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How does that Glade commercial go: "Plug it in, plug it in!"

x=3 and y=9
3(x+7y)
3(3+7*9)

Now you have to know the order of operations to know what to calculate first. The first step is to do what is inside the parentheses, and multiplication comes befoe addition:
3(3+63)

Next, add within the parentheses:
3(66)
198

For additional explanation on topics like this, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for several topics on Signed Numbers, Order of Operations, and Variables. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Given y=-3x, the slope of this line is m=-3.

Any line parallel to this line has the SAME SLOPE, so m= -3 for any line paralle.

Any line perpendicular to this line has a slope that is the NEGATIVE RECIPROCAL of this slope. This slope would be m=+1/3.

For a complete explanation of this topic in my own FREE curriculum, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Intermediate Algebra", and look in "Chapter 4" for Section 4.02. Scroll down the to page 389 for the EXACT explanation that you need. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
It might be easier to multiply if you write it like this:
z^2 (8z^2+2z)

By distributive property (and when you multiply you must add the exponents!)
8z^4 + 2z^3

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

P.S. I noticed that another tutor went the other way with this problem and FACTORED it. Did your instructions say to multiply the answer by using the distributive property, or were you asked to factor the problem?

For additional help with this type of problem, I have my own curriculum posted on my website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for the distributive property.

However, if the other tutor wss correct that you were supposed to FACTOR the answer completely, then I have several topics on Factoring. Of course, you need to see the one called "Factoring the Common Factor." This topic is in Chapter 2 of my Basic Algebra. In either chapter, you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

Check also for my VIDEO on factoring that was made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "Basic Algebra" and look for the topic on "Factoring." If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Subtract from 180 degrees.

180 - 87 = 93 degrees.

Check: 87+93= 180

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Area =
If h= 3 meters, then



meters.

For additional explanation on Geometric Topics, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link near the bottom of my Homepage called "Topics from Geometry." In particular, look for the link called "Perimeters, Areas, and Volumes". Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
I think you may have an error in this one. You can't really have an equal sign and and a > sign in the same statement.

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
I recommend that you solve for y in order to write the equation in slope-intercept form.
x/-2 + y/8 =1
Multiply both sides by 8 to clear the fractions:
-4x + y = 8

Add +4x to each side:
y=4x+8

y=mx+b

The coefficient of x in this form is the slope. Slope m=4.

For additional explanation on Slope of a Line, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 4" for several topics on Graphing and Slope. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!
Check also for my VIDEO on "Graphing and Slope of a Line" that was made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "Basic Algebra" and look for the topic on mentioned above. If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
The degree of the numerator is equal to the degree of the denominator, so the horizontal asymptote is y= the ratio of the leading coefficients.

Thia is y = -1/1 , or y =-1 Horizontal Asymptote

Vertical asymptotes can be found by setting the denominator equal to zero.

x^2+x-12=0
(x+4)(x-3)=0
x=-4 or x=3 Vertical Asymptotes

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Let x = length of the mat.

x^2 = 676
x= +- sqrt(676)

Got a calculator?
x=26 feet.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Let x = score of Vikings
x+18 = score of Raiders

x + x+18=46
2x+18=46
2x=46-18=28
2x=28
x=14
x+18=32

Check: 14+32=46

The score was 32-14 Raiders

For additional explanation on WORD PROBLEMS, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for TWO sections on Word Problems. Of course, you need to see the one called "Factoring Trinomials." Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Opposite angles of a parallelogram are EQUAL. The answer is 72 degrees.

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

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This is a FACTORING problem! In fact, because it starts off with a 2x^2 term, I call this one "Advanced Trinomial Factoring," and I have an entire section explaining this topic on my own website. I'll mention that later. First, let's solve the problem!!

2x^2 -7x - 20

This is a trinomial so we hope it factors into the product of two binomials. The First times First has to give you 2x^2, so it has to look like this:
(2x______)(x_______)

Next, the Last times Last has to give you a product of -20. Because the -20 is NEGATIVE, the signs within the binomials must be OPPOSITE. Moreover, because the middle term is an ODD number, it CANNOT be an EVEN number times an EVEN number. I think the most likely product to give you 20 is 5 times 4. There are two ways to write the 5*4 . If this doesn't work we'll try some other combinations to find the one that works.

(2x___5)(x____4) or (2x___4)(x___5)

Now, the middle term is -7x. You have to calculate the OUTER TIMES OUTER and the INNER TIMES INNER so the DIFFERENCE of these terms is -7x. In the first case above

(2x___5)(x____4)

the outer times outer is 2x*4=8x and the inner times inner is 5x. Since the difference here is NOT -7x, I conclude that this is NOT a possible factoring of this one.

Now, after trying the other possibilities on separate paper, I concluded that this does NOT factor. I also used a technique from higher math called calculating b^2-4ac, and I further concluded that this does NOT factor. Perhaps you miscopied the problem, or perhaps someone is playing what I consider a cruel trick on you by giving you a problem like this that is actually PRIME!!! As a teacher/author, I would NOT have done this to you.

The final answer is PRIME!!

For more information on my "Advanced Trinomial Factoring" please do visit my website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 2" for several topics on Factoring. Of course, you need to see the one called "Advanced Trinomial Factoring." Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

Check also for my VIDEO on factoring that was made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "Basic Algebra" and look for the topic on "Factoring." If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
This is a classic "Factoring by Grouping" problem. You need to group the first two terms and the last two terms together, and take out common factors in each grouping. From the first two terms, you can factor out the x^4, and from the last two terms there is only a -1 to factor out.

x^6 - 9x^4 - x^2 + 9 = 0
x^4(x^2 - 9) - 1(x^2 - 9) = 0

This gives you a common factor of (x^2-9) that you can take out.
(x^2 - 9)(x^4 - 1) = 0

Each of these binomial factors factors again:
(x-3)(x+3)(x^2-1)(x^+1)=0

Factoring again:
(x-3)(x+3)(x-1)(x+1)(x^2+1)=0

Now, are you factoring with REAL solutions only, or are you expected to find complex solutions as well? For real solutions, you will have four answers:

x=3, x=-3, x=1, x=-1, and x^2+1=0 gives no real solutions. If complex solutions are allowed (or expected!), then you must also solve x^2=-1, so with complex solution, you also have x=i and x=-i.

For more factoring explanations like this, please , please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "MATH IN LIVING COLOR." Click on "College Algebra", and look in "Chapter 1" for "Section 1.04 Factoring." I also have some explanation on a slightly lower level in Intermediate Algebra. For this explanation, from my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Click on "Intermediate Algebra" and look in "Chapter 2" for a very thorough explanation of Factoring.

Check also for my VIDEO on factoring in Intermediate Algebra that was made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "Intermediate Algebra" and look for the topic on "Factoring." If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Ler x= original width
4x= original length

x+2 = new width
4x-10 = new length

2W + 2L = P
2(x+2) + 2(4x-10)=80
2x+4+8x-20=80
10x -16=80
10x = 96
x=9.6 original width
4x= 38.4 = original length

Check:

New width = 9.6 + 2 = 11.6 inches
New lenth = 38.4-10 = 28.4 inches

Perimeter = 2*11.6 + 2*28.4=80 inches

NEAT PROBLEM!! Where did you find this one???

For additional explanation on WORD PROBLEMS, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 1" for TWO sections on WORD PROBLEMS. Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Can you be more specific in your question? Are you talking about square roots being written as fractional exponents? If so, I have a page on my own website that will explain this in detail.

Are you talking about taking square roots of negative numbers? If so, this involves complex numbers, and I have a page on my website about this too. Please either re-post the question, or respond to this question and I'll be glad to give you more details.

In the mean time, if you want to visit my website, To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. You can send me an Email from any page of my website.

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
It may help to re-write this

c^2 -16c + 55

(c______)(c______)

Find 2 numbers whose product is 55 that will add up to 16. This would be 11*5.
(c-11)(c-5)

For additional explanation on factoring trinomials, please see my own website. To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Click on the link there that will take you to the Homepage of my website, which is a subwebsite at Seminole State College of Florida. From my "Homepage", look for the link "Basic, Intermediate, and College Alegebra: One Step at a Time." Click on "Basic Algebra", and look in "Chapter 2" for several topics on Factoring. Of course, you need to see the one called "Factoring Trinomials." Here you will find my own complete non-traditional, user-friendly explanation of the topics that my own students found MUCH easier to understand than the traditional textbooks! Many of my exercises here are explained in great detail in the MATH IN LIVING COLOR pages that go with this curriculum. Best of all, it's all FREE!

Check also for my VIDEO on factoring that was made a few years before I retired of me actually teaching this topic. To see the videos, from my Homepage, look for "Rapalje Videos in Living Color." Then click on "Basic Algebra" and look for the topic on "Factoring." If you have RealPlayer installed on your computer, then this is a FREE download. If you do not have RealPlayer, then you will have to download RealPlayer, but this too is a FREE download.

