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Let x = air speed
250+x = speed with the wind
250-x= speed against the wind

Distance with the wind = Distance against the wind=576







TOTAL TIME = 5


Multiply both sides by (250-x)(250+x):


(I'm on vacation, and I don't have my calculator. Use it if you have one!!)








, which I can do even WITHOUT a calculator!!!

mph--a pretty strong wind!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
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x^2 -10+3x=x^2 -4x+4 + 1

Subtract x^2 from each side, and all the x^2 terms are gone. Therefore, this is NOT a quadratic equation after all.

-10+3x= -4x+5

Add +4x to each side:
-10+3x+4x=-4x+4x+5
-10+7x=5

Add +10 to each side:
7x= 15

Divide both sides by 7:
x=15/7

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
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Is Blake one of the algebra.com tutors? Somehow related to math? If so, try re-posting your question, and see if you can get a better solution. Good questions deserve good answers, and NO ONE should be a JERK about it!!

Dr. Robert J. Rapalje, Retired

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Square both sides of the equation:




Check:


It checks!!

Dr. Robert J. Rapalje, Retired

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9 square root of 7x - 6 square root 7x

Just combine like radicals:
9 apples -6 apples = 3 apples

Likewise
9 square root of 7x - 6 square root 7x= 3 square root 7x!

You should see my own website for additional explanation on Square Roots, and especially to see a FREE hour and a half video of me teaching this lesson a few years ago. To find my website, click on my tutor name "Rapaljer" anywhere in algebra.com. From my homepage, click on "Rapalje Videos in Color", choose "Basic Algebra", and look for the video "Radicals (Square Roots)". In addition to this video explanation, I have a written explanation that you will probably find easier to understand than your textbook. From my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and then select "Chapter 5". The entire chapter is my own non-traditional explanation of Square Roots, which is also supported by my "MATH IN LIVING COLOR" pages.

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

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False!! Any square root that is not of a perfect square is irrational.

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You should see my own website for additional explanation on Square Roots, and especially to see a FREE hour and a half video of me teaching this lesson a few years ago. To find my website, click on my tutor name "Rapaljer" anywhere in algebra.com. From my homepage, click on "Rapalje Videos in Color", choose "Basic Algebra", and look for the video "Radicals (Square Roots)". In addition to this video explanation, I have a written explanation that you will probably find easier to understand than your textbook. From my Homepage, look for "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and then select "Chapter 5". The entire chapter is my own non-traditional explanation of Square Roots, which is also supported by my "MATH IN LIVING COLOR" pages.

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

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The square root of a negative number is an imaginary number.

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Take the log of each side:


Subtract logx from each side:


Factor out the logx:


Divide both sides by (log2-1):



Finally, raise both sides as a power of 10:
.

This comes out to approximately .137609.

I checked this with a graphing calculator, and it is correct!!!

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

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Solve for y in this equation by subtracting 2y from each side.
y=3+5x+2y
y-2y=3+5x+2y-2y
-y=3+5x

Now divide both sides by -1, and you get
y=-3 -5x

This is a straight line graph with y intercept of -3 and slope of -5. Any value of x is allowed in this equation, since there are no denominators and no radicals in the equation. Therefore the domain is all real values of x. The graph goes all the way up and all the way down on a graph, so the range is also all real values.

You may want to see my own website for my own explanation of Domain and Range, and also a FREE video (or TWO!) that I had recorded in my classes a few years ago. To see my website, click on my tutor name "Rapaljer" anywhere in algebra.com. On my Homepage, look for "Rapalje Videos in Living Color". There, you will find a video in "Intermediate Algebra" and also one in "College Algebra" called "Functions, Domain, and Range." These are different videos, the one from Intermediate Algebra being presented on a lower level with less depth of coverage. I call it "FDR Lite"!! The videos were taken of me teaching in my class a few years ago, but they might help you understand this concept.

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

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Just combine like terms:
4z-9

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I'm not sure if you mean or ??? Can you clarify???

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

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Is there supposed to be a y somewhere in this equation??

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

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x^2+2x+8=0

Calculate
b^2-4ac
2^2 -4*1*8
4-32 , which is a negative. Since this is negative, this means that you have complex roots.

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

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From the general nature of your question concerning factoring, I think you might find some extra help on my own website. Why don't you click on my tutor name "Rapaljer" anywhere in algebra.com, and on my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra" and look in "Chapter 2" for the various topics on Factoring. This is my own curriculum that I wrote especially for students who have a hard time understanding math. My own students found it a LOT easier to understand than traditional textbooks. In addition, I have solved a lot of these problems in COLOR in my "MATH IN LIVING COLOR" pages.

