Chapter 7

Solve. $$-8 x 2-4 x-12+2(x+2) x 2+4 x-60=1 x+2$$

Working alone, Monique takes 6 hours to record the inventory of the entire shop, while it takes Audrey only 4 hours to do the same job. How long will it take them working together if Monique leaves 2 hours early?

Simplify. $$ 3 x 9 x 2-16-13 x+4 $$

Simplify. (Assume all denominators are nonzero.) $$ 27 a 3+b 3 a b 3 a+b $$

Applications involving variation. The distance, \(d\), an object in free fall drops varies directly with the square of the time, \(t\), that it has been falling. If an object in free fall drops 36 feet in 1.5 seconds, then how far will it have fallen in 3 seconds? Hooke's law suggests that the extension of a hanging spring is directly proportional to the weight attached to it. The constant of variation is called the spring constant.

State the restrictions and then simplify. $$ 3 x 2+4 x-15 x 2-9 $$

Simplify. $$ 1100-1 \times 2110-1 x $$

Solve. $$x x+2-20 x 2-x-6=-4 x-3$$

Simplify. $$ 2 x x 2-1+1 x 2+x $$

Applications involving variation. If a hanging spring is stretched 5 inches when a 20 -pound weight is attached to it, then determine its spring constant.

Solve. $$x+7 x-1+x-1 x+1=4 x 2-1$$

Simplify. $$ x(4 x-1) 2 x 2+7 x-4-x 4+x $$

Applications involving variation. If a hanging spring is stretched 3 centimeters when a 2 -kilogram weight is attached to it, then determine the spring constant.

Simplify. $$ 3 x-1 x-55 x+2-2 x $$

Solve. $$x-2 x-5-x-5 x-2=8-x x-5$$

Simplify. $$ 2 x x-4-11 x+4 x 2-2 x-8 $$

Simplify. (Assume all denominators are nonzero.) $$ x y+4+4 y x x y+3+2 y x $$

Applications involving variation. If a hanging spring is stretched 6 centimeters when a 4 -kilogram weight is attached to it, then how far will it stretch with a 2 -kilogram weight attached?

Divide. (Assume all denominators are nonzero.) $$ (a-2 b) 22 b \div(2 b 2+a b-a 2) $$

Solve. $$x+7 x-2-81 x 2+5 x-14=9 x+7$$

Simplify. $$ x 2 x+1+6 x-242 x 2-7 x-4 $$

Simplify. (Assume all denominators are nonzero.) $$ 1+11+12 $$

The breaking distance of an automobile is directly proportional to the square of its speed. If it takes 36 feet to stop a particular automobile moving at a speed of 30 miles per hour, then how much breaking distance is required if the speed is 35 miles per hour?

State the restrictions and then simplify. $$ x-99-x $$

Solve. $$ 6 x-6=22 x-1 $$

Simplify. $$ 1 x 2-x-6+1 x 2-3 x-10 $$

Simplify. (Assume all denominators are nonzero.) $$ 2-11+13 $$

The breaking distance of an automobile is directly proportional to the square of its speed. After an accident, it was determined that it took a driver 80 feet to stop his car. In an experiment under similar conditions, it takes 45 feet to stop the car moving at a speed of 30 miles per hour. Estimate how fast the driver was moving before the accident. Boyle's law states that if the temperature remains constant, the volume, \(V\), of a given mass of gas is inversely proportional to the pressure, \(p\), exerted on it.

State the restrictions and then simplify. $$ 3 x-22-3 x $$

Solve. $$ x x-6=x+2 x-2 $$

Simplify. $$ x x 2+4 x+3-3 x 2-4 x-5 $$

Simplify. (Assume all denominators are nonzero.) $$ 11+11+x $$

The breaking distance of an automobile is directly proportional to the square of its speed. A balloon is filled to a volume of 216 cubic inches on a diving boat under 1 atmosphere of pressure. If the balloon is taken underwater approximately 33 feet, where the pressure measures 2 atmospheres, then what is the volume of the balloon?

State the restrictions and then simplify. $$ x+66+x $$

Solve. $$ 13 x-29=1 x $$

Solve. $$x-5 x-10+5 x-5=-5 x x 2-15 x+50$$

The breaking distance of an automobile is directly proportional to the square of its speed. If a balloon is filled to 216 cubic inches under a pressure of 3 atmospheres at a depth of 66 feet, then what would the volume be at the surface, where the pressure is 1 atmosphere?

State the restrictions and then simplify. $$ 3 x+11+3 x $$

Solve. $$ 2 x-5+35=1 x-5 $$

Solve. $$5 x 2+5 x+4+x+1 x 2+3 x-4=5 x 2-1$$

Simplify. (Assume all denominators are nonzero.) $$ 1-1 x x-1 x $$

To balance a seesaw, the distance from the fulcrum that a person must sit is inversely proportional to his weight. If a 72 -pound boy is sitting 3 feet from the fulcrum, then how far from the fulcrum must a 54 - pound boy sit to balance the seesaw?

State the restrictions and then simplify. $$ (2 x-5)(x-7)(7-x)(2 x-1) $$

Solve. $$1 x 2-2 x-63+x-9 x 2+10 x+21=1 x 2-6 x-27$$

Simplify. $$ 3 x 2+24 x 2-2 x-8-12 x-4 $$

The breaking distance of an automobile is directly proportional to the square of its speed. The current, \(I\), in an electrical conductor is inversely proportional to its resistance, \(R\). If the current is \(1 / 4\) ampere when the resistance is 100 ohms, then what is the current when the resistance is 150 ohms?

State the restrictions and then simplify. $$ (3 x+2)(x+5)(x-5)(2+3 x) $$

Solve. $$4 x 2-4+2(x-2) x 2-4 x-12=x+2 x 2-8 x+12$$

Simplify. $$ 4 x 2+28 x 2-6 x-7-28 x-7 $$

The breaking distance of an automobile is directly proportional to the square of its speed. The number of men, represented by \(y,\) needed to lay a cobblestone driveway is directly proportional to the area, \(A\), of the driveway and inversely proportional to the amount of time, \(t,\) allowed to complete the job. Typically, 3 men can lay 1,200 square feet of cobblestone in 4 hours. How many men will be required to lay 2,400 square feet of cobblestone given 6 hours?