Answers NC-PrecalculusRational Inequalities

Rational Inequalities — Unit test Answers

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Which inequality is equivalent to ?

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A cliff diver leaps from a 100-foot cliff into the Pacific. The diver’s height above the water is modeled by the functionP(x) = –16x 2 + 10x + 100, where x is time in seconds.During which interval is the diver at least halfway down?

2.0 < x < 2.1 seconds

2.1 < x < 2.8 seconds

3.0 < x < 3.4 seconds

3.4 < x < 3.5 seconds

What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

–24, –3, 12

–12, 3, 24

–4, –2, 3

–3, 2, 4

For , which expression represents the correct form of the partial fraction decomposition?

StartFraction A Over x + 1 EndFraction + StartFraction B Over (x + 1) squared EndFraction + StartFraction C Over (x + 1) cubed EndFraction + StartFraction D x + E Over x squared + 1 EndFraction + StartFraction F x + G Over (x squared + 1) squared EndFraction

StartFraction A Over x + 1 EndFraction + StartFraction B squared Over (x + 1) squared EndFraction + StartFraction C cubed Over (x + 1) cubed EndFraction + StartFraction D x + E Over x squared + 1 EndFraction + StartFraction (F x + G) squared Over (x squared + 1) squared EndFraction

StartFraction A Over x + 1 EndFraction + StartFraction B Over (x + 1) squared EndFraction + StartFraction C x + D Over x squared + 1 EndFraction + StartFraction E x + F Over (x squared + 1) squared EndFraction + StartFraction G x + H Over (x squared + 1) cubed EndFraction

StartFraction A Over x + 1 EndFraction + StartFraction B squared Over (x + 1) squared EndFraction + StartFraction C x + D Over x squared + 1 EndFraction + StartFraction (E x + F) squared Over (x squared + 1) squared EndFraction + StartFraction (G x + H) cubed Over (x squared + 1) cubed EndFraction

Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?

2.4 hours

2.5 hours

3.0 hours

4.0 hours

What is the solution of ?

–1 < x < 1 or

x < –1 or

Regular exercise can help a person lower their resting heart rate. Suppose an individual’s resting heart rate, in beats per minute, is modeled by the function f(x) = –0.1x 3 + 0.6x 2 + 85 after x weeks of regular exercise.How many weeks of exercise are necessary to lower the individual’s resting heart rate below 70 beats per minute?

7 weeks

8 weeks

9 weeks

10 weeks

Which graph shows the solution set of ?

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What are the roots of the polynomial equation ? Use a graphing calculator and a system of equations.

–2, –1, 0, 2

–2, 0, 1, 2

–1, 0

0, 1

You can use a system of equations to graph and solve the polynomial equation . Which statement is true?

The system has one solution, and the equation has three zeroes.

The y-coordinates of the solutions to the system and the zeroes of the equation are not equal.

The x-coordinates of the solutions to the system and the zeroes of the equation are not equal.

The equation has one zero, and the system has three solutions.

A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.