Chapter 11: Problem 60
Write the equation in standard form. (Lesson 9.5 for 11.7 ) $$6 x^{2}=5 x-7$$
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Use the following information. You are choosing a business partner for a student lawn-care business you are starting. It takes you an average of 35 minutes to mow a lawn, so your rate is 1 lawn in 35 minutes or \(\frac{1}{35}\) of a lawn per minute. Let \(x\) represent the average time (in minutes) it takes a possible partner to mow a lawn. Write an expression for the partner's rate (that is, the part of a lawn the partner can mow in 1 minute). Then write an expression for the combined rate of you and your partner (the part of a lawn that you both can mow in 1 minute if you work together).
Simplify the expression. (Review \(8.3 \text { for } 11.7)\) $$\frac{42 x^{4} y^{3}}{6 x^{3} y^{9}}$$
You will write and simplify a general expression for the average speed traveled when making a round trip. Let \(d\) represent the one-way distance. Let \(x\) represent the speed while traveling there and let \(y\) represent the speed while traveling back. What do you notice about the variables in the final answer? If your distance is doubled what happens to the average speed?
Simplify the expression. (Review \(8.3 \text { for } 11.7)\) $$\frac{4 m^{2}}{6 m}$$
Simplify the expression. $$\frac{2 x}{x+5}-\frac{3 x+2}{x+5}-\frac{4}{x+5}$$
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