Answers CR - Algebra 2 26-27 - S1Unit Test

Unit Test — Unit test Answers

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Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the equation, where t is the number of hours it would take to clear the field together.How long will it take Ted and Jacob to clear the field together?

12 minutes

50 minutes

1 hour 12 minutes

2 hours 30 minutes

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Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together.How long will it take Maxine and Jan to mow the lawn together?

30.0 minutes

45.0 minutes

67.5 minutes

135.0 minutes

If f(–2) = 0, what are all the factors of the function ? Use the Remainder Theorem.

(x + 2)(x + 60)

(x – 2)(x – 60)

(x – 10)(x + 2)(x + 6)

(x + 10)(x – 2)(x – 6)

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?

The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).

The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.

The equation is not quadratic in form because it cannot be solved by using the quadratic formula.

The equation is not quadratic in form because there is no real solution.

A polynomial function has a root of –3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?

Option

Let a, b, and c be real numbers where a b c 0. Which of the following functions could represent the graph below?

f(x) = x2(x – a)2(x – b)4(x – c)

f(x) = x3(x – a)3(x – b)(x – c)2

f(x) = x4(x – a)(x – b)3(x – c)3

f(x) = (x – a)2(x – b)(x – c)6

What is the remainder when (x4 + 36) is divided by (x2 – 8)?

100

117

What is the quotient of (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)?

x – 2

x + 2

x – 4

x + 1

What is the cube root of ?

Option

The price that a company charged for a basketball hoop is given by the equation where x is the number of hoops that are produced, in millions. It costs the company $30 to make each basketball hoop. The company recently reduced its production to 1 million hoops but maintained its profit of 15 million dollars. Approximately how many basketball hoops did the company previously produce to make the same profit?

1.3 million hoops

1.4 million hoops

15 million hoops

30 million hoops

What are the solutions of the equation (x – 3)2 + 2(x – 3) – 8 = 0? Use u substitution to solve.

x = –5 and x = 1

x = –1 and x = 5

x = –1 and x = –7

x = 1 and x = 7

What is the factored form of ?

Option

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

–6, 6

–4, 1, 3

–3, –1, 4

1, 3

Which graph represents the function ?

On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.25.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.25.

Carlos graphed the system of equations that can be used to solve .What are the roots of the polynomial equation?

–3, –2, 3

–3, 2

18, 32

18, 32, 66

Which expression is equivalent to ? Assume .

StartFraction 5 Over x Superscript 12 Baseline y Superscript 30 Baseline EndFraction

StartFraction 1 Over 5 x Superscript 8 Baseline y Superscript 13 Baseline EndFraction

StartFraction 5 Over x Superscript 4 Baseline y Superscript 7 Baseline EndFraction

StartFraction y Superscript 7 Baseline Over 5 x Superscript 4 Baseline EndFraction

Which expression is equivalent to ? Assume .

StartFraction 8 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction

StartFraction 10 m Superscript 7 Baseline n Superscript 6 Baseline Over 3 EndFraction

StartFraction 8 m Superscript 16 Baseline n Superscript 12 Baseline Over 3 EndFraction

StartFraction m Superscript 4 Baseline n Superscript 6 Baseline Over 3 EndFraction

The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function , where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?

The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses.

The horizontal asymptote of y = 0 means that the person’s temperature will approach 0ºF as time elapses.

The horizontal asymptote of y = 4 means that the person’s temperature will approach 102.6ºF as time elapses.

The horizontal asymptote of y = 4 means that the person’s temperature will approach 4ºF as time elapses.

Which equation is quadratic in form?

3x5 + 8x3 + 6 = 0

6x4 + 7x2 – 3 = 0

5x6 + x4 + 12 = 0

x9 + x3 – 10 = 0

If (x – 2k) is a factor of f(x), which of the following must be true?

f(2k) = 0

f(–2k) = 0

A root of f(x) is x = –2k.

A y intercept of f(x) is x = 2k.

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