There is also a VIDEO (or two!) on FACTORING that you can download for free from my website. From my homepage, look for "Rapalje Videos in Living Color." Select "Basic Algebra" and look for the video on "Factoring." Did I mention that, just like algebra.com, it's all FREE???

Now to solve your problems,

1. There is NO common factor. This one is the difference of two squares, since 81 and 121 are both perfect squares:
81x^2 - 121
(9x-11)(9x+11)

2. This one is ALSO a DIFFERENCE of two SQUARES:
(u-2v)^2 -9
(u-2v-3)(u-2v+3)

3. Now, you FINALLY have a COMMON FACTOR, uv. Take out the uv.
uv^3-u^3v
uv(v^2-u^2)

Now you have another difference of two squares:
uv(v-u)(v+u)

This other problem appears to be a trinomial problem, but FIRST, there is a common factor of 3 that you can take out. Do this first, and then take a look at what is left. It may factor again.

4. 9x^4-12x^2y^2+36y^4
3(3x^4 -4x^2y^2+ 12y^4)

I have a thought that you may have miscopied this one, because these usually factor as trinomials. This one does not.

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

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There is not enough information. What was the question?

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

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-27+20w=73

Start by adding +27 to each side to get all the number terms on the right side:
-27+27+20w= 73+27
20w= 100

Next, divide both sides by 20:



If you need additional help with the topic of Equation Solving, please see my website. Click on my tutor name "Rapaljer" anywhere in algebra.com, which will take you to my Homepage. On my Homepage, look for "Basic, Intermediate, and College Alegebra: One Step at a Time". Choose "Basic Algebra", look in "Chapter 1" for "Section 1.08" for my complete nontraditional, explanation of Equation Solving. These lessons are supported by my MATH IN LIVING COLOR pages.

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

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Just combine like terms:

(-6-7i)-(1+3i)
-6-7i-1-3i
-7-10i

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

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Since the degree of the numerator (which is 1) is LESS than the degree of the denominator (which is 2), the horizontal asymptote is always y=0.

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

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A=k*W, where k is a constant.

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

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A right triangle is a triangle that has two sides mutually perpendicular to each other. One of the angles will be exactly 90 degrees--that is, a "RIGHT" angle.

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

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Therefore,





Check: There are NO cases in which x=2 results in a log of a negative, so the answer checks! Actually, it really can be checked, by substituting x=2:



If you need additional help with the topic of LOGARITHMS, please see my website. Click on my tutor name "Rapaljer" anywhere in algebra.com, which will take you to my Homepage. On my Homepage, look for "Basic, Intermediate, and College Alegebra: One Step at a Time". Choose "College Algebra", look in "Chapter 4" for my complete nontraditional, explanation of Logarithms. This particular question actually comes from "Section 4.04 Exponential and Logarithmic Equations." These lessons are supported by my MATH IN LIVING COLOR pages.

In addition, there are TWO two hour videos of me teaching the topic of Logarithms in my own classroom a few years aog. These are FREE. To see the videos, look on my Homepage for "Rapalje Vidoes in Living Color." Choose "College Algebra" and look for "Logarithms Part II."

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

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Is this three separate questions??

1. Complement of 70 is 90-70= 20 degrees.

2. 75+40=115. Now, subtract 180-115= 65 degrees.

3. Supplement of 100.5 is 180-100.5 = 79.5 degrees.

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

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In Domain, the denominator must NEVER be zero. So must not equal 0. You can have any value of x EXCEPT
x(x+3) must NOT equal zero.

x cannot equal 0, x cannot equal -3.

Domain is all real values except 0 and -3.

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Seminole State College of Florida

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y2-12y+36=0
(y-6)(y-6)=0
y=6

Since this seems to be a two-dimensional problem, in an xy coordinate system, you have a HORIZONTAL line that is 6 units above the x axis.
It looks like this;


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

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You got it!!!

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

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The basic definition of a logarithm is the BASE NUMBER raised to the power of, in this case t, equals 36.

6^t=36

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
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Set x+pi/4=0
You get x=-pi/4, so it is a phase shift of pi/4 to the LEFT, since the value is negative.

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Seminole State College of Florida
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To find the phase shift, set the angle equal to zero.

2x-1=0
2x=1
x=1/2

If the value of x is positive, then the shift is to the right. If it is negative, then the phase shift is to the left.

Dr. Robert J. Rapalje, Retired
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Because the , the answer is theta =

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
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The basic formula is D=r*t. You are given that D=10 mi and r=40 mph, and time t is the unknown:

10=40t

Divide both sides by 40, and you get t=10/40=1/4 hour. In other words 15 minutes.

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