Chapter 3 & 5 Test

1) Solve for x using the square root method:

9 and 1

9

9 and -1

629

The correct answer is 9 and -1 because when using the square root method to solve for x, we need to find the square root of both sides of the equation. The square root of 9 is 3, so x = 3. However, the square root of -1 is not a real number, so x = -1 is an extraneous solution and should be discarded. Therefore, the final solution is x = 3.

Explanation

The correct answer is 9 and -1 because when using the square root method to solve for x, we need to find the square root of both sides of the equation. The square root of 9 is 3, so x = 3. However, the square root of -1 is not a real number, so x = -1 is an extraneous solution and should be discarded. Therefore, the final solution is x = 3.

2) Rewrite

as a single logarithm. Answer Choices: A.

B.

C.

D.

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

3) Give the coordinates for the vertex of the quadratic function

.

(1, -27)

(-1, -15)

(3, -15)

(1, 27)

The coordinates (1, -27) represent the vertex of the quadratic function. In a quadratic function, the vertex is the highest or lowest point on the graph, depending on whether the coefficient of the x^2 term is positive or negative. In this case, the vertex is a downward-facing parabola, and the point (1, -27) is the lowest point on the graph. The x-coordinate of the vertex is 1, and the y-coordinate is -27.

Explanation

The coordinates (1, -27) represent the vertex of the quadratic function. In a quadratic function, the vertex is the highest or lowest point on the graph, depending on whether the coefficient of the x^2 term is positive or negative. In this case, the vertex is a downward-facing parabola, and the point (1, -27) is the lowest point on the graph. The x-coordinate of the vertex is 1, and the y-coordinate is -27.

4) Solve for x using factoring:

5 and 4

-2 and -3

-4 and -1

4 and 1

The given answer, 4 and 1, suggests that when factoring the given expression, the factors are (x + 4) and (x + 1). By setting each factor equal to zero and solving for x, we find that x = -4 and x = -1 are the solutions to the equation.

Explanation

The given answer, 4 and 1, suggests that when factoring the given expression, the factors are (x + 4) and (x + 1). By setting each factor equal to zero and solving for x, we find that x = -4 and x = -1 are the solutions to the equation.

5) If a ball is dropped from the top of a 400-ft-high building, its height S in feet is given by

, where t is in seconds. In how many seconds will it take the ball to hit the ground?

400 seconds

25 seconds

5 seconds

5 and -5 seconds

The ball will take 5 seconds to hit the ground because the equation given represents the height of the ball at any given time. When the ball hits the ground, its height will be 0. By substituting S = 0 into the equation, we can solve for t.

Explanation

The ball will take 5 seconds to hit the ground because the equation given represents the height of the ball at any given time. When the ball hits the ground, its height will be 0. By substituting S = 0 into the equation, we can solve for t.

6) Consider the graph of the function

, how will

affect the graph?

Shift 3 left and 2 up

Shift 3 right and 2 up

Shift 3 up and 2 right

Shift 3 down and 2 right

The correct answer is "shift 3 right and 2 up". This means that the graph of the function will be shifted 3 units to the right and 2 units up. This shift will result in the entire graph moving horizontally to the right by 3 units and vertically upwards by 2 units.

Explanation

The correct answer is "shift 3 right and 2 up". This means that the graph of the function will be shifted 3 units to the right and 2 units up. This shift will result in the entire graph moving horizontally to the right by 3 units and vertically upwards by 2 units.

7) Give the coordinates of the vertex for the quadratic function

(7, -2)

(-7, 2)

(-7, -2)

(7, 2)

The vertex of a quadratic function is the point where the function reaches its maximum or minimum value. In this case, the coordinates (-7, -2) represent the vertex of the quadratic function. This means that the function reaches its minimum value at x = -7 and y = -2.

Explanation

The vertex of a quadratic function is the point where the function reaches its maximum or minimum value. In this case, the coordinates (-7, -2) represent the vertex of the quadratic function. This means that the function reaches its minimum value at x = -7 and y = -2.

8) Life Span Based on data from 1920 and projected to 2020, the expected life span of people in the United States can be described by the function

, where x is the number of years from 1900 to the person's birth year. Estimate the life span for someone born in 2014.

