If a 0.00000293, b 1.582 1014, and c 2.8064 1012, use a

State the property of real numbers being used3x  2y 2y  3x

State the property of real numbers being used1a  b2 1a b2 1a b2 1a  b2 27

State the property of real numbers being used41a  b2 4a  4b

State the property of real numbers being used1A  12 1x  y2 1A  12x  1A  12y

Express the interval in terms of inequalities, and then graph the interval.32, 62

Express the interval in terms of inequalities, and then graph the interval.1q, 44

Express the inequality in interval notation, and then graph the corresponding interval.x 5

Express the inequality in interval notation, and then graph the corresponding interval.1  x  5

Evaluate the expression... . @ @

Evaluate the expression.1 1 0 1 0

Evaluate the expression.23 32 12

Evaluate the expression.23 125

Evaluate the expression.. 2161/3

Evaluate the expression.642/3

Evaluate the expression.1242 12

Evaluate the expression.1 4 4 1 4 324

Evaluate the expression.21/2 81/2

Evaluate the expression.12 150

Simplify the expression.x 2 12x2 4 x 3

Simplify the expression.1a2 2 3 1a3 b2 2 1b3 2 4

Simplify the expression.13xy2 2 3 1 2 3 x1 y2 2

Simplify the expression.a r 2 s4/3 r 1/3 s b 6

Simplify the expression.23 4 1x 3 y2 2

Simplify the expression.2x 2 y4

Simplify the expression.a 9x 3 y y3 b 1/2

Simplify the expression.a x2 y3 x 2 y b 1/2 a x 3 y y1/2 b 2

Simplify the expression.8r 1/2 s3 2r 2 s4

Simplify the expression.a ab2 c3 2a3 b4 b 2 8r

Write the number 78,250,000,000 in scientific notation

Write the number 2.08 108 in ordinary decimal notation.

If a 0.00000293, b 1.582 1014, and c 2.8064 1012, use a calculator to approximate the number ab/c. 3

If your heart beats 80 times per minute and you live to be 90 years old, estimate the number of times your heart beats during your lifetime. State your answer in scientific notation.

Factor the expression completely..12x 2 y 4 3xy 5  9x 3 y 2

Factor the expression completely..x 2 9x  18

Factor the expression completely..x 2  3x 10

Factor the expression completely..6x 2  x 12

Factor the expression completely..4t 2 13t 12 3

Factor the expression completely..x 4 2x 2  1

Factor the expression completely..25 16t 2

Factor the expression completely..2y 6 32y 2

Factor the expression completely...x 6 1

Factor the expression completely...y 3 2y 2 y  2

Factor the expression completely..x1/2 2x 1/2  x 3/2 4

Factor the expression completely..a4 b2  ab5

Factor the expression completely.4x 3 8x 2  3x 6 4

Factor the expression completely.8x 3  y 6

Factor the expression completely.1x 2  22 5/2  2x1x 2  22 3/2  x 22x 2  2

Factor the expression completely.3x 3 2x 2  18x 12

Perform the indicated operations and simplify.12x  12 13x 22 514x 12 1

Perform the indicated operations and simplify.12y 72 12y  72

Perform the indicated operations and simplify.11  x2 12 x2 13 x2 13  x2 1

Perform the indicated operations and simplify.1x 1 1x  12 121x 12

Perform the indicated operations and simplify.x 2 1x 22  x1x 22 2

Perform the indicated operations and simplify..x 2 2x 3 2x 2  5x  3 x

Perform the indicated operations and simplify..x 2  2x 3 x 2  8x  16 # 3x  12 x 1

Perform the indicated operations and simplify.t 3 1 t 2 1

Perform the indicated operations and simplify.x 2 2x 15 x 2 6x  5 x 2 x 12 x 2 1 t 3

