13. Module A Outcome 3 Solving Absolute Value Eq and Ineq.

A carpenter is using a lather to shape the final leg of a handcrafted table. In order for the leg to fit, it needs to be 150 millimeters wide allowing for a margin of error of 2.5 millimeters. Check all of the statements that are true regarding the information.

• The absolute value inequality that can be used to model the informations is

  $\left|x-150\right|\le2.5$

• The absolute value inequality that can be used to model the information is $\left|x-150\right|\ge2.5$

• The domain that represents the size of the leg that can fit is [147.5, 152.5]

• The domain that represents the size of the leg that can fit is $147.5<x<152.5$

Sydney Harbor Bridge in Australia is 1149 meters long. Because of changes in temperature, the bridge can expand and contract by as much as 420 millimeters (0.42meters). Check all of the statements that are true regarding the information

• The longest the bridge can expand to is 1149.42 meters and the shortest the bridge can contract to is 1148.58 meters. The bridge will fail if the lengths go outside that domain.

• The domain that represents the length of the bridge can be written as [1148.58, 1149.42]

• (-2.33,-.33)

• [-2.33, -.33]

•  (−∞,-2.33]∪[-0.33,∞)  

•  (−∞,-2.33)∪(-0.33,∞) 

• (-2.33,-0.33)

• [-2.33, -0.33]

• The range of the graph is  [5, ∞)

• f(4) = -27

• The function is decreasing on the interval (0,∞) 

• f(-1) = 3

Find the midpoint between the points (-2, 1) and (6, 7)

Video:

youtube mattdoesmath

Video Title: Find the Distance and Midpoint of a Segment

• (2,4)

• (4,4)

• (4, 8)

• (2, 3)

 Choose the correct solution that best describes the inequality

 $\left|3x-15\right|>27$  

• x < -4

• x < -4 or x >14

• x < 14 and x > -4

• x > 14

Given the function

 $m\left(x\right)\ =\ \sqrt{x-5}$  check all that apply.

• The Domain of the function is  $\left[5,\infty\right)$  

• f(54) = 7

• The range of the function is  $\left[0,\infty\right)$  

• f(9) = 3

Given the function

 $s\left(x\right)\ =\ \left|\left(x-2\right)^2+\frac{3}{2}\right|$   and the function t(x)= 3x.  for what interval is  $t\left(x\right)\ge\ s\left(x\right)$  

• [.902, 6.098]

• (.902, 6.098)

•  $\left(-\infty,\ .902\right]\cup\left[6.098,\infty\right)$  

•  $\left(-\infty,\ .902\right)\cup\left(6.098,\ \infty\right)$  

What is the distance between the points (2, -8) and (-4, 6)

Video

Youtube: MattdoesMath

Video: Find the Distance and Midpoint of a Segment

• 15.23

• 12.23

• 13.23

• 14.23