I have explanations on nearly every topic in algebra and many from geometry as well, and many videos from my younger days as well. Everything is FREE, and I don't even have advertising on the pages!! If you don't need help with math, then visit my website to see the JOKE PAGE--all clean jokes, safe for the little ears in your family!!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
y=3/5 x + 2

First clear the fraction, by multiplying both sides by 5:
5y = 3x + 10

Next, subtract 3x from each side to get the variables all on the left side:
5y-3x=10

The tradition in standard form is to have the x coefficient positive, so multiply both sides by -1:

3x-5y = -10


Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
There are NO SOLUTIONS to this equation, since any value raised to an EVEN power must be greater than or equal to 0. Then, if you add +400 to this quantity, the result will always be positive, NEVER equal to 0. NO SOLUTION!!

Dr, Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Let x = vertex angle
x+21 = each base angle

x+x+21+x+21=180
3x+42=180
3x=138
x= 46 degrees vertex angle
x+21 =67 degrees base angles

Dr. Rapalje

You can put this solution on YOUR website!
4x-5

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For a complete explanation of exponential functions, please see my own website To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Then click on my website that you will find there, and it goes directly to my Homepage. From my Homepage, look for the link that says, "Basic, Intermediate, adn College Algebra." Choose "College Algebra", then "Chapter 4", and look for "Section 4.01 Logarithms and Exponential Functions."
Also, my "Basic, Intermediate, and College Algebra: One Step at a Time" sections are supported by my "MATH IN LIVING COLOR" sections, where the most frequently asked problems are solved IN COLOR!!

I also have a number of vidoes on selected topics from my own classes a few years before I retired. These can be found by looking on my "Rapalje Videos in Living Color." In particular, see the videos in College Algebra on Logarithms Part I. The videos and everything else on the website are all FREE!

I hope you like my website, and that you will recommend it friends and family. If you have trouble finding it, then just do a Google search for "Math in Living Color". It comes right up there for you.

Oh, and Merry Christmas to all!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

You can put this solution on YOUR website!
To find the y intercept, always let x = 0 and solve for y. In this case, 2y=6, so y=3.

To find the x intercept, always let y = 0 and solve for x. In this case, -3x=6, so x=-2

To find the median, arrange the numbers in NUMERICAL order, which they are in this case. Choose the middle number, which is 237. If there happen to be an even number of numbers, then take the middle TWO numbers when arranged in order, and average these two numbers.

If you didn't understand intecetps, then you really need to see my website!! I have an explanation here that is probably easier than the one in your textbook!!

To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Then click on my website that you will find there, and it goes directly to my Homepage. From my Homepage, look for the link that says, "Basic, Intermediate, adn College Algebra." Choose "Basic Algebra", then "Chapter 4", and look for "Section 4.03 Intercept Method of Graphing." If you have trouble with this section, then take a look at the previous sections in this chapter. Math is cumulative, so if you don't understand the earlier sections, that might explain your problems later on.

Also, my "Basic, Intermediate, and College Algebra: One Step at a Time" sections are supported by my "MATH IN LIVING COLOR" sections, where the most frequently asked problems are solved IN COLOR!!

I also have a number of vidoes on selected topics from my own classes a few years before I retired. These can be found by looking on my "Rapalje Videos in Living Color." In this case, look in Basic Algebra for the video called "Graphing and Slope of a Line." EVERYTHING, EVEN THE VIDEOS, IS FREE ON THIS WEBSITE.

I hope you like my website, and that you will recommend it friends and family. If you have trouble finding it, then just do a Google search for "Math in Living Color". It comes right up there for you.

Oh, and Merry Christmas to all!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

You can put this solution on YOUR website!
By the distributive property, this is -(4x-8)=-4x+8.

If you didn't understand this one, then you really need to see my website!! I have an explanation here that is probably easier than the one in your textbook!!

To find my website, click on my tutor name "rapaljer" anywhere in algebra.com. Then click on my website that you will find there, and it goes directly to my Homepage. From my Homepage, look for the link that says, "Basic, Intermediate, adn College Algebra." Choose "Basic Algebra", then "Chapter 1", and look for "Section 1.06 Combining Like Terms and the Distributive Property." If you have trouble with this section, then take a look at the previous sections. Math is cumulative, so if you don't understand the earlier sections, that might explain your problems later on.

Also, my "Basic, Intermediate, and College Algebra: One Step at a Time" sections are supported by my "MATH IN LIVING COLOR" sections, where the most frequently asked problems are solved IN COLOR!!