Perform the indicated operations and simplify.2 x  1 x 2  3 1x 22 2

Perform the indicated operations and simplify. 1x 1 2 x 2 1 2

Perform the indicated operations and simplify.1 x  2  1 x 2 4 2 x 2 x 2 1

Perform the indicated operations and simplify.1 x 1 2 x 2

Perform the indicated operations and simplify.1 x 1 x  1 1 x  1 x  1

Perform the indicated operations and simplify.16 13  12 1rationalize the denominator2

Perform the indicated operations and simplify.2x  h 1x h 1rationalize the numerator2

Find all real solutions of the equation.7x 6 4x  9 6

Find all real solutions of the equation.8 2x 14  x

Find all real solutions of the equation.x  1 x 1 3x 3x 6 2

Find all real solutions of the equation.1x  22 2 1x 42 2 x

Find all real solutions of the equation.x 2 9x  14 0 7

Find all real solutions of the equation.x 2  24x  144 0

Find all real solutions of the equation.2x 2  x 1

Find all real solutions of the equation.3x 2  5x 2 0

Find all real solutions of the equation.4x 3 25x 0 7

Find all real solutions of the equation.x 3 2x 2 5x  10 0 7

Find all real solutions of the equation.3x 2  4x 1 0 7

Find all real solutions of the equation.1 x  2 x 1 3

Find all real solutions of the equation.x x 2  1 x  2 8 x 2 4 1

Find all real solutions of the equation.x 4 8x 2 9 0 7

Find all real solutions of the equation. x 7 0 4 0

Find all real solutions of the equation.0 2x 5 0 9

The owner of a store sells raisins for $3.20 per pound and nuts for $2.40 per pound. He decides to mix the raisins and nuts and sell 50 lb of the mixture for $2.72 per pound. What quantities of raisins and nuts should he use?

Anthony leaves Kingstown at 2:00 P.M. and drives to Queensville, 160 mi distant, at 45 mi/h. At 2:15 P.M. Helen leaves Queensville and drives to Kingstown at 40 mi/h. At what time do they pass each other on the road?

A woman cycles 8 mi/h faster than she runs. Every morning she cycles 4 mi and runs mi, for a total of one hour of exercise. How fast does she run?

The hypotenuse of a right triangle has length 20 cm. The sum of the lengths of the other two sides is 28 cm. Find the lengths of the other two sides of the triangle.

Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60 min to paint a living room with all three working together, how long would it take Abbie if she works alone?

A homeowner wishes to fence in three adjoining garden plots, one for each of her children, as shown in the figure. If eachplot is to be 80 ft2 in area and she has 88 ft of fencing material at hand, what dimensions should each plot have?

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.3x 2  11 8

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.1  2x  5  3

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.x 2  4x 12  0

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.x 2  1

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.x 4 x 2 4  0

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.5 x 3 x 2 4x  4  0 x

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.x 5 0  3

Solve the inequality. Express the solution using interval notation and graph the solution set on the real number line.0 x 4 0  0.02

Solve the equation or inequality graphically.x 2 4x 2x  7 9

Solve the equation or inequality graphically.1x  4 x 2 5

Solve the equation or inequality graphically.4x 3  x 2

Solve the equation or inequality graphically.x 3 4x 2 5x  2

Two points P and Q are given. (a) Plot P and Q on a coordinate plane. (b) Find the distance from P to Q. (c) Find the midpoint of the segment PQ. (d) Sketch the line determined by P and Q, and find its equation in slope-intercept form. (e) Sketch the circle that passes through Q and has center P, and find the equation of this circle.P12, 02, Q15, 122 P

Two points P and Q are given. (a) Plot P and Q on a coordinate plane. (b) Find the distance from P to Q. (c) Find the midpoint of the segment PQ. (d) Sketch the line determined by P and Q, and find its equation in slope-intercept form. (e) Sketch the circle that passes through Q and has center P, and find the equation of this circle.P17, 12, Q12, 112

Sketch the region given by the set.51x,y2 0 4  x  4 and 2  y  26

Sketch the region given by the set.51x,y2 0 x  4 or y  26

Which of the points or is closer to the point ?

