<< 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

A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
Practice Key Terms 4

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask