A new American graduate is contemplating buying a Japanese, German, or an American car. No matter the type of car, he plans to buy a new one at the end of 8 years.
Japanese car will cost $30,000 and have a fuel usage of 23 Miles Per gallon (mpg) for the first 2
years, and will decrease by 3% per year thereafter. Repair cost will start at $700 per year, and
increase by 3% per year. At the end of year 8, the car can be sold for $5000. Insurance cost will
be $700 for the first year, increasing by 2% per year thereafter.

 Japanese car

Step-by-step explanation:

Given

  problem details in Attachment 1

Find

  the most economical car

Solution

The attached spreadsheet shows the costs of repairs, insurance, and gas for each of the cars, using the cost factors described in the problem statement. (Numbers are displayed rounded to dollars.)

Mileage each year is assumed to be 150,000/8 = 18,750.

The "present value" line shows the present (year 0) value of the listed costs. The present value is the sum of values divided by 1.05^(year number). It is calculated using the spreadsheet NPV function.

The green total is the sum of present values to its right and the initial cost. The end value is subtracted after it is discounted by 1.05^8.

The Japanese car has the lowest present value.

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The third attachment is the spreadsheet in Open Office format.

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc