Math 3 Check-In 2 (Calculator Active)
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Questions and Answers

Which expression is equivalent to 2x/(3x + 2) + x/(3x + 2)?

  • 3x 6x + 4
  • 1 2
  • 3x 3x + 2 (correct)
  • x x + 2

    • Which expression is equivalent to 3/(2 - x) + 1/(x + 4) + 4/(6x + 1)?

  • 2x -6 -x + 12
  • -x² - 4x + 12 8x² + 32
  • 3x³ + 5x² - 22x 2x² - 4x – 48 (correct)
  • x² + 4x - 12 x² - 2x - 24

    • What is the value of x in this equation? (2x² - 4)/(x + 2) = 3

  • 8
  • 6
  • 4 (correct)
  • 2

    • Which scenario could be modeled by the graph of the function f(x) = 100(1.002)^x?

    <p>An ant colony that has an initial population of 100 increases by 0.2% per year.</p> Signup and view all the answers

    What is the difference between the minimum value of f(x) and the minimum value of g(x) = x² + 4x - 8?

    <p>10 units</p> Signup and view all the answers

    What is the solution to the equation shown? x² + 5x - 14 / x - 2 = -21

    <p>-7</p> Signup and view all the answers

    What is the smallest zero of h(x) = x³ + 2x² - 5x - 6?

    <p>-3</p> Signup and view all the answers

    The function f is defined as f(x) = (x - 4)²(x + 3). The cubic function g(x) has a root at 5, a double root at -2, and a leading coefficient of 1. What is the horizontal distance, in units, between the relative minimum of f(x) and the relative maximum of g(x)?

    <p>7</p> Signup and view all the answers

    What is the diameter of the circle defined by x² - 6x + y² + 4y - 23 = 0?

    <p>10</p> Signup and view all the answers

    Kim is comparing two functions:

    • The quadratic function f(x) has roots at -4 and 2 and a y-intercept at 2.
    • The graphic of cubic function g(x) is shown.

    <p>2</p> Signup and view all the answers

    What coordinate pair is the center of the circle represented by (x - 3)² + (y + 4)² = 9?

    <p>(3, -4)</p> Signup and view all the answers

    The coverage area for a certain radio station can be modeled as a circle with the center at the station's transmitter and a radius of 25 miles. The population density for the coverage area is 14.2 residents per square mile. To the nearest hundred, how many people reside within the station's coverage area?

    <p>111,500</p> Signup and view all the answers

    Which expression is equivalent to (2x + 7)/(3x - 5) - (4x + 6)/(x + 3)?

    <p>-10x² + 15x + 51 (x + 3)(3x - 5)</p> Signup and view all the answers

    A boat takes 30 minutes to travel 10 miles upstream. The river is flowing at a constant rate of 3 mph. What is the speed of the boat in still water?

    <p>17 mph</p> Signup and view all the answers

    An experiment attempts to simulate temperatures in degrees Fahrenheit for the first 10 hours of the day. This piecewise function models the progression at any time, x, during the experiment. f(x) = {48 + 5x for 0 < x ≤ 4 {60 + 2x for 4 < x ≤ 7 {81 - 1x for 7 < x ≤ 10 What is the maximum temperature simulated during the experiment?

    <p>81°F</p> Signup and view all the answers

    A farmer is enclosing a rectangular garden using one side of his barn. The farmer has 80 meters of fencing for the remaining 3 sides. The length will be longer than the width. This diagram shows the barn and the garden.

    <p>20</p> Signup and view all the answers

    This shows an equation.
    3x³ + hx² + 16 / x +1 = 3x² / x + 1 + 15 / x + 1 What value for h will make the equation true if x ≠ -1?

    <p>-2</p> Signup and view all the answers

    Tiffany is a member of the chess club. She won 75% of her first 32 games this year. How many games in a row does she need to win to have a winning percent of exactly 80%?

    <p>16</p> Signup and view all the answers

    A definition for a function, f, is shown. f(x) = 1/(x - 3) - (x - 3)(x + 2) Which choice describes x = 3 for this function?

    <p>the location of a removable discontinuity of <em>f</em></p> Signup and view all the answers

    Janet is comparing the functions h(x) and g(x).

    • This shows the graph for h(x)
    • The function g(x) is defined as -x² - 2x + 6.

    <p>h(x) has a larger maximum value than g(x), and h(x) has a smaller value at x = 3.</p> Signup and view all the answers

    This shows a table for f(x)

    <p>k(x) = 1.5x + 3</p> Signup and view all the answers

    A circle is represented by the equation -20 = x² + y² + 8x - 6y. Which statement is true about the circle?

    <p>The center of the circle is located at (-4, 3), and the radius of the circle is 5 units.</p> Signup and view all the answers

    A track has the dimensions shown.
    The track has 8 lanes. Each lane is 1.2 meters wide.

    To the nearest tenth of a meter, what is the perimeter of the outside of the track?

    <p>543.1</p> Signup and view all the answers

    A function is shown: f(x) = x + 2 / x² - 3x - 10 At what positive x value does the function have a discontinuity?

    <p>5</p> Signup and view all the answers

    The equation of a circle is x² + y² - 4x - 6y + 5 = 0. What is the value of the y-coordinate of the circle's center?

    <p>3</p> Signup and view all the answers

    A rectangular prism is made of stainless steel.

    • The prism measures 15 cm long, 10 cm wide, and 2 cm high.
    • The density of stainless steel is 7.9 g/cm³ What is the mass, in grams, of the prism?

    <p>2370</p> Signup and view all the answers

    Study Notes

    NC Check-In 2 - Math 3 (Calculator Active)

    • Question 1: Find the equivalent expression for 2x/(3x + 2) + x/(3x + 2). The correct answer is x + 2

    • Question 2: Find the equivalent expression for 2x/(x² - 2x - 24). The correct answer is (2x - 6)/(x² - 2x - 24) simplified to 2 / (x + 4)

    • Question 3: Solve for x in the equation 2x² - 4 = x³/ 2. The correct answer is 4.

    • Question 4: An ant colony that has an initial population of 100 increases by 0.2% per year is described by the function f(x)=100(1.002)^x

    • Question 5: Find the difference between the minimum values of f(x) and g(x) = x² + 4x - 8. The correct answer depends on the table of values for f(x)

    • Question 6: Find the solution to the equation x² + 5x – 14 = -21. The correct solution is 1.

    • Question 7: Find the smallest zero of h(x) = x³ + 2x² – 5x - 6. Correct Answer depends on possible solutions

    • Question 8: The function f(x) is defined as f(x)= (x− 4)² (x + 3). A cubic function g(x) has a root at 5, a double root at -2, and a leading coefficient of 1. Find the horizontal distance between the relative minimum of f(x) and the relative maximum of g(x). Correct answer depends on the functions

    • Question 9: Find the diameter of the circle defined by x² - 6x + y² + 4y - 23 = 0. Correct Answer is dependent on the problem. Find the radius of the circle and multiply by 2.

    • Question 10: The quadratic function f(x) has roots at -4 and 2, and a y-intercept at 2. The cubic function g(x) is graphically shown on the page.

    • Question 11: Find the center of the circle (x-3)² + (y+4)² = 9. The correct answer is (3, -4).

    • Question 12: A radio station's coverage area is modeled as a circle with a 25-mile radius. The population density is 14.2 residents/mi². Calculate the total population within the coverage area (to the nearest hundred). Answer depends on the calculation

    • Question 13: Find the equivalent expression for (2x² + 7x - 4x - 6) / (x + 3). The correct answer is dependent on the correct simplification of the dividend.

    • Question 14: A boat takes 30 minutes to travel 10 miles upstream. The river's flow is 3 mph. Calculate the boat's speed in still water. Answer is 17 mph

    • Question 15: Find the maximum temperature simulated in an experiment, given a piecewise function describing temperature over 10 hours. The correct answer depends on the piecewise function

    • Question 16: A farmer uses 80 meters of fencing to enclose a rectangular garden beside a barn, with the length longer than the width. Find the width that maximizes the garden area. Answer depends on calculation from diagram

    • Question 17: Given the equation 3x³ + hx² + 16 / ( x+1) = 3x² + 15 / (x+1) + 15/ (x + 1). Find the value of h for the equation to hold true when x does not equal -1. The correct answer depends on possible values

    • Question 18: Tiffany won 75% of her first 32 games. How many more games must she win in a row to reach an 80% overall win rate? The correct answer depends on the calculation

    • Question 19: Which description describes x = 3 for a given function f(x) ? Correct Answer is dependent on the function.

    • Question 20: Janet is comparing functions h(x) and g(x) = x² - 2x + 6. The graph of h(x) is shown.

    • Question 21: Find the function with an average rate of change over the interval [5, 8] closest to the rate of change of a given table of f(x) values. The correct answer depends on the calculation and the given table of values

    • Question 22: A circle is presented by −20 = x² + y² + 8x − 6y. Identify the center and radius of the circle. The correct answer depends on the calculation

    • Question 23: Calculate the perimeter of an oval-shaped track (with given dimensions and 8 lanes) to the nearest tenth of a meter. The correct answer depends on the calculation and the diagram.

    • Question 24: Given a rational function f(x), determine the positive x-value where there is a discontinuity. Answer depends on the function

    • Question 25: Find the y-coordinate of the center of a circle given its equation (x² + y² - 4x - 6y + 5 = 0)

    • Question 26: A rectangular stainless steel prism has given dimensions and density. Determine its mass in grams. The correct answer depends on the calculation

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    Description

    Test your knowledge with this NC Check-In 2 quiz for Math 3. It covers various topics including equivalent expressions, solving equations, and analyzing functions. Utilize your calculator to help solve the problems presented in this quiz, and see how well you understand the material!

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