Radical Equations and Extraneous Roots

A farm irrigation system waters a large field. Consider the center of the field as the origin and the rest of the field as a grid measured in yards. The first irrigation unit is located at the point (–400, –200) and waters 500 yards in every direction. The second is located at (200, 300) and waters 400 yards in every direction. The system of inequalities represents this scenario.

A

(100, 100)

B

(–100, 100)

C

(100, –100)

D

(–100, –100)

22

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Samir begins riding his bike at a rate of 6 miles per hour. Twelve minutes later, Chris leaves from the same point and bikes along the same route at 9 miles per hour. How long after Chris begins riding does he catch up to Samir?

A

4 min

B

12 min

C

24 min

D

40 min

23

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?

A

(–6, 0.8)

B

(–6, 3.2)

C

(6, 3.2) ✓ Correct

D

(6, 0.8)

24

Which region represents the solution to the given system of inequalities?

A

B

C

D

25

The constraints of a problem are listed below. What are the vertices of the feasible region?

A

mc008-2.jpg

B

mc008-3.jpg

C

mc008-4.jpg

D

mc008-5.jpg

26

Which point is a solution of x2 + y2 > 49 and y ≤ –x2 – 4?

A

(–8, –1)

B

(–3, 1)

C

(1, –9)

D

(0, –6)

27

When a baseball is hit by a batter, the height of the ball, h(t), at time t, , is determined by the equation . If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

A

Option

B

Option

C

Option

D

Option

28

A quadratic inequality contains the values less than or equal to the quadratic function that has a vertex of (–9, –27) and contains the point on the boundary.

A

y less-than-or-equal-to two-thirds (x minus 9) squared + 27

B

y less-than-or-equal-to negative two-thirds (x minus 9) squared + 27

C

y less-than-or-equal-to two-thirds (x + 9) squared minus 27

D

y less-than-or-equal-to negative two-thirds (x + 9) squared minus 27

29

An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (–18, 14) to (16, –13). Which system of equations can be used to determine whether the commuter jet’s flight path intersects the closed airspace?

A

StartLayout Enlarged Left-Brace 1st Row y = one-fourth (x minus 5) squared + 10 2nd Row y = negative one-half x + 5 EndLayout

B

StartLayout Enlarged Left-Brace 1st Row y = one-fourth (x minus 5) squared + 10 2nd Row y = negative 2 x minus 22 EndLayout

C

StartLayout Enlarged Left-Brace 1st Row y = one-fourth (x minus 10) squared + 6 2nd Row y = Negative StartFraction 27 Over 34 EndFraction x minus Five-seventeenths EndLayout

D

StartLayout Enlarged Left-Brace 1st Row y = one-fourth (x minus 10) squared + 6 2nd Row y = negative 2 x minus 22 EndLayout

30

Jamilla solved the inequality and graphed the solution as shown below. What is the value of b and the missing symbol in Jamilla’s inequality?

A

b = –1,

B

b = –1,

C

b = 1,

D

b = 1,

31

The graph of a quadratic inequality is shown.

A

y greater-than 3 (x + 15)(x + 3)

B

y greater-than-or-equal-to (x + 15)(x + 3)

C

y greater-than 0.25 (x minus 15)(x minus 3)

D

y greater-than-or-equal-to (x minus 15)(x minus 3)

32

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Which statement must be true?

A

The circle has a radius greater than 7.

B

The circle has a radius equal to 7.

C

The slope of the line is equal to 7.

D

The slope of the line is not equal to 7.

33

Elise, Jake, Malik, and Xiao each solved the same inequality.Elise’s WorkJake’s WorkMalik’s WorkXiao’s Workno solutionall real numbersWhose work is correct?

A

Elise’s work

B

Jake’s work

C

Malik’s work

D

Xiao’s work

34

Review the graph.

A

x2 + y2 > 9 and y < –x2 + 2

B

x2 + y2 < 9 and y < –x2 + 2

C

x2 + y2 > 9 and x < –y2 + 2

D

x2 + y2 < 9 and x < –y2 + 2

35

The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 – 5t2, where t is the time in seconds. A high-speed camera is ready to film the person between 15 m and 10 m above the ground. For which interval of time should the camera film the person?

A

Option

B

Option

C

Option

D

t < 2

36

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measures 42,000 ft2. What is a dimension of the parking lot?

A

120 ft

B

205 ft

C

210 ft

D

375 ft

37

What is one of the solutions to the following system?

A

(–5, 2)

B

(–2, 1)

C

(2, 5)

D

(8, 5)

38

Which graph represents the solution of y ≤ x2 + 1 and x > y2 – 5?

A

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 1) and goes through (2, 6). Another parabola opens to the right and goes through (4, 3), has vertex (negative 5, 0), and goes through (4, negative 3). Everything outside of the first parabola and inside of the second parabola is shaded.

B

On a coordinate plane, a parabola opens up and goes through (negative 2, 6), has vertex (0, 1) and goes through (2, 6). Another parabola opens to the right and goes through (4, 3), has vertex (negative 5, 0), and goes through (4, negative 3). Everything inside of both parabolas is shaded.

C

On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside of both parabolas is shaded.

D

On a coordinate plane, a parabola opens up and goes through (negative 3, 4), has vertex (0, negative 5), and goes through (3, 4). Another parabola opens to the right and goes through (5, 2), has vertex (1, 0), and goes through (5, negative 2). Everything inside the first parabola and outside of the second parabola is shaded.

39

Which system is equivalent to ?

A

StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row 12 x squared + 4 y squared = 22 EndLayout

B

StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row negative 12 x squared + 4 y squared = 22 EndLayout

C

StartLayout Enlarged left-brace 1st Row 6 x squared minus 8 y squared = 25 2nd row negative 6 x squared minus 2 y squared = 11 EndLayout

D

StartLayout Enlarged left-brace 1st Row 6 x squared minus 8 y squared = 50 2nd row negative 6 x squared minus 2 y squared = 11 EndLayout

40

Two boats depart from a port located at (–10, 0) in a coordinate system measured in kilometers, and they travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (0, 5), and the second boat follows a path that can be modeled by a linear function and passes through the point (10, 4). At what point, besides the common starting location of the port, do the paths of the two boats cross?

A

(–6, 0.8)

B

(–6, 3.2)

C

(6, 3.2)

D

(6, 0.8)

Radical Equations and Extraneous Roots — Unit test Answers

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