Chapter 9 Algebra and calculator review
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Chapter 9
Algebra and calculator practice
Spring 2016
(1/16/16)
Note: this course presumes a High School proficiency with Algebra. Based on this, I’ve
selected only those parts of this chapter needed to review for:
Chapter 5
Chapter 8
Chapter 10
Chapter 11
If you need more High School Algebra review, read all Chapter 9 especially sections 1, 2
in text pages 247 – 267 and more depending on your competence level. Seek a tutor
available for Math 102 students. Some who need remedial work might consider Max 100
available as a lead-in course to this.
Learn how to use your calculator. Each comes with a printed set of instructions, an online manual, and maybe an on-line help-desk.
Chapter 9 Algebra and calculator review
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Linear functions
Functions - a function is an expression of dependence. A variable (y) is a function of
another variable (x) written as an equation. Linear functions are drawn as
straight lines.
Examples:
Your weekly pay (y) is a function of how many hours you worked (x).
Your salary is $18 per hour…
y = 18x
Sales revenue (y) is a function of how many units sold (x).
Each sale is $56
y = 56x
Translate a verbal expression into a linear function:
six more than a number
x+6
six times a number
6x
six more than a number is 10
x + 6 = 10
a number decreased by 13 is 6 times the number x - 13 = 6x
Writing and solving a linear function
Example: ABCD House cleaning service charges $20.00 fee, plus $32.50 per hour for
labor. One particular service bill was $117.50. How many labor hours were charged?
let n = number labor hours
$32.50n = labor cost
Service charge = $117.50 = $32.50n + $20.00
117.50 - 20.00 = 32.50n
n = 117.50 - 20.00 = 3
32.50
Example: Your promotion to Broadcast Manager at WXYZ Action News requires you to
plan ahead for next year’s TV crew expenses for on scene reporting. Your predecessor,
familiar with budgeting, left the following algorithm for estimating annual budget
increases
solve for x in the equation 4x - 0.48 = 0.8x + 4 (linear function)
4x - 0.8x = 4 + 0.48
3.2 x = 4.48
x = 4.48
3.2
x = 1.4
budget will increase by 40%
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Calculator work – learn your calculator for these problem types. (Recall policy
regarding graphing calculators)
Example: Solve: A = p(1 + rt)
when p = 3,000
r = .018
t=2
A
A
A
A
= 3,000(1 + .018(2))
= 3,000(1 + .036)
= 3,000(1.036)
= 3,108
Example: Solve: A = p(1 + r/n) nt
when p = 3,000
r = .018
n = 12
t=2
A = 3000(1 + .018/12) 12(2)
A = 3000(1 + .0015) 24
A = 3000(1.0015) 24
A = 3000(1.036627885) = 3109.883655
Example: Solve for E when
is 0.5 and n = 500
E =2
( 1n
E =2
.5(1-.5)
500
=2
)
=
2
.25
500
5.-04
on my calculator 5.-04 means 5.0 (10) -4 = .0005
yours might be shown differently
= 2 .0005
= 2(.022360679) = .044721359
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Graph a linear function
A linear function is a straight line when drawn on coordinate axes. Any 2 points will
describe the line.
Example: x = 4 is a straight line with x having no dependence on y….x is always 4
7
6
5
4
3
2
1
x=4
x
-7 -6 -5 -4 -3 -2 -1
-2
-3
-4
1 2 3 4 5 6 7
Example: y = 4 is a straight line with y having no dependence on x….y is always 4
7
6
5
4
3
2
1
y=4
x
-7 -6 -5 -4 -3 -2 -1
-2
-3
-4
1 2 3 4 5 6 7
8
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Example: x + 2y = 2
For this course, use the intercepts method. There are 3 other methods, but the intercepts
method is best for this course.
Set x = 0, solve for y
Set y = 0, solve for x
x + 2y = 2
(0) + 2y = 2
2y = 2
y = 1 (0,1)
x + 2y = 2
x + 2(0) = 2
x = 2 (2,0)
y
3
2
1
(0, 1)
(2, 0)
x
1
2
3
4
5
6
x + 2y = 2
Example: x - 2y = 6
Set x = 0, solve for y
Set y = 0, solve for x
x - 2y = 6
(0) - 2y = 6
2y = -6
y = -3 (0,-3)
x - 2y = 6
x - 2(0) = 6
x = 6 (6,0)
y
3
2
1
x
1
2
3
4
5
6
x + 2y = 2
(0, -3)
Chapter 9 Algebra and calculator review
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Practice problems page 272
17.) combine terms: 7x + 3y - 4x + 8y
3x + 11y
24.) combine terms: 4s + 3t + 8 - 2t
4s + t +8
32.) combine terms: 0.9(2.3x - 2) + 1.7(3.2x - 5)
2.07x - 1.8 + 5.44x - 8.5
7.51x -10.3
40.) solve for x: 12 = 3x + 6
12 - 6 = 3x
6 = 3x
2=x
50.) solve for r:
r + 2r = 7
3
.3333333333333 is written as .33
.33r + 2r = 7
2.33 r = 7
r = 7/2.33 = 3
65.) Paint (1 gal. covers 825 ft2) needed for 6600 ft2
let x = gals. needed
x = 6600 ft2
825 ft2/gal.
x = 6600/825 = 8 gals.
68.) (There’s another 68 [later] but it’s a different problem)
Bag of topsoil = 40 lbs.
Bag of topsoil = 12 ft2
a.) how many lbs. = 480 ft2
40 lbs. = 12 ft2
no.bags = 480 ft2 = 40 bags
12 ft2/bag
40 bags = 40 lbs. (40 bags) = 1600 lbs.
Bag
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Chapter 9 Algebra and calculator review
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Page 366 practice problems
81.) Solve: A = p(1 + rt)
when p = 465
r = .0275
t = 1.25
A
A
A
A
= 465(1 + .0275(1.25))
= 465(1 + .034375)
= 465(1.034375)
= 480.98
143.) Solve: A = p(1 + r/n) nt
when p = 7,000
r = .055
n = 12
t=3
A = 7000(1 + .055/12) 12(3)
A = 7000(1 + .004583333333) 36
A = 7000(1.004583333333) 36
A = 7000(1.178948602) = 8252.640216
Page 237 practice problem
68.) (There’s another 68 [earlier] but it’s a different problem)
Solve for E when = 0.4 and n = 1,000
E =2
( 1n
=2
.4(1-.4)
1000
=2
2.4-04
= 2 .00024
)
=
2
.24
1000
(on some calculators: 2.4-04 is shown 2.4E-4)
= 2 (.015491933) = .030983866
Chapter 9 Algebra and calculator review
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Practice problems page 277: 204,206
204.) Set x = 0, solve y
Set y = 0, solve x
3x + 6y = 9
3(0) + 6y = 9
y = 9/6 = 1.5
(0, 1.5)
3x + 6y = 9
3x + 6(0) = 9
x = 9/3 = 3
(3, 0)
y
1.5
1
3x + 6y = 9
0.5
x
.5
206.) Set x = 0, solve y
Set y = 0, solve x
6x - 3y = 9
6(0) - 3y = 9
y = 9/-3 = -3
(0, -3)
6x - 3y = 9
6x - 3(0) = 9
x = 9/6 = 1.5
(1.5, 0)
1
1.5
2
2.5
3
y
3
2
6x - 3y = 9
1
x
-1
-2
-3
.5
1
1.5
2
2.5
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