Transcript August 30/31

Reviewing What We Have Learned
August 30/31
Using Linear Models
ALGEBRA 2 LESSON 2-4
Pages 81–84 Exercises
1. d = 62.5h + 15
3. h = 8x + 60
5. y = 0.5x + 0.75;
3.25 lb
2-4
Using Linear Models
ALGEBRA 2 LESSON 2-4
7. y = 1.75x + 1.75;
$8.40
9.
13. a.
Linear model is
reasonable; models
may vary. Sample:
y = 2.6x – 0.6
11.
Answers may vary.
Sample:
y = 125x + 975
not reasonable
2-4
Using Linear Models
ALGEBRA 2 LESSON 2-4
19. a. y = 29.95
b. y = 2.95x; slope = 2.95, y-intercept = 0
c. Answers may vary. Sample:
Either way, you will average the same costs over
the long run.
2-4
Using Linear Models
ALGEBRA 2 LESSON 2-4
21. a. population
b–c.
d. 2 million
e. Answers may vary. Sample: Strong; the points
fall close to a straight line.
2-4
Absolute Value Functions and Graphs
ALGEBRA 2 LESSON 2-5
Pages 88–90 Exercises
1–9. Tables may vary.
Samples are given.
1.
5.
3.
2-5
Absolute Value Functions and Graphs
ALGEBRA 2 LESSON 2-5
11.
7.
9.
2-5
Absolute Value Functions and Graphs
ALGEBRA 2 LESSON 2-5
15.
19.
17.
13.
2-5
Absolute Value Functions and Graphs
ALGEBRA 2 LESSON 2-5
21.
25.
27.
23.
2-5
Let’s Review
• This will be turned in as a HW grade
• NO CALCULATORS TODAY
• We need to learn how to do stuff without a
calculator
• Once we know how, calculators can then be
used to speed up our process and check for
errors
• No decimals or mixed numbers today
• We are going to get used to putting everything
as an “improper” fraction
• Once you get to the very end, then you can
convert it
So…a few concepts to review
We are going to do problems with these ideas later today. But let’s first cover
them in generalities
When a problem tells us to “solve” the equation, what are we trying to do?
In an equation, when we do something to one side, what must we do to the
opposite side?
In an inequality, if we divide or multiply by a negative number, what must we
do to the inequality sign?
If something is written as f(x)=whatever, we know that it is ___________
Let’s Review—You will turn this in as a HW grade
simplify
1. 15+3
2. 15-3
3. -15-3
4. -15+3
5. 15/3
6. -15/3
7. 15/-3
8. -15/-3
Simplify | 4 |, |–9.2|, |3 – 8|, and |-22+8|
Algebraic Expressions
ALGEBRA 2 LESSON 1-2
Evaluate (k – 18)2 – 4k for k = 6.
(k – 18)2 – 4k = (6 – 18)2 – 4(6)
Substitute 6 for k.
= (–12)2 – 4(6)
Subtract within parentheses.
= 144 – 4(6)
Simplify the power.
= 144 – 24
Multiply.
= 120
Subtract.
1-2
Algebraic Expressions
ALGEBRA 2 LESSON 1-2
8
The expression – 100y 2 + 3y models the percent increase of
Hispanic voters in a town from 1990 to 2000. In the expression, y
represents the number of years since 1990. Find the approximate
percent of increase of Hispanic voters by 1998.
Since 1998 – 1990 = 8, y = 8 represents the year 1998.
−8
−8
–100y2 + 3y = –100(8)2 + 3(8)
−8
= –100(64) + 24=
Substitute 8 for y
512
− 100+24 =
512 2400
-100+ 100 =
1888
=18.88
100
The number of Hispanic voters had increased by about 19%.
1-2
Solving Equations
ALGEBRA 2 LESSON 1-3
Solve 4(m + 9) = –3(m – 4).
4(m + 9)
= –3(m – 4)
4m + 36
Property
= –3m + 12
7m + 36
7m
m
24
7
Distributive
= 12
Add 3m to each side.
= –24
=–
Subtract 36 from each side.
Divide each side by 7.
1-3
Solving Equations
ALGEBRA 2 LESSON 1-3
x
Solve a + 8 = b for x. Find any restrictions on a and b.
x
a +8
a(ax
) + a(8)
x + 8a
x
=b
= ab
Multiply each side by the
least common denominator (LCD), a.
= ab
Simplify.
= ab – 8a
Subtract 8a from each side.
The denominator cannot be zero, so a =/ 0.
1-3
Solving Equations
ALGEBRA 2 LESSON 1-3
A plane takes off from an airport and flies east at a speed of
350 mi/h. Thirty-five minutes later, a second plane takes off from the
same airport and flies east at a higher altitude at a speed of 400 mi/h.
How long does it take the second plane to overtake the first plane?
Relate: distance first plane travels = distance second plane travels.
Define: Let t = the time in hours for the second plane.
Then t + 35
= the time in hours for the first plane.
60
Write:
7
400t = 350 (t + 12
)
400t = 350t + 1225
Distributive Property
6
1-3
Solving Equations
ALGEBRA 2 LESSON 1-3
(continued)
50t = 1225
Solve for t.
6
1
t = 4 12
h or about 4 h 5 min
Check: Is the answer reasonable? In 4 h, the second plane travels 1600
mi. In 4 2 h, the first plane travels about 1600 mi. The answer is
3
reasonable.
1-3
Solve the following inequalities:
1. −2𝑥 < 3(𝑥 − 5)
2. 7𝑥 < 7 2 + 𝑥
3. 14𝑥 > 7(4 + 2𝑥)
Solve:
1. 4 − 2 𝑥 + 9 = −5
2. −2 𝑥 + 1 + 5 ≥ −3
3. 5 𝑥 + 3 > 10
Find f(3) and f(-3) for each function:
1. 𝑓 𝑥 = −𝑥 2 + 1
2. 𝑓 𝑥 = 3𝑥
2
3. 𝑓 𝑥 = 1−𝑥