Find an equation of the circle that has center and radius

Find an equation of the circle that has center and passes through the origin.

Find an equation of the circle that contains the points and and has the midpoint of the segment PQ as its center

Determine whether the equation represents a circle, represents a point, or has no graph. If the equation is that of a circle, find its center and radius.x 2  y 2  2x 6y  9 0

Determine whether the equation represents a circle, represents a point, or has no graph. If the equation is that of a circle, find its center and radius.2x 2  2y 2 2x  8y 1 2

Determine whether the equation represents a circle, represents a point, or has no graph. If the equation is that of a circle, find its center and radius.x 2  y 2  72 12x

Determine whether the equation represents a circle, represents a point, or has no graph. If the equation is that of a circle, find its center and radius.x 2  y 2 6x 10y  34 0 1

Test the equation for symmetry, and sketch its graph..y 2 3x 1

Test the equation for symmetry, and sketch its graph.2x y  1 0

Test the equation for symmetry, and sketch its graph.x  3y 21

Test the equation for symmetry, and sketch its graph.x 2y  12

Test the equation for symmetry, and sketch its graph.y 16 x 2 1

Test the equation for symmetry, and sketch its graph.8x  y 2 0

Test the equation for symmetry, and sketch its graph.x 1y

Test the equation for symmetry, and sketch its graph.y 21 x 2 x

Use a graphing device to graph the equation in an appropriate viewing rectangle.y x 2 6x 1

Use a graphing device to graph the equation in an appropriate viewing rectangle.y 25 x

Use a graphing device to graph the equation in an appropriate viewing rectangle.y x 3 4x 2 5x 12

Use a graphing device to graph the equation in an appropriate viewing rectangle.x 2 4  y2 1

Find an equation for the line that passes through the points and .

Find an equation for the line that passes through the point and has slope

Find an equation for the line that has x-intercept 4 and y-intercept 12.

Find an equation for the line that passes through the point and is perpendicular to the line

Find an equation for the line that passes through the origin and is parallel to the line 3x  15y 22.

Find an equation for the line that passes through the point and is parallel to the line passing through and

Find equations for the circle and the line in the figure. 129.

Find equations for the circle and the line in the figure. 129.

Hookes Law states that if a weight is attached to a hanging spring, then the stretched length s of the spring is linearly related to . For a particular spring we have where s is measured in inches and in pounds. (a) What do the slope and s-intercept in this equation represent? (b) How long is the spring when a 5-lb weight is attached?

Margarita is hired by an accounting firm at a salary of $60,000 per year. Three years later her annual salary has increased to $70,500. Assume that her salary increases linearly. (a) Find an equation that relates her annual salary S and the number of years t that she has worked for the firm. (b) What do the slope and S-intercept of her salary equation represent? (c) What will her salary be after 12 years with the firm?

Suppose that M varies directly as z, and M 120 when

Suppose that z is inversely proportional to y, and that z 12 when y 16. Write an equation that expresses z in terms of y. 1

The intensity of illumination I from a light varies inversely as the square of the distance d from the light. (a) Write this statement as an equation. (b) Determine the constant of proportionality if it is known that a lamp has an intensity of 1000 candles at a distance of 8 m. (c) What is the intensity of this lamp at a distance of 20 m?

The frequency of a vibrating string under constant tension is inversely proportional to its length. If a violin string 12 inches long vibrates 440 times per second, to what length must it be shortened to vibrate 660 times per second?

The terminal velocity of a parachutist is directly proportional to the square root of his weight. A 160-lb parachutist attains a terminal velocity of 9 mi/h. What is the terminal velocity for a parachutist weighing 240 lb?

The maximum range of a projectile is directly proportional to the square of its velocity. A baseball pitcher throws a ball at 60 mi/h, with a maximum range of 242 ft. What is his maximum range if he throws the ball at 70 mi/h?