amount of money she eared.

amount of money earned = (number of sweaters)(cost of each sweater)

amount of money earned = s(21)(c)

However, because the price of each sweater is given in terms of cents, the amount of money s(21)(c) will be equal to the number of cents she makes. The question, though, asks us to find the amount of money in dollars. We must use a conversion factor to change the number of cents to dollars. Remember that there are 100 cents per dollar.