University of Maryland Global Campus Coordinate Plane Algebra Questions

3 – Suppose receiving stations A, B, and C are located on a coordinate plane at the points (1, 4), (-3, -1), and (5, 2). Let the distances from the earthquake epicenter to these stations be 2 units, 5 units, and 4 units, respectively. Where on the coordinate plane is the epicenter located?

6- Find the function g(x)=ax+b
whose graph can be obtained by translating the graph of f(x)=3−xdown 2 units and to the right 3 units.

8- An artist has sold a painting for $410,000. He needs some of the money in 6 months and the rest in 1 year. He can get a Treasury bond for 6 months at 2.65% and one for a year at 2.91%. His broker tells him the two investments will earn a total of $8671. How much should be invested at each rate to obtain that amount of interest? First indicate the amount to be invested at 2.65%, then indicate the amount to be invested at 2.91%. (Round your answers to the nearest whole number and do not use commas or dollar symbols in your answer.)

11- A PTA group sold homemade donuts to raise money for new computers. The donuts were sold for $7.00 per box and $0.50 for a single donut. If the PTA group raised $600 and sold 78 boxes, how many single donuts did they sell?

13- The area of a single room apartment is advertised as 171 square feet. You call the facility and are told that the length of the room is 10 feet longer than its width. Which of the following is one of the two dimensions of the room?

14- Find two numbers whose sum is 7500 and whose product is the maximum value. (Round your answer to the nearest whole number.)

20- A standard piece of notebook paper measuring 8.5 inches by 11 inches is to be made into a box with an open top by cutting equal-size squares from each corner and folding up the sides. Let x{“version”:”1.1″,”math”:”x”}
represent the length of a side of each such square (in inches). Find the maximum volume of the box in cubic inches. (Round your answer to four significant digits.)

22 – The millage rate is the amount of property tax per $1000 of the taxable value of a home. For a particular county, the millage rate is 29 mil. A city within the county also imposes a flat fee of $101 per home. Which of the following models the taxable value of a home (in $1000) based on x dollars of property tax paid on the home?

28- The traditional IRA (individual retirement account) is a common tax-deferred saving plan in the United States. Eared income deposited into an IRA is not taxed in the current year, and no taxes are incurred on the interest paid in subsequent years. However, when you withdraw the money from the account after age 59.5, you pay taxes on the entire amount you withdraw.

Suppose you deposited $5000 of earned income into an IRA, you can earn an annual interest rate of 4%, and you are in a 25% tax bracket. Also, suppose that you deposit the $5000 at age 25 and withdraw it at age 60, and that interest is compounded continuously. Suppose that instead of depositing the money into an IRA, you pay taxes on the money and the annual interest. How much money will you have at age 60?