Questions: The points at -6 and -1 shown on the number line below are the real solutions to the polynomial equation x^2+7x+6=0 and represent the boundary points for the polynomial inequality x^2+7x+6>0. The points at -6 and -1 divide the number line into which three intervals? Choose the correct answer below. A. (-∞,-6),(-6,-1), and (-1, ∞) B. (-∞, 1),(1,6), and (6, ∞) C. (-∞,-1),(-1,-6), and (-6, ∞) D. (-∞,-6],[-6,-1], and [-1, ∞)

The points at -6 and -1 shown on the number line below are the real solutions to the polynomial equation x^2+7x+6=0 and represent the boundary points for the polynomial inequality x^2+7x+6>0. The points at -6 and -1 divide the number line into which three intervals? Choose the correct answer below. A. (-∞,-6),(-6,-1), and (-1, ∞) B. (-∞, 1),(1,6), and (6, ∞) C. (-∞,-1),(-1,-6), and (-6, ∞) D. (-∞,-6],[-6,-1], and [-1, ∞)
Transcript text: The points at -6 and -1 shown on the number line below are the real solutions to the polynomial equation $\mathrm{x}^{2}+7 \mathrm{x}+6=0$ and represent the boundary points for the polynomial inequality $\mathrm{x}^{2}+7 \mathrm{x}+6>0$. The points at -6 and -1 divide the number line into which three intervals? Choose the correct answer below. A. $(-\infty,-6),(-6,-1)$, and $(-1, \infty)$ B. $(-\infty, 1),(1,6)$, and $(6, \infty)$ C. $(-\infty,-1),(-1,-6)$, and $(-6, \infty)$ D. $(-\infty,-6],[-6,-1]$, and $[-1, \infty)$
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the boundary points

The boundary points are -6 and -1.

Step 2: Determine the intervals

The boundary points divide the number line into three intervals:

  1. From negative infinity to -6: (-∞, -6)
  2. From -6 to -1: (-6, -1)
  3. From -1 to positive infinity: (-1, ∞)

Final Answer:

The correct answer is A. (-∞, -6), (-6, -1), and (-1, ∞)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients, In clinical trials, among 4460 patients treated with the drug, 139 developed the adverse reaction of nausea. Construct a 95% confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion p. 0.031 (Round to three decimal places as needed.) b) Identify the value of the margin of error E . E= (Round to three decimal places as needed.)
failedAnswered
Select all that apply Not all mRNA molecules are equally stable; select all of the ways that this can affect gene regulation. The protein that an mRNA encodes may be destroyed. An mRNA molecule may be degraded before it is translated. An mRNA molecule may be degraded before it is transcribed. An mRNA molecule may persist long enough to be translated many times.
failedAnswered
A ship travels 52 km on a bearing of 20 degrees, and then travels on a bearing of 110 degrees for 113 km. Find the distance from the starting point to the end of the trip, to the nearest kilometer.
failedAnswered
The fuel gauge shows how much fuel is left in a 12 gallon tank. How far can you drive if the car's average fuel consumption is 40 miles per gallon?
failedAnswered
Which constitutional amendment proposed by the 66th Legislature in 1979 was approved by voters? a. A single property tax appraisal district was established in each county. b. A Texas Salary Commission was established for elected and appointed officials. c. Fourteen courts of appeals were granted broad civil jurisdiction. d. The governor's removal power over appointed statewide officials was abolished.