MATH 099 HOMEWORK TWO

Transcription

1 MATH 099 HOMEWORK TWO STUDENT S NAME 1) Matthew needs to rent a car for 1 day. He will be charged a daily fee of $30.00 in addition to 5 cents for every mile he drives. Assign the variable by letting x be the number of rental miles he drives y be the total cost. a) Write an expression for the total cost to rent a car. b) Which part of the formula represents the variable cost? c) Which part of the formula represents the fixed cost? d) What is the total cost if Matthew drives 200 miles? 2) A painter has a painting worth $10,000 but knows that it is appreciating at a rate of 4% per year. The painter is interested in making some money from it so the painter decided to wait a few years before selling the painting. a) Write an expression for the total cost of the painting. b) Which is the independent variable and which is the dependent variable? c) Make a table by hand for values of 2, 4, 6, and 8 years of appreciation. 3) Assume a new product costing $15,000 depreciates the same amount each year. Its remaining value can be found by subtracting the product of $1000 and the years of service from $15,000. a) Represent this function by a formula, a table of values, and a graph. b) What is the range of values for the product? USE THE FOLLOWING INFORMATION FOR PROBLEMS 5-8 British Airways Airline Company charges $ plus $0.50 per mile of travel. 4) Let x represent the number of miles of travel and let y represent the cost (in dollars) of the travel. a) Write a formula that shows how y depends upon x.

2 b) What is the independent variable? c) What is the dependent variable? 5) By hand, create a table of values with inputs of x = 100, 200, 300, and 400 miles. 6) How much will it cost to travel 700 miles on British Airways? 7) Jack and Jill buy a total of 52 lottery tickets. Jill buys 8 less than twice the number of tickets that Jack buys. How many tickets did Jack buy? How many tickets did Jill buy? 8) Each month Rachel has spring water delivered to her apartment. She rents a water dispenser for $6.50 per month. Each jug each jug of water costs $3.75. She budgets $30.00 per month for water and the dispenser. How many jugs of water can she buy each month? 9) The perimeter of a rectangle is 98 feet. The width of the rectangle is 5 feet more than one third the length. Use the seven steps for problem solving to find the width and length of the rectangle. 10) Two insects are 100 feet apart at 11:00 A.M. The insects move toward each other, with the junior insect traveling 8 feet per minute and the older insect traveling 12 feet per minute. At what time will they meet? 11) The weekly savings (S) for an employee is given by the formula S =.06P + 20, where P is his weekly pay. Find his pay if he saves $70.00.

3 14a) Are the expressions x + + and equivalent? Explain. 14b) Use the order of operations to evaluate ) For the equation 2x 2y 6: (a.) Find the x- intercept. (b.) Find the y- intercept. (c.) Draw the graph of the equation. Be sure to show the appropriate scale and label the x and y axis. 16) Solve for x and y using an algebraic method(substitution, elimination or graphically): y 9x 6 x 2y 12 17) Find the slope and the y- intercept of the line with the equation: 6x 3y ) Evaluate the formula y mx b for m 2,x9 and b = ) Graphically solve the following system of equations (draw a graph). Clearly label the solution: y 3x 2 4 3x y 20) Given the following table of values: x y 0-4

4 (a.) Identify the x- and y- intercepts. (b.) Use the intercepts from part (a.) to draw the graph below. (c.) Find the slope. (d.) Use the slope and y- intercept to write an equation. 21) Determine whether (4, -3) is a solution to the equation 3x 3y = 21 22) Find the slope and y- intercept of the line with the equation -3x 7y = -8 23) Write the equation of the line with a slope of and y- intercept of (0, -2). 24) Solve for x and y by using an algebraic method(substitution or elimination): 2x 4y = 14 and 5x + 3y = 9 25) Solve for x and y and reduce your answers to lowest terms: a) = b) = + 26) Solve for z: -2(z-1) +5(z-1) = 9

5 27) Simplify: (-2x-3 )-(-5-2x)+(3x-4 ) 28) Evaluate: 29) For the equation x y = 1: a) Find the x-intercept. b) Find the y-intercept c) Draw the graph of the equation. Be sure to show the appropriate scale and label the x and y- axis. 30) Draw a grid or coordinate plane and graphically solve the following system of equations. Clearly label everything. Y = 3x + 1 and Y = 2x ) Given the following table of values for a linear function: x y a) Identify the x- and y-intercepts. b) Use the intercepts from part a) to draw a graph. c) Find the slope. d) Use the slope and y-intercept to write an equation. 32) The sum of two numbers is 78. The difference of the numbers is 29. What are the two numbers?

6 33) Jim runs faster than Dave. Jims gives Dave a 15 minute head start in the race. If Jim runs 9 miles per hour and Dave runs 7 miles per hour, how long does it take Jim to catch up to Dave? If you were to solve this problem by using a system of equations, would the system of equations be consistent or inconsistent? 34) Jennifer has $5000 to invest. She wants to maximize her income but portion her investments to reduce risk. She decides to invest in a CD paying 6% interest per year and a lower grade bond paying 11% per year. How much should she put into each investment in order to earn an overall yield of 8%? 35) A checking account pays an annual interest rate of 0.3% and a savings account pays an annual interest rate of 0.7%. If you have $25,000 to invest, how much would you have to invest in each account in order to earn $150 in interest for a year? 36) a) Write in standard decimal notation. B) Write 13,275.0 in scientific notation. 37) a) What is 33% of 150? B) What percent is 25 out of 175? 38) At a local gas station, the price of gasoline rose from $3.29 per gallon to $3.59 per gallon. Find the percent increase. 39) Solve the following proportions for x: A) = B) + =

7 40) Latasha can read 15 pages in 25 minutes. At this rate, how long will it take her to read a 1045 page novel?