Homework LogThurs & Fri

10/22

Lesson Rev

Learning Objective: To remember everything in Ch 2

Hw: #216 Pg. 155 #1 – 85 odd

Homework LogMon

10/24

Lesson Rev

Learning Objective: To remember everything in Ch 2

Hw: Extra Credit Test Review

10/22/15 Chapter 2 Review

Advanced Math/Trig

Learning Objective

To remember everything in Chapter 2!

Solve a Rational Equation

1.

x + 3(1 – x) = –1(1 – x)

x + 3 – 3x = –1 + x

3 – 2x = –1 + x

–3x = –4

x

LCD:x(1 – x)

2. – 7 – 7

– 4 – 4

2x – 3 = 4 or 2x – 3 = – 4

2x = 7 2x = –1x = or x =

Absolute Value Equations

Warm–up #2 Solutions3. Solve x + 5 = 3x – 2 or x + 5 = –(3x – 2)–2x = –7 or x + 5 = –3x + 2 4x = –3x = or x = Nope!Check for extraneous solutions!

Solving for a Variable4. Solve for S:

PS + PF = S – PS – PS

PF = S – PS PF = S(1 – P)

(S + F)

(S + F)

Simple Interest5. Part of $20,000 is to be invested at 15% and the remainder at 9%. How much should be invested at each rate to yield an annual interest income of $2520.

Principal rate time Interest

Inv 1

Inv 2

Total 20000

x20000 – x

.15.09

11

• • =.15x

.09(20000 – x)2520

equation!.15x + .09(20000 – x) = 2520

.15x + .09(20000 – x) = 2520 .15x + 1800 – .09x = 2520 .06x = 720 x = 12000

20000 – 12000 = 8000

$12,000 at 15%$8,000 at 9%

Simple Interest #5 cont’d

Investment6. If $9000 is invested at 7% per year, how much additional money needs to be invested at 14% per year so that the total annual interest income from the investments is $1330?Principal rate time Interest

Inv 1

Inv 2

Total 9000 + x

9000x

.07.14

11

• • =9000(.07) = 630

.14x1330

equation!630 + .14x = 1330

630 + .14x = 1330.14x = 700

x = 5000

$5,000 at 14%

Investment Cont’d

Mixture7. I want to dilute 40 L of a solution that is 80% acid to one that is 50% acid. How much water should be added to the acid solution?

Amount % Total

Solution 1

Solution 2

Mix 50(40 + x)

80

40 + x

x

40

0

50

40(80) = 32000

3200 = 50(40 + x)

• =24 L

Distance Problem8. Laura & Luke left school at the same time and went in opposite directions. Laura was driving 40 mph faster than Luke. After 3 hours, they were 330 miles apart. How fast was Laura driving?Rate Time Distance

Laura

Luke

Total

3

x

x + 40

3

3(x + 40)

3x

3(x + 40) + 3x = 3303x + 120 + 3x = 330x = 35

• =330

75 mph

Drain/Work Problem9. An Olympic sized pool can be filled by pipe A in 12 hours and by pipe B in 10 hours.  There is also a drain pipe that drains the entire pool in 6 hours.  If the valves of pipe A, pipe B and the drain pipe are open, how long will it take to fill the pool?

AloneRate

Time Together

Part of Job

Completed

Pipe A

Pipe B

Drain Pipe

x

x

• =x

𝟏𝟏𝟐𝟏𝟏𝟎

−𝟏𝟔

𝒙𝟏𝟐𝒙𝟏𝟎

−𝒙𝟔

Pipe A’s part + Pipe B’s part + Drain’s part= 1 Whole Job Completed(60) (60) (60)(60)

x = 60 hours

Drain/Work Problem #9 Cont’d

AloneRate

Time Together

Part of Job

Completed

Pipe A

Pipe B

Drain Pipe

x

x

• =x

𝟏𝟏𝟐𝟏𝟏𝟎

−𝟏𝟔

𝒙𝟏𝟐𝒙𝟏𝟎

−𝒙𝟔

𝑥12

+𝑥

10−𝑥6

=1

5x + 6x – 10x = 60

Work Problem10. Working together, Scott and Jenna can sweep a porch in 10 minutes. If Jenna worked alone, it would have taken her 15 minutes. How long does it take Scott to sweep the porch alone?Alone

RateTime

TogetherPart of

JobComplete

d

Scott

Jenna

10

10

Scott’s part + Jenna’s part = 1 Whole Job Completed

• =𝟏𝟏𝟓

𝟏𝒙

𝟏𝟎𝒙𝟏𝟎𝟏𝟓

Work Problem #10 Cont’d

10𝑥

+1015

=1(1 5𝑥 ) (1 5𝑥 )

(1 5𝑥 )

150 + 10x = 15x150 = 5x

30 minutes

AloneRate

Time Together

Part of Job

Completed

Scott

Jenna

10

10

Scott’s part + Jenna’s part = 1 Whole Job Completed

• =𝟏𝟏𝟓

𝟏𝒙

𝟏𝟎𝒙𝟏𝟎𝟏𝟓

11. Less ThAND

2x – 5 < 3 and 2x – 5 > – 3 + 5 + 5 +5 +5 2x < 8 2x > 2 2 2 2 2x < 4 and x > 1 1 < x < 4

Solve Absolute Value Inequalities

(1, 4)

12. GreatOR

5x + 3 > 7 or 5x + 3 < – 7 – 3 – 3 – 3 – 35x > 4 5x < – 10 5 5 5 5x > 4/5 or x < – 2

Solve Absolute Value Inequalities

(–, –2) (, )

13. – 5

All Real Numbers

Absolute Value is always positive & will ALWAYS be greater than a negative number!!

Solve Absolute Value Inequalities

(–, )

14. 20

No Solution

Absolute Value is always positive & will NEVER be less than a negative number!!

Solve Absolute Value Inequalities

∅

Solve by Factoring15.

x(2x – 1)(x + 3) = 0

x = 0 x + 3 = 0 2x – 1 = 0

{–3, 0, }

2 #s that mult to

–6

5& add to

6 –1

Solve by Completing the Square

16. = 0

– 20 – 20

= – 20 +

x – 4 =

√❑√❑

16 16

=

Or

Solve by Completing the Square

17.

4 4 4

+

√¿¿

❑¿

√¿¿

❑¿

Solve by Factoring18.

u(u – 7) + 2(u – 7) = 0

(u – 7)(u + 2) = 0

Let

2 #s that mult to–14

–5& add to

–7 2

Solve by Factoring18. (u – 7)(u + 2) = 0

((x +2) – 7)((x +2) + 2) = 0

(x – 5)(x + 4) = 0

x – 5 = 0 x + 4 = 0

{– 4, 5}

Now replace u with

2 Answers!!

Highest Power is 2!!

Sum – Product Rule

x2 – (sum)x + product = 0

sum: 5 + –3 = 2

product: (5)(–3) = –

15x2 – (2)(x) + (–15) = 0

x2 – 2x – 15 = 0

19. Find a monic quadratic eq’n whose roots are 5 & –3

2 4

2

b b acx

a

Quadratic Formula

Xavier is a negative boy who couldn’t decide (yes or no) whether to go to a radical party.

It turns out that this boy is a total square because he missed out on 4 awesome chicks.

And the party was all over at 2 AM.

2Given: 0ax bx c

DiscriminantDiscriminant – tells the nature of the roots

(Part under the radical)

Discriminant Roots

Zero 1 real double root

Positive 2 real roots

Negative 2 imaginary roots