Questions: x<0 x ≤ -2

x<0 x ≤ -2
Transcript text: 4. $\left.\begin{array}{l}x<0 \\ x \leq-2\end{array}\right)$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the lines and points on the graph

The graph shows three lines with different slopes and intercepts. The lines intersect at specific points, and some points are marked with open or closed circles.

Step 2: Determine the equations of the lines

  • The first line passes through the points (-2, 2) and (0, 0). The slope (m) is calculated as: \[ m = \frac{2 - 0}{-2 - 0} = -1 \] The equation of the line is \( y = -x \).

  • The second line passes through the points (0, 0) and (4, -2). The slope (m) is calculated as: \[ m = \frac{-2 - 0}{4 - 0} = -\frac{1}{2} \] The equation of the line is \( y = -\frac{1}{2}x \).

  • The third line is horizontal and passes through the point (4, -2). The equation of the line is \( y = -2 \).

Step 3: Identify the regions and inequalities

  • For the line \( y = -x \):

    • Above the line: \( y > -x \)
    • Below the line: \( y < -x \)

  • For the line \( y = -\frac{1}{2}x \):

    • Above the line: \( y > -\frac{1}{2}x \)
    • Below the line: \( y < -\frac{1}{2}x \)

  • For the line \( y = -2 \):

    • Above the line: \( y > -2 \)
    • Below the line: \( y < -2 \)

Final Answer

The equations of the lines are:

  1. \( y = -x \)
  2. \( y = -\frac{1}{2}x \)
  3. \( y = -2 \)

The inequalities defining the regions are:

  1. \( y > -x \) and \( y < -x \)
  2. \( y > -\frac{1}{2}x \) and \( y < -\frac{1}{2}x \)
  3. \( y > -2 \) and \( y < -2 \)
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
A population of values has a normal distribution with μ=77.1 and σ=19.9. a. Find the probability that a single randomly selected value is greater than 82. Round your answer to four decimal places. P(X>82)= b. Find the probability that a randomly selected sample of size n=161 has a mean greater than 82. Round your answer to four decimal places. P(M>82)=
failedAnswered
Name each compound and determine the charge an each ion in the compounds. Spelling counts. Li2O name of Li2O: Li charge O charge: CaS name of CaS: Ca charge: S charge
failedAnswered
Sickle cell disease impact on circulatory system (Keyboard Navigable Alternate Version) Complete the following paragraph to explain the physiological impact of sickle-cell disease on the circulatory system. a. The structure of (Click to select) ; suits its function in gas exchange. Because red blood cells are responsible for delivering hemoglobin and oxygen to every cell of the body, any change in the structure of hemoglobin will change the (Click to select) of the red blood cell. b. With sickle cell disease, the hemoglobin in red blood cells is (Click to select) . This in turn changes the shape and damages the (Click to select) , the major type of cell in the circulatory system. c. Sickle red blood cells (Click to select) : together, blocking small blood vessels and causing painful and damaging problems. d. Sickle cell disease also prevents the hemoglobin in red blood cells from carrying (Click to select) :to all parts of the body. As oxygen concentration of the body drops in the individual, a condition called (Click to select) develops.
failedAnswered
What would be the best way to paraphrase the underlined passage from section 5 of Franklin's Daylight Saving? People who have never read the almanac have never seen the sunrise. People who don't understand astronomy couldn't understand what time the sun would rise. People who sleep until noon would be surprised to know that the sun does rise and shine so early.
failedAnswered
Supply: Thinking Like a Seller - End of Chapter Problem Lina is the owner and manager of a small coffee shop that employs three workers who use the shop's one coffee machine to make and serve coffee to paying customers. Business has begun to pick up; lines are getting longer every day in her shop. On a busy morning, she sees her baristas scrambling to take orders, get cups, fill coffee from the coffee machine, add cream and sugar, and serve customers in a timely manner. She figures if she hires three more baristas she'll be able to sell twice as much coffee. 2. Do you think she's likely to be right? Why or why not?