family feud review - georgia southern university...question 2 the equation 5x + kx 34 = kx k + 1 is...

Family Feud Review

Math 1111: College Algebra

February 5, 2013

Lambert Family Feud

Question 1

Solve for x in the following equation

3 = 2x − 7.

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Answer 1

Answer3 = 2x − 7

10 = 2x5 = x

Lambert Family Feud

Answer 1

Answer3 = 2x − 7

10 = 2x

5 = x

Lambert Family Feud

Answer 1

Answer3 = 2x − 7

10 = 2x5 = x

Lambert Family Feud

Question 2

The equation 5x + kx − 34 = kx − k + 1 is really a family ofequations, because for each value of k , we get a different equationfor the unknown x . The letter k is called a parameter for thisfamily. What value should we pick for k to make x = 10 a solutionfor the resulting equation.

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Answer 2

Answer5x + kx − 34 = kx − k + 1

5x − 34 = −k + 15(10)− 34 = −k + 1

16 = −k + 115 = −k−15 = k

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Answer 2

Answer5x + kx − 34 = kx − k + 1

5x − 34 = −k + 1

5(10)− 34 = −k + 116 = −k + 1

15 = −k−15 = k

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Answer 2

Answer5x + kx − 34 = kx − k + 1

5x − 34 = −k + 15(10)− 34 = −k + 1

16 = −k + 115 = −k−15 = k

Lambert Family Feud

Answer 2

Answer5x + kx − 34 = kx − k + 1

5x − 34 = −k + 15(10)− 34 = −k + 1

16 = −k + 1

15 = −k−15 = k

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Answer 2

Answer5x + kx − 34 = kx − k + 1

5x − 34 = −k + 15(10)− 34 = −k + 1

16 = −k + 115 = −k

−15 = k

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Answer 2

Answer5x + kx − 34 = kx − k + 1

5x − 34 = −k + 15(10)− 34 = −k + 1

16 = −k + 115 = −k−15 = k

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Question 3

What is the discriminant of the quadratic equationax2 + bx + c = 0, where a, b, and c are constants with a 6= 0?

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Answer 3

AnswerThe discriminant is given by b2 − 4ac.

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Question 4

Determine whether the following statements are true or false. Ifthe statement is true, explain why the given statement is true (aproof is not necessary), otherwise provide a counterexample.

For real numbers a, b, and c with a 6= 0 the quadratic equationax2 + bx + c = 0 has exactly two real solutions for x .

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Question 4

Determine whether the following statements are true or false. Ifthe statement is true, explain why the given statement is true (aproof is not necessary), otherwise provide a counterexample.For real numbers a, b, and c with a 6= 0 the quadratic equationax2 + bx + c = 0 has exactly two real solutions for x .

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Answer 4

AnswerThis statement is false.

One counterexample would be x2 + x + 1 = 0, which has no realroots since the discriminant is −3.Another counterexample would be x2 + 2x + 1 = 0, which has onlyone real root since it can be factored into (x + 1)2 = 0.

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Answer 4

AnswerThis statement is false.One counterexample would be x2 + x + 1 = 0, which has no realroots since the discriminant is −3.

Another counterexample would be x2 + 2x + 1 = 0, which has onlyone real root since it can be factored into (x + 1)2 = 0.

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Answer 4

AnswerThis statement is false.One counterexample would be x2 + x + 1 = 0, which has no realroots since the discriminant is −3.Another counterexample would be x2 + 2x + 1 = 0, which has onlyone real root since it can be factored into (x + 1)2 = 0.

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Question 5

Determine whether the following statements are true or false. Ifthe statement is true, explain why the given statement is true (aproof is not necessary), otherwise provide a counterexample.

For real numbers a, b, and c we find if a ≥ b, then ca ≥ cb.

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Question 5

Determine whether the following statements are true or false. Ifthe statement is true, explain why the given statement is true (aproof is not necessary), otherwise provide a counterexample.For real numbers a, b, and c we find if a ≥ b, then ca ≥ cb.

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Answer 5

AnswerThis statement is false.

Notice that 1 ≥ 0, but (−2)(1) ≤ (−2)0.

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Answer 5

AnswerThis statement is false.Notice that 1 ≥ 0, but (−2)(1) ≤ (−2)0.

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Question 6

Solve the following inequality and write your answer in intervalnotation.

−3 ≤ 5x − 4 < 7

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Answer 6

Answer

−3 ≤ 5x − 4 < 7

1 ≤ 5x < 11

1

5≤ x <

11

5[1

5,

11

5

)

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Answer 6

Answer

−3 ≤ 5x − 4 < 7

1 ≤ 5x < 11

1

5≤ x <

11

5

[1

5,

11

5

)

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Answer 6

Answer

−3 ≤ 5x − 4 < 7

1 ≤ 5x < 11

1

5≤ x <

11

5[1

5,

11

5

)

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Question 7


x2 = 49.

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Answer 7

Answer

x2 = 49

x = ±√

49

x = ±7

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Question 8

Two fishing boats depart a harbor at the same time, one travelingeast, the other south. The eastbound boat travels at a speed 5miles per hour faster than the southbound boat. After 6 hours theboats are 42 miles apart. Find the speed of both boats. Clearlylabel the speed of the southbound boat along with the speed ofthe eastbound boat.

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Answer 8

AnswerLet x be the speed of the southbound boat.

[6(x)]2 + [6(x + 5)]2 = 422

x2 + (x + 5)2 = 72

x2 + x2 + 10x + 25 = 49

2x2 + 10x − 24 = 0

x2 + 5x − 12 = 0

The southbound boat is traveling at −5+√

732 miles per hour.

The eastbound boat is traveling at 3 + −5+√

732 miles per hour.

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Question 9


x2 − 5x + 6 = 0.

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Answer 9

Answer

x2 − 5x + 6 = 0

(x − 2)(x − 3) = 0

x = {2, 3}

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Question 10


x − 9√

x − 10 = 0.

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Answer 10

Answer

x − 9√

x − 10 = 0

(√

x − 10)(√

x + 1) = 0.

x = 100

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family feud review - georgia southern university...question 2 the equation 5x + kx 34 = kx k + 1 is...

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