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A man has 72 ft. of fencing to put around a rectangular garden. If the length is 3 times the width, find the dimensions of his garden.

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A truck rental is $25 plus $.30/mi. Find out how many miles Ken traveled if his bill was $50.20.

84 mi

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Complex Numbers

For the following exercises, use the quadratic equation to solve.

2 x 2 + 3 x + 7 = 0

x = 3 4 ± i 47 4

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For the following exercises, name the horizontal component and the vertical component.

−2 i

horizontal component −2 ; vertical component −1

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For the following exercises, perform the operations indicated.

( 9 i ) ( 4 7 i )

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( 2 + 3 i ) ( 5 8 i )

7 + 11 i

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( 3 5 i ) 2

−16 30 i

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2 ( 8 5 )

−4 i 10

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Quadratic Equations

For the following exercises, solve the quadratic equation by factoring.

3 x 2 + 18 x + 15 = 0

x = −1 , −5

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  7 x 2 9 x = 0

x = 0 , 9 7

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For the following exercises, solve the quadratic equation by using the square-root property.

( x 4 ) 2 = 36

x = 10 , −2

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For the following exercises, solve the quadratic equation by completing the square.

4 x 2 + 2 x 1 = 0

x = 1 ± 5 4

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For the following exercises, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state No real solution .

15 x 2 x 2 = 0

x = 2 5 , 1 3

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For the following exercises, solve the quadratic equation by the method of your choice.

x 2 = 10 x + 3

x = 5 ± 2 7

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Other Types of Equations

For the following exercises, solve the equations.

x 1 2 4 x 1 4 = 0

x = 0 , 256

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4 x 3 + 8 x 2 9 x 18 = 0

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3 x 5 6 x 3 = 0

x = 0 , ± 2

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3 x + 7 + x + 2 = 1

x = −2

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| 2 x + 3 | 5 = 9

x = 11 2 , −17 2

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Linear Inequalities and Absolute Value Inequalities

For the following exercises, solve the inequality. Write your final answer in interval notation.

2 x + 5 > x 7

( , 4 )

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x 1 3 + x + 2 5 3 5

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| 3 x + 2 | + 1 9

[ 10 3 , 2 ]

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| x 3 | < −4

No solution

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For the following exercises, solve the compound inequality. Write your answer in interval notation.

3 y < 1 2 y < 5 + y

( 4 3 , 1 5 )

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For the following exercises, graph as described.

Graph the absolute value function and graph the constant function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.

| x + 3 | 5

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Graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y -values of the lines. See the interval where the inequality is true.

x + 3 < 3 x 4

Where the blue is below the orange line; point of intersection is x = 3.5.

( 3.5 , )


A coordinate plane with the x and y axes ranging from -10 to 10.  The lines y = x + 3 and y = 3x -4 graphed on the same axes.

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Chapter practice test

Graph the following: 2 y = 3 x + 4.

y = 3 2 x + 2

x y
0 2
2 5
4 8


A coordinate plane with the x and y axes ranging from -10 to 10.  The line going through the points (0,2); (2,5); and (4,8) is graphed.

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Find the x- and y -intercepts for the following:

2 x 5 y = 6

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Find the x- and y -intercepts of this equation, and sketch the graph of the line using just the intercepts plotted.

3 x 4 y = 12

( 0 , −3 ) ( 4 , 0 )


A coordinate plane with the x and y axes ranging from -10 to 10.  The points (4,0) and (0,-3) are plotted with a line running through them.

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Find the exact distance between ( 5 , −3 ) and ( 2 , 8 ) . Find the coordinates of the midpoint of the line segment joining the two points.

Write the interval notation for the set of numbers represented by { x | x 9 } .

( , 9 ]

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Solve for x : 5 x + 8 = 3 x 10.

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Solve for x : 3 ( 2 x 5 ) 3 ( x 7 ) = 2 x 9.

x = −15

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Solve for x : x 2 + 1 = 4 x

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Solve for x : 5 x + 4 = 4 + 3 x 2 .

x −4 , 2 ; x = 5 2 , 1

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The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side.

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Solve for x . Write the answer in simplest radical form.

x 2 3 x = −1 2

x = 3 ± 3 2

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Solve: 3 x 8 4.

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Solve: | 2 x + 3 | < 5.

( −4 , 1 )

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Solve: | 3 x 2 | 4.

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For the following exercises, find the equation of the line with the given information.

Passes through the points ( 4 , 2 ) and ( 5 , −3 ) .

y = −5 9 x 2 9

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Has an undefined slope and passes through the point ( 4 , 3 ) .

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Passes through the point ( 2 , 1 ) and is perpendicular to y = 2 5 x + 3.

y = 5 2 x 4

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Add these complex numbers: ( 3 2 i ) + ( 4 i ) .

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Simplify: −4 + 3 −16 .

14 i

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Multiply: 5 i ( 5 3 i ) .

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Divide: 4 i 2 + 3 i .

5 13 14 13 i

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Solve this quadratic equation and write the two complex roots in a + b i form: x 2 4 x + 7 = 0.

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Solve: ( 3 x 1 ) 2 1 = 24.

x = 2 , 4 3

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Solve: x 2 6 x = 13.

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Solve: 4 x 2 4 x 1 = 0

x = 1 2 ± 2 2

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Solve:

x 7 = x 7

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Solve: 2 + 12 2 x = x

4

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Solve: ( x 1 ) 2 3 = 9

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For the following exercises, find the real solutions of each equation by factoring.

2 x 3 x 2 8 x + 4 = 0

x = 1 2 , 2 , −2

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( x + 5 ) 2 3 ( x + 5 ) 4 = 0

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Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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