Module 1 Topic 3 MidTopic

• x ∈ (−5, 7)

• (−10, 0)

• x ∈ (10, 0)

• x ∈ (−7, 5)

Answer explanation

To solve the inequality x^2 + 2x - 21 < 14, first simplify to x^2 + 2x - 35 < 0. Factoring gives (x - 5)(x + 7) < 0. The solution set is x ∈ (−5, 7), where the product is negative.

Which statement about the relationship between a function and its inverse is true?

• The function and its inverse are always the same function.

• The function and its inverse do not have any relationship.

• The graph of the inverse function is the reflection of the function across the line y = x.

• The inverse of a function is always a linear function.

Answer explanation

The correct statement is that the graph of the inverse function is the reflection of the function across the line y = x. This means that if you were to fold the graph along this line, the function and its inverse would match.

Tags

CCSS.HSF-BF.B.4C

Answer explanation

To find the inverse, set y = 4x^2 - 16. Rearranging gives x^2 = (y + 16)/4. Taking the square root yields x = ±√((y + 16)/4), thus the inverse is f^{-1}(y) = ±√((y + 16)/4).

Tags

CCSS.HSF-BF.B.4A

• (−∞, 5) ∪ (10, ∞)

• (−∞, -5] ∪ [10, ∞)

• (−∞, -10) ∪ (−5, 10)

• [−5, 10]

Answer explanation

To solve the inequality x^2 - 5x - 50 ≥ 0, we first rewrite it as x^2 - 5x - 50 = 0. The roots are x = -5 and x = 10. The solution set is where the quadratic is greater than or equal to zero, which is (−∞, -5] ∪ [10, ∞).

• t ≈ 1.06, t ≈ 11.24

• t ≈ 0.7, t ≈ 8.7

• t ≈ 0.5, t ≈ 12.0

• t ≈ 2.50, t ≈ 9.75

Answer explanation

To find when the baseball is above 100 feet, set h(t) = -16t^2 + 150t + 0.1 > 100. Solving the quadratic equation gives t ≈ 1.06 and t ≈ 11.24. Thus, the correct answer is t ≈ 1.06, t ≈ 11.24.

Johnny and Franky are playing a guessing game. Johnny tells Franky that he is thinking of two negative integers. The first number minus the second number is 3. The square of the first number minus 3 times the second number is equal to 19. Solve the system of equations.

• (5,2)

• x = -3, y = -6

• x = -1, y = -4

• (-2, -5)

Answer explanation

To solve the equations: 1) x - y = 3 and 2) x^2 - 3y = 19. Substituting y = x - 3 into the second equation gives x = -3 and y = -6. Thus, the correct answer is x = -3, y = -6.

Tags

CCSS.HSA.REI.C.7

7. Johnny and Franky are playing a guessing game. Johnny tells Franky that he is thinking of two negative integers. The first number minus the second number is 3. The square of the first number minus 3 times the second number is equal to 19. Which of the following is the correct system of equations for the situation?

Answer explanation

The first equation, x - y = 3, represents the difference between the two integers. The second equation, x^2 - 3y = 19, captures the relationship involving their squares and multiples. Thus, the correct system is x - y = 3 and x^2 - 3y = 19.

Tags

CCSS.HSA.REI.C.7

Solve the system of equations algebraically over the set of real numbers.

The answer is (0, 3) and (-6, -15).

• (-3, -6)

• (2, 9) and (0, 5)

• (1, 6)

• (0, 3) and (-6, -15)

Answer explanation

To solve the system, substitute values from the equations. (0, 3) and (-6, -15) satisfy both equations, while the other options do not. Thus, the correct solutions are (0, 3) and (-6, -15).

• The graph is a downward-opening parabola with vertex at (0, -7).

• The graph is a circle centered at (0, 7) with a radius of 5.

• The graph is an upward-opening parabola with vertex at (0, 7).

• The graph is a straight line with a slope of 1.

Answer explanation

The function f(x) = (1/2)x^2 + 7 is a quadratic function with a positive leading coefficient, indicating it opens upward. The vertex form shows the vertex at (0, 7), confirming the correct choice.

Tags

CCSS.HSF-IF.C.7A

Answer explanation

The correct inverse is f^{-1}(y) = "\sqrt{2}(y-7)". This is not a function because it does not pass the vertical line test; it produces multiple outputs for some inputs.