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College Algebra K/DCWednesday, 09 September 2015

• OBJECTIVE TSW solve problems involving sets of numbers, absolute value, and substitution.

• ASSIGNMENT DUE (wire basket)– WS Mean, Median, Mode– I will take a few questions first

• TESTS are graded.

R-2

Set of Numbers and Absolute Value R.2:

R-3

Sets of Numbers

s s

s

s

s

R-4

Sets of Numbers

Decide whether the statement is true or false. If false, give one counterexample.

a) Every whole number is an integer.

b) Every integer is a rational number.

c) Every rational number is an integer.

true

true

false: ½

R-5

Absolute Value

Absolute value is the distance on the number line from a number to 0.

The absolute value of a number is always positive or 0.

R-6

Evaluating Absolute Values

Evaluate each expression:

(a) (b)

(c) (d)

R-7

Evaluating Absolute Value Expressions

Let m = 13 and n = –9. Evaluate each expression.

(a)

(b)

1

4

6

Assignment: 09/09/2015

• The packet is yours; put your name on it. • Put your work on notebook paper; do NOT turn in

the packet!

• PP. 17-18 (3-16 ALL, 33-45 ODD, 63-68 ALL, 77-82 ALL)• Due in 30 minutes (basket).

• QUIZ over Mean, Median, Mode, Absolute Value on TUESDAY, 09/15/2015.

R-8

Working with Absolute Value

Ex: Find all values for x such that| x | = 14.

Solution: x = 14 or x = 14

Working with Absolute Value

Ex: Find all values for x such that| x 18 | = 23.

Solution: x 18 = 23 or x 18 = 23

x = 41 x = 5

Working with Absolute Value

Ex: Find all values for x such that| 25 x | = 1.

Solution: 25 x = 1 or 25 x = 1x = 24 x = 26x = 24 x = 26

Absolute Value Applications

You will not have to write the whole problem, but you will have to show all work.

Absolute Value Applications

Systolic blood pressure is the maximum pressure produced by each heartbeat. Both low blood pressure and high blood pressure may be cause for medical concern. Therefore, health care professionals are interested in a patient’s “pressure difference from normal,” or Pd. If 120 is considered a normal systolic pressure, then Pd = |P – 120|, where P is the patient’s recorded systolic pressure. Find Pd for a patient with a systolic pressure, P, of 113.

Absolute Value Applications

Systolic blood pressure is the maximum pressure produced by each heartbeat. Both low blood pressure and high blood pressure may be cause for medical concern. Therefore, health care professionals are interested in a patient’s “pressure difference from normal,” or Pd. If 120 is considered a normal systolic pressure, Pd = |P – 120|, where P is the patient’s recorded systolic pressure. Find Pd for a patient with a systolic pressure, P, of 113.

Pd = |P – 120|= |113 – 120|= |–7|= 7

Absolute Value Applications

If a problem asks you to find a value and answer a question, use complete sentences.

“What does this represent?”“What does this mean?”“Why or why not?”

(What follows is part of the assignment so you should follow along.)

Absolute Value Applications

95. In the 2007 Masters Golf Tournament, Zach Johnson won the final round with a score that was 3 under par, while the 2006 tournament winner, Phil Mickelson, finished with a final-round score that was 5 over par. Using –3 to represent 3 under par and +5 to represent 5 over par, find the difference between these scores (in either order) and take the absolute value of the difference. What does this final number represent?

Absolute Value Applications

95. In the 2007 Masters Golf Tournament, Zach Johnson won the final round with a score that was 3 under par, while the 2006 tournament winner, Phil Mickelson, finished with a final-round score that was 5 over par. Using –3 to represent 3 under par and +5 to represent 5 over par, find the difference between these scores (in either order) and take the absolute value of the difference. What does this final number represent?

difference = |–3 – 5|= |–8|= 8

This number represents the difference in their scores.

Distance on a Number Line

If P and Q are points on the number line with coordinates a and b, respectively, then the distance d (P, Q) between them is

, .b a bQ ad P or

REMEMBER: Distance is always positive or 0!

Absolute Value Applications

•Assignment– Sec. R.2 – pp. 18-19 (83-98 ALL, 105-108 ALL,

115-119 ALL)– This assignment is due on Monday, 09/14/2015.

• QUIZ on Tuesday over MMM and Absolute Value.