I also have a number of vidoes on selected topics from my own classes a few years before I retired. These can be found by looking on my "Rapalje Videos in Living Color."

I hope you like my website, and that you will recommend it friends and family. If you have trouble finding it, then just do a Google search for "Math in Living Color". It comes right up there for you.

Oh, and Merry Christmas to all!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

You can put this solution on YOUR website!
Let x=original ticket price
720/x= number of tickets originally

Equation is based upon NEW ticket price times NEW number of tickets = 720
(x+2)(720/x - 4)=720
720 - 4x +1440/x - 8 = 720
-4x +1440/x - 8 = 0
-4x^2+1440 -8x=0
x^2 +2x -360=0
(x+20)(x-18)=0
x=-20 reject
x=$18 = Original Ticket Price
x+2= $20 = New Ticket Price

Check:
Number of tickets originally =40
Number of tickets after dropouts = 36

18*40 = 20*36 = $720

Nice Problem!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
y-y1 = m(x-x1)
y-(-1) = 3(x-(-2))
y+1 = 3(x+2)
y+1=3x+6

Subtract y from each side:
1=3x-y +6

Subtract 6 from each side:
1-6=3x-y
-5=3x-y
3x-y=-5

Here is a NEAT trick! Check the answer by substituting the point (-2,-1) to see if it works:
3x-y=-5
3(-2) -(-1) = -5
-6 + 1 = -5
IT CHECKS!!

Dr. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Let N= number of Nickels, each worth 5 cents
Let D= number of Dimes, each worth 10 cents

5N + 10D = 210
5(N+24)+ 10(3D) = 630

5N + 10D = 210
5N+120 + 30D=630

In the second equation, subtract 120 from each side:
5N + 10D = 210
5N + 30D = 510

Multiply both sides of first equation by -1 to eliminate the N variables:
-5N - 10D = -210
5N + 30D = 510

Add the two equations together:
20D = 300

Divide both sides by 20
D=300/20=15 Dimes

5N + 10D = 210
5N + 10*15= 210
5N + 150 = 210
5N = 60
N= 12 Nickels

Check:
5(N+24) + 10(3D) = 630
5(36) + 10(45) = 630
180 + 450 = 630

IT CHECKS!!

Dr. Robert J. Rapalje, Retired

You can put this solution on YOUR website!
x+y=7
x+y=-1

y=-x+7
y=-x-1



The lines are parallel, so there is NO SOLUTION. The system is INCONSISTENT.

Dr. Rapalje

You can put this solution on YOUR website!
This equation doesn't look right to me. Was there supposed to be something between the + and the = signs??

You can put this solution on YOUR website!
If the food is NOT good, then I won't eat too much
~q -> ~p

I think you already constructed a truth table for this, and it was correctly done. If not, please let me know.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida

You can put this solution on YOUR website!
Rewrite the second equation in standard form:
8a + 40b = 16

Notice that this equation can be obtained by multiplying both sides of the first equation by 2. Therefore these two equations represent the SAME LINE. There are infinitely many solutions, since the ENTIRE LINE is the solution.

For additional help with SYSTEMS OF EQUATIONS, please take a look at my own website. To see it click on my tutor name "rapaljer" anywhere in algebra.com. Look for the link to my website there. From my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", click on "Basic Algebra," and then "Chapter 4." Look for Section 4.07 Systems of Equations.

See also the solutions of many of these exercises in the "MATH IN LIVING COLOR" pages, where the problems are solved in COLOR. My own students and others have been unanimous in telling me that my own explanations are easier to understand than the expensive textbooks that are written for mathematicians and publishers!! MY EXPLANATIONS WERE WRITTEN FOR STUDENTS WHO HAVE A HARD TIME UNDERSTANDING MATH!! And they are all FREE!!

I hope you like my website!!! If you do, please recommend it to your family and friends!! At least check out the JOKE PAGE--all safe jokes for the little ears in your family!!

Merry Christmas!!!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

You can put this solution on YOUR website!
Let D= number of poles of Dan
Let G= number of poles of Gary

You must solve the following system of equations:
D+G=13
6D+11G= 103

Elimination method, multiply the first equation by -6, so the D terms will subtract out.
-6D-6G = -78
6D+11G = 103

Add the two equations together:
5G = 25
G= 5 Poles by Gary

D+G=13
D+5=13
D= 8 Poles by Dan

Check: See if there are a total of 103 worms
6D + 11G = 103
6*8 + 11*5 = 103
48 + 55 = 103

It checks!!

Dr. Robert J. Rapalje
Seminole State College of Florida