1. Solve each of the following system of equations algebraically. Describe the graph of the system. (You do not need to actually graph the system.) a. 0.6y = 0.9x + 12 6x − 4y = −10 b. 6x − 22 = −y 3x + 1 y = 11 2
2. You’re interested in buying a new car and want to compare the cost of owning a standard gasoline engine with that of a hybrid-electric car. The costs to purchase and to drive x miles for two models of cars are given by the functions Gasoline Engine: Hybrid-Electric: CA = 18,000 + 0.225x CB = 25,000 + 0.094x
b. What do the coeﬃcients 0.225 and 0.094 represent on the graph, and what do they represent in terms of the car ownership costs? c. What do the constant terms 18,000 and 25,000 represent on the graph, and what do they represent in terms of the car ownership costs? d. Label the point on the graph where the two car’s costs are equal. Make a visual estimate of the coordinates of this point, and interpret what the coordinates mean in terms of car ownership costs. e. Solve the equations algebraically to ﬁnd the the mileage when the costs for the two cars will be equal. What is the cost at this mileage? 3. A coﬀee shop’s special blend contains 50% Kona coﬀee and is mixed from 100% Kona coﬀee and a commercial coﬀee blend which contains 20% Kona coﬀee. Suppose the coﬀee house wants to mix 40 lbs of its special blend. Let x be the number of pounds of the 100% Kona coﬀee used and y the number of pounds of the commercial coﬀee blend used. Find a system of two equations which x and y satisfy and then solve the system. 4. Simplify the following expressions. Write your ﬁnal answers with only positive exponents. Assume all variables represent positive numbers. a. b. 3(cx)−2 (3c)3 x−4
a. Sketch the graph of this system of equations over the interval 0 ≤ n ≤ 60,000.
96x7 y 8
3x4 y √ √ √ c. 3t 98t − 2t 50t + 5 18t3
5. Scientists believe the Milky Way galaxy formed 14 billion... [continues]
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