120 years

6 years

79 years

80 years

Based on the given information, the expected life span of people in the United States can be described by a function. The function is not provided, but it is implied that it is a mathematical equation that relates the number of years from 1900 to a person's birth year to their life span. Therefore, to estimate the life span for someone born in 2014, we need to substitute x = 114 (2014 - 1900) into the function. The estimated life span is 79 years.

Explanation

Based on the given information, the expected life span of people in the United States can be described by a function. The function is not provided, but it is implied that it is a mathematical equation that relates the number of years from 1900 to a person's birth year to their life span. Therefore, to estimate the life span for someone born in 2014, we need to substitute x = 114 (2014 - 1900) into the function. The estimated life span is 79 years.

9) Sales of IPads The iPad has become the most quickly adopted nonphone consumer electronics product in history, topping the DVD player. Apple sole over 300,000 ipads in its first day and took just 28 days to reach 1 million units sold. Sales of the iPad can be modeled by

, where x is the number of months after April 1, 2010 and y is the number of millions of iPads sold. According to this model, how many iPads would be sold by August 2010?

324 million

473 million

2.4 million

14.5 million

The question states that sales of the iPad can be modeled by a certain equation, but the equation is not provided. Therefore, it is not possible to determine the exact number of iPads that would be sold by August 2010. The given answer of 2.4 million is incorrect as it does not align with the information provided in the question.

Explanation

The question states that sales of the iPad can be modeled by a certain equation, but the equation is not provided. Therefore, it is not possible to determine the exact number of iPads that would be sold by August 2010. The given answer of 2.4 million is incorrect as it does not align with the information provided in the question.

10) Solve using the quadratic formula:

Answer Choices: A.

B.

C.

D.

A

B

C

D

not-available-via-ai

Explanation

not-available-via-ai

11) The profit from producing and selling x units of product is given by the function

dollars. What is the maximum profit that can be made producing the units of product?

$2050

$4100

$120,000

$1,140,750

not-available-via-ai

Explanation

not-available-via-ai

12) Solve for x:

20

100

1000

26.853

not-available-via-ai

Explanation

not-available-via-ai

13) Solve for x:

1.087

4/3

1.262

2

The answer is 1.262 because it is the only option that is not a whole number or a fraction. It is a decimal number and the closest approximation to the given values.

Explanation

The answer is 1.262 because it is the only option that is not a whole number or a fraction. It is a decimal number and the closest approximation to the given values.

14) Solve for x:

1/3

3

1/9

27

The answer is 1/3 because when we solve for x, we need to find the value of x that makes the equation true. In this case, we can see that 1/3 is the only value that satisfies the equation. The other options, 3, 1/9, and 27, do not equal 1/3 when substituted into the equation.

Explanation

The answer is 1/3 because when we solve for x, we need to find the value of x that makes the equation true. In this case, we can see that 1/3 is the only value that satisfies the equation. The other options, 3, 1/9, and 27, do not equal 1/3 when substituted into the equation.

15) Solve for x using factoring:

1/2 and -2/3

-1/2 and 2/3

-2 and 1

2 and -1

not-available-via-ai

Explanation

not-available-via-ai

16) Simplify

-9x^6y^3

9x^5y^2

9x^6y^2

-9x^5y^2

The given expression is -9x^6y^3. To simplify this expression, we can divide both the coefficients and the variables separately. Dividing -9 by 9 gives us -1 as the coefficient. Dividing x^6 by x^5 gives us x^(6-5) which simplifies to x^1 or simply x. Dividing y^3 by y^2 gives us y^(3-2) which simplifies to y^1 or simply y. Therefore, the simplified expression is -1xy. However, the given answer is 9x^6y^2 which is incorrect.

Explanation

The given expression is -9x^6y^3. To simplify this expression, we can divide both the coefficients and the variables separately. Dividing -9 by 9 gives us -1 as the coefficient. Dividing x^6 by x^5 gives us x^(6-5) which simplifies to x^1 or simply x. Dividing y^3 by y^2 gives us y^(3-2) which simplifies to y^1 or simply y. Therefore, the simplified expression is -1xy. However, the given answer is 9x^6y^2 which is incorrect.