<< Chapter < Page Chapter >> Page >

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.

Got questions? Get instant answers now!

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

84 mi

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

−2 i

horizontal component −2 ; vertical component −1

Got questions? Get instant answers now!

For the following exercises, perform the operations indicated.

( 9 i ) ( 4 7 i )

Got questions? Get instant answers now!

( 2 + 3 i ) ( 5 8 i )

7 + 11 i

Got questions? Get instant answers now!

( 3 5 i ) 2

−16 30 i

Got questions? Get instant answers now!

2 ( 8 5 )

−4 i 10

Got questions? Get instant answers now!

Quadratic Equations

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

3 x 2 + 18 x + 15 = 0

x = −1 , −5

Got questions? Get instant answers now!

  7 x 2 9 x = 0

x = 0 , 9 7

Got questions? Get instant answers now!

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

( x 4 ) 2 = 36

x = 10 , −2

Got questions? Get instant answers now!

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

4 x 2 + 2 x 1 = 0

x = 1 ± 5 4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

x 2 = 10 x + 3

x = 5 ± 2 7

Got questions? Get instant answers now!

Other Types of Equations

For the following exercises, solve the equations.

x 1 2 4 x 1 4 = 0

x = 0 , 256

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

3 x 5 6 x 3 = 0

x = 0 , ± 2

Got questions? Get instant answers now!

3 x + 7 + x + 2 = 1

x = −2

Got questions? Get instant answers now!

| 2 x + 3 | 5 = 9

x = 11 2 , −17 2

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

x 1 3 + x + 2 5 3 5

Got questions? Get instant answers now!

| 3 x + 2 | + 1 9

[ 10 3 , 2 ]

Got questions? Get instant answers now!

| x 3 | < −4

No solution

Got questions? Get instant answers now!

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 )

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

2 x 5 y = 6

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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 ]

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

x = −15

Got questions? Get instant answers now!

Solve for x : x 2 + 1 = 4 x

Got questions? Get instant answers now!

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

x −4 , 2 ; x = 5 2 , 1

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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

x 2 3 x = −1 2

x = 3 ± 3 2

Got questions? Get instant answers now!

Solve: 3 x 8 4.

Got questions? Get instant answers now!

Solve: | 2 x + 3 | < 5.

( −4 , 1 )

Got questions? Get instant answers now!

Solve: | 3 x 2 | 4.

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

y = 5 2 x 4

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Simplify: −4 + 3 −16 .

14 i

Got questions? Get instant answers now!

Multiply: 5 i ( 5 3 i ) .

Got questions? Get instant answers now!

Divide: 4 i 2 + 3 i .

5 13 14 13 i

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

x = 2 , 4 3

Got questions? Get instant answers now!

Solve: x 2 6 x = 13.

Got questions? Get instant answers now!

Solve: 4 x 2 4 x 1 = 0

x = 1 2 ± 2 2

Got questions? Get instant answers now!

Solve:

x 7 = x 7

Got questions? Get instant answers now!

Solve: 2 + 12 2 x = x

4

Got questions? Get instant answers now!

Solve: ( x 1 ) 2 3 = 9

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
what is the meaning
Dominic
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
×/×+9+6/1
Debbie
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
16
Makan
x=16
Makan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
Practice Key Terms 4

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask