1. The following equations are given: Equation #1: 3x + z + y = 8 Equation #2: 5y - x = -7 Equation #3: 3z + 2x - 2y = 15 Equation #4: 4x + 5y - 2z = -3 a. Is it possible to solve for any of the variables using only Equation #1 and Equation #2? Explain your answer. If possible, solve for the variables using only equations #1 and #2. b. Is it possible to solve for any of the variables using only Equation #1, Equation #2, and Equation #3? Explain your answer. If possible, solve for the variables using only equations #1, #2, and #3. c. If you found solutions in part b, do these solutions also hold for Equation #4? B i U Font Family AVA DE EE . O2. If you have a savings account, contact your bank and find out the interest rate on that account. (If you don't have your own account, contact a local bank to ask what the interest rate would be if you set up a savings account today.) a. State the interest rate the bank quoted. b. Write an exponential growth equation that models the yearly growth if you put $625 in the account and left it there for a years. c. What will be the value of the account in 25 years? d. Which of the following would result in more money: $625 deposited in your bank at the current interest rate for 6 years, or deposit $625 into a money market account with a 5% rate for 1 year? Show how you determined your answer. B i U Font Family BEB3. The function f (t) represents water going into a swimming pool with respect to the number of hours (t) water is owing in where t represents time. f(t) = t2 - 8t + 9 There is a leak in the pool and it's losing water at a rate represented by d(t) d(t) = t2 1115 + 4 a. Write a function w(t) to represent the amount of water in the pool using the two functions. b. Use the new function to determine if the pool will leak all of the water. c. If the pool will drain of all water, how much time will it take? d. Will f(t) and d(t) intersect on a graph? Explain what it means if they do. 6. What is the domain of f(t), d(t). and w(t). Explain your answer. B i g FontFamily 'AA' A. .0 Fv VSE v cD y El II II @ :V @ 4. You are purchasing a new car. In order to determine which car will provide maximum savings, you've researched miles per gallon (mpg) ratings of cars. If gas is $3.45 per gallon and you drive an average of 18,000 miles per year, the following rational equation is given: g(x) = 3.45( old miles per gallon ) -3. new miles per gallon 18,000 g(a) calculates the dollar savings for one year for driving a car that gets a higher miles per gallon rate. a. In the formula what do you find when you divide old miles per gallon 18,000 b. The car you drive now gets 18 mpg; the car you are looking to buy will get 27 mpg. How many dollars will you save in the first year by switching to the 27 mpg car? c. How much would you save after 5 years? d. The other car you are considering buying will get 33 mpg, but it costs $3000 more than the 27 mpg car. Would the additional savings in gas be worth the extra $3000 over a 5 year loan? e. What gas mileage would your new car have to be if you saved $800 per year over your 18 mpg current car? B i U Font FamilyAll changes saved 5. In the summer time your friend wants to have a snow cone stand at a local grocery store parking lot. You want to make sure he actually makes money. The grocery store charges $300 per month. All products are calculated to be 25 cents per customer. Your plans are to sell each cone for $1.25. a. Write a mathematical expression representing the cost of operation for a month. b. Write a mathematical expression representing sales. c. Create an equation that will represent overall profit of the operation for a month. d. Simplify the equation into slope intercept form and standard form. What is the slope and explain its meaning in the context of selling snow cones? What is the intercept and what is its meaning? e. Describe the method of graphing the slope intercept form and also the standard form of the equation. f. What is the domain and range of the equation? Is the relation a function, why? g. How many snow cones do you need to sell to break even in the first month? h. How much is the profit if you sell 425, 550 or 700 snow cones in the first month of business? B i U Font Family AADEE EGO +V6. You work for a roofing company and must order the correct number of tiles to complete the final side of the roof. It is in the shape of a trapezoid. The numbers of tiles in each row form a sequence. We know we will have 20 rows to complete the job. The first row has ten tiles. Each row has two more tiles than the previous row. a. Is this sequence arithmetic or geometric? Explain. b. How many tiles are needed for each of the first four rows? c. Write the equation for the sequence in this situation. d. How many tiles are in the fifteenth row? e. How many total tiles will be needed to complete the job? B i U Font Family AADEE E .@67. The following equation represents the volume of a rectangular prism with a width of w inches: V=2w37w2+3w at What is the volume if the width is 5 inches? b. Factor this polynomial completely and describe what each factor means in terms of the dimensions of the rectangular prism. c. If the width is 5 inches, what are the other dimensions? How does this relate to your answer to part a? d. Graph the polynomial on a graphing calculator or an online graphing application. What are the z-intercepts? What do these mean in terms of the situation? e, What are the domain and range in terms of the situation? Justify your answers. B i g FontFamily 'AA' A. y Fv': vE v CD y El II II g :V g