# Algebra

1. The mass of Earth is about 6 x 10^21 metric tons. The mass of the sun is about 1.998 x 10^27 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation.

2. The perimeter P of a square of side x is given by the polynomial equation: P=4x. A baseball diamond is a square 90 ft on a side. Find the perimeter of a baseball diamond.

3. Hadley Electronics is marketing a new kind of plasma TV. The firm determines that when it sells x TVs, its total revenue R (the total amount of money taken in) will be R = 280x - 0.4x^2 dollars. What is the total revenue from the sale of 75 TVs?

4. The polynomial equation C = 0.041h - 0.018A - 2.69 can be used to estimate the lung capacity C, in liters, of a female of height h, in centimeters, and age A, in years. Find the lung capacity of a 20-year-old woman who is 165 cm tall.

5. A researcher wants to investigate the potential spread of germs by contact. She knows that the number of possible handshakes within a group of x people, assuming each person shakes every other person's hand only once, is given by the following formula.

Use this formula for the following exercises. N = (1/2)(x^2 - x).

a. There are 100 people at a party. How many handshakes are possible?

b. Everyone at a meeting shook hands with each other. There were 300 handshakes in all. How many people were at the meeting?

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#### Solution Preview

Please refer to the attachment for the solutions.

1. Earth vs. Sun. The mass of Earth is about 6 x 1021 metric tons. The mass of the sun is about 1.998 x 1027 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation.

Solution:

Mass of Sun/ Mass of Earth = 1.998 x 1027 metric tons/6 x 1021 metric tons = 333000

= 3.33 x 105.

So, the mass of the Sun is about 3.33 x 105 times the mass of the Earth.

2. Perimeter of a Baseball Diamond. The ...

#### Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given algebra problems and provides a clear perspective of the underlying concepts.

Algebra Homework Help 5: To show your work, you will need to include the algebra used to compute the solution to any equations.

1. The following graph shows how a 4-color web printing press depreciates from the year 2006 to the year 2010. It was purchased new in the year 2006; therefore x = 0 represents the year 2006.

X - axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years

Y - axis (vertical) = price in $ amounts

a) List the coordinates of any two points on the graph in (x, y) form.

(___, ___),(___, ___)

b) Find the slope of this line:

c) Find the equation of this line in slope-intercept form.

d) If trend for the depreciation of the press continued, what would be its value in the year 2015? Show how you obtained your answer using the equation you found in part c).

2. Suppose that the length of a rectangle is three cm longer than twice the width and that the perimeter of the rectangle is 90 cm.

a) Set up an equation for the perimeter involving only W, the width of the rectangle.

b) Solve this equation algebraically to find the length of the rectangle. Find the width as well.

Length ______, Width ______

3) A temporary agency offers two payment options for administrative help:

Option1: $25 daily fee plus $10/hour; or

Option 2: No daily fee but $15/hour

Let x = total hours worked.

a) Write a mathematical model representing the total temp cost, C, for a four-day temporary administrative assistant in terms of x for the following:

Option 1: C=_________________

Option 2: C=_________________

b) How many total hours would the temp need to work in the four day period for the cost of option 1 to be less than option 2. Set up an inequality and show your work algebraically using the information in part a. Don't forget about the daily fee in Option 1 (it's a four day proposition!). Do not assume an eight our workday. Any number of hours per day is possible.

4) Use the graph of y = 7 - 6x - x2 to answer the following:

a) Without solving the equation (or factoring), determine the solutions to the equation 7 - 6x - x2 = 0 using only the graph. Explain how you obtain your answer(s) by looking at the graph:

b) Does this function have a maximum or a minimum? Explain how you obtain your answer by looking at the graph:

c) What is the equation of the line (axis) of symmetry for this graph?

d) What are the coordinates of the vertex in (x, y) form?

5) The profit function for the Recklus Hang gliding Service is P(x) = -0.4x2 + fx - m, where f represents the set up fee for a customer's daily excursion and m represents the monthly hanger rental. Also, P represents the monthly profit in dollars of the small business where x is the number of flight excursions facilitated in that month.

a) If $40 is charged for a set up fee, and the monthly hanger rental is $800; write an equation for the profit, P, in terms of x.

b) How much is the profit when 30 flight excursions are sold in a month?

c) How many flight excursions must be sold in order to maximize the profit? Show your work algebraically. Trial and error is not an appropriate method of solution - use methods taught in class.

d) What is the maximum profit?

6. Graph the equations on the same graph by completing the tables and plotting the points. You may use Excel or another web-based graphing utility.

a) y = 2x - 5

Use the table; find at least 3 points using any values for x.

x y

-1

1

3

b) y = 3x - x2

Use the values of x provided in the table.

x y

-1

0

1

2

3

4