Algebra Answers

If you share a six-bar chocolate among the following number of people, how much will each receive? Illustrate your answer
1. 6 people.
2. 3 people.
3. 5 people.

A. Give the definition of linear and quadratic function in terms of formula and geometric meaning.

B. Define exponential function and give its practical significance.

C. Define logarithmic function and give its practical significance.

A manufacturer of graphing calculators has determined that 9,000 calculators per week will be sold at a price of $85 per calculator. At a price of $80, it is estimated that 11,000 calculators will be sold.

1. Determine a linear function that predicts the number of calculators that will be sold per week at a price of x dollars.


2. Use the function to find the cost of using the cellular phone for 13 min in 1 month.

A manufacturer of graphing calculators has determined that 9,000 calculators per week will be sold at a price of $85 per calculator. At a price of $80, it is estimated that 11,000 calculators will be sold.

1. Determine a linear function that predicts the number of calculators that will be sold per week at a price of x dollars.

y = ____

2. Use this model to predict the number of calculators that will be sold at a price of $65.

Karen is throwing an orange to her brother Saul, who is standing on the balcony of their home. The height h, in feet, of the orange above the ground t seconds after it is thrown is given by
h(t) = −16t2 + 32t + 5, 0 ≤ t ≤ 2.118.

If Saul's outstretched arms are 19 feet above the ground, will the orange ever be high enough so that he can catch it?

A. No. The orange will reach a maximum height of 10 feet.
B. No. The orange will reach a maximum height of 5 feet.
C. Yes. The orange will reach a maximum height of 21 feet.
D. There is not enough information given to answer the question.
E. Yes. The orange will reach a maximum height of 42 feet.

A university employs a total of 680 teaching assistants and research assistants. There are three times as many teaching assistants as research assistants. Find the number of research assistants employed by the university.

1. A cellular phone company charges $60 per month for a service plan that includes 500 free text messages. In addition to the basic monthly rate, the company charges $0.15 for each additional text message over 500. A customer on this plan receives a bill for $111.30. How many text messages did this customer send and receive during the month?

2. You have a choice of receiving a wage of $34,000 per year, $2940 per month, $690 per week, or $16.10 per hour. Which pay choice would you take? Assume a 40-hour work week and 52 weeks of work per year.
A. $34,000 per year
B. $2940 per month
C. $690 per week
D. $16.10 per hour

Dean Baker, co-director at the Center for Economic and Policy Research in Washington, D.C., suggests that the buy-versus-rent question can be answered using the price-to-rent ratio. Find two houses of similar size and quality in comparable neighborhoods, one for sale and the other for rent. Divide the price of the house for sale by the total cost of the rental for 1 year. If the quotient is higher than 20, renting might be the better option. If the quotient is below 15, buying might be the better option.

1. A house in Orlando, Florida, is priced at $150,000. The rent on a comparable house is $850 per month. Find the price-to-rent ratio. Round to the nearest tenth.

2. Does the ratio suggest that you buy or rent a home in Orlando?
A. Yes
B. No

A. What is an equation?

B. Explain the difference between a linear and a quadratic equation in terms of degree and solution.

C. Give a concise definition of the following:
1. Rate
2. Ratio
3. Proportion

There are 7 notes of "A" on a standard piano. When the third A is struck, the string associated with the key vibrates 220 times per second. The next A above the given A vibrates twice as fast. An exponential function with a base of two is used to determine the frequency of the 11 notes between the two A's.

Find this function. Hint: The function is of the form f(x) = k · 2(cx),where k and c are constants. Also f(0) = 220 and f(12) = 440.