You can put this solution on YOUR website!
5x+8 +x+4 = 90
6x+12 =90
6x=78
x=13

Angle A = 5x +8
Angle A = 5*13 + 8 = 65+8=73 degrees

Angle B = x+4
Angle B = 13+4 = 17 degrees

Check: 73 + 17=90

R^2

Dr. Robert J. Rapalje
Altamonte Campus
Seminole State College
Florida

You can put this solution on YOUR website!
The basic formula is d=rt, and since the equation is based upon the fact that time up stream is equal to time downstream, it will be helpful to solve for t.

Let x = rate of current.
24 = rate in still water

24+x = rate downstream
24-x = rate upstream

time downstream =
time upstream =

Solve the equation:

Since means that ,
means that

Get out your calculator:



km/h

R^2

Dr. Robert J. Rapalje
Altamonte Springs Campus
Seminole State University

You can put this solution on YOUR website!
(1) x + y = 60
(2)2x +6y = 192

The second equation has a 2x, while the first equation has only x. You need to make the x terms subtract out, so in order to subtract out the 2x, you need a -2x. To get that, you have to multiply the first equation by -2. You could also have eliminated the y terms by multiplying the first equation by -6. We usually try to eliminate using the smaller number.

R^2

You can put this solution on YOUR website!
x^2 + 6x +8 just happens to factor into (x+2)(x+4)

So, if x+2 is the width, then x+4 must be the length.

If x=3, then the width is x+2, which is 5 feet, the length is x+4, which is 7 feet, and the area is the product 5*7 which is 35 square feet.

R^2

You can put this solution on YOUR website!
If the volume of a baseball is 8 times that of a table tennis ball, then the radius is 2 times as much. If the radius is twice as much, then the diameter is twice as much, and the circumference which is is also twice as much. Therefore the circumference is TWO times 4.5 inches or 9 inches.

R^2

You can put this solution on YOUR website!
Did you copy this one correctly? Should the second equation should be 5=x+y? Either one is somewhat ugly, so I'll go with your problem as stated.

In the second equation, subtract y from each side.
5y=x+y
4y=x

Substitute this into the first equation for x:
4x+y=5
4(4y)+ y = 5
16y + y=5
17y=5
y=5/17

To solve for x, go back to the equation x=4y
x=4y
x=4(5/17)
x=20/17

The solution is (20/17,5/17)

Check in the OTHER equation
4x+y =5



It checks!!

R^2

You can put this solution on YOUR website!
x+5y=10

Graph by plotting the x and y intercepts:

If x = 0, then 5y=10 so y=2

If y=0, then x=10

It should look like this:



R^2

You can put this solution on YOUR website!
Do you mean ??? Or do you mean ??

If it is the first, then the answer is .

If it is the second, then it is





R^2

You can put this solution on YOUR website!
One of the most important rules of first level algebra is "WHEN YOU MULTIPLY OR DIVIDE BOTH SIDES OF AN INEQUALITY BY A NEGATIVE NUMBER, YOU MUST REVERSE THE DIRECTION OF THE INEQUALITY SIGN!"

You have to do this here, when you multiply both sides by -1/2:




R^2

You can put this solution on YOUR website!
x+2y=32
9x-2y=28

Add the equations together:
10x = 60
x=6

Substitute x=6 into the first equation:
x+2y=32
6+2y=32
2y=32-6
2y=26
y=13

Check in the second equation:
9x-2y=28
9(6)-2(13)=28
54 - 26=28
It checks!!

R^2

You can put this solution on YOUR website!
Kelly = 12-x
Ami = 6 + x

12-x=6+x

Add x to each side:
12-x +x = 6+x+x
12=6 + 2x

Subtract 6 from each side:
12-6=6+2x-6
6=2x
x=3 = ANSWER!

Check:
Kelly =12 - x
Kelly = 12 - 3 = 9
Ami = 6 + x
Ami = 6 + 3 = 9

R^2

You can put this solution on YOUR website!
A variable!

R^2

You can put this solution on YOUR website!
Denominators MUST NEVER EQUAL 0, so
x-1 must not equal 0
x cannot equal 1.
By the way, on my website, I now have two videos explaining Functions, Domain, and Range. If you click on my tutor name "Rapaljer" anywhere in algebra.com, look for the link on my homepage "Rapalje Videos", and select either "Intermediate Algebra" or "College Algebra".

R^2
Dr. Robert J. Rapalje
Seminole State College
Altamonte Springs, FL

You can put this solution on YOUR website!
v=-1/3t + 3
v= -1/3*6+3
v=-2+3
v=1



Of course, the horizontal variable x is actually time t, and the vertical variable y is actually value v.

Plot the point (6,1) on the given graph.

R^2

Dr. Robert J. Rapalje

You can put this solution on YOUR website!
Post a problem???

You can put this solution on YOUR website!
It's probably a perfect square trinomial. But first, take out the common factor of 4. ALWAYS TAKE OUT THE COMMON FACTOR FIRST!!

4(4w^2 - 28w + 49)

Now, try this, using perfect squares 4w^2 and 49.

4(2w - 7)(2w-7)
4(2w-7)^2

One more time, please see my own website by clicking on my tutor name "Rapaljer" anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color".

R^2

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

You can put this solution on YOUR website!
The first step is to write it in descending order:
9x^2 +18xy - 7y^2
It starts out
(3x____)(3x____).

Next, look at the last term. You need to find two numbers whose product is -7y^2, that will give you the middle term which is 18xy. This is a harder problem than the last two that I posted for you, and I call this "Advanced Trinomial Factoring." The LAST times LAST will have to be either 7y times y or y times 7y. You just have to try them and see which one works for you.
(3x__7y)(3x__y) The middle term is 3xy and 21xy, whose difference is 18xy. This is correct.

Now the signs must be OPPOSITE in order to give you the -7y^2, and the middle term has to be a positive 18xy, so make the signs like this:
(3x+7y)(3x -y).

That should do it!! By all means, especially if you don't have a book, or if you don't understand YOUR book, then try MY BOOK, which is FREE on my website. If you are interested in seeing my explanation of this, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials", "Advanced Trinomial Factoring". See also my link "Rapalje Videos" for a complete two hour explanation (by me!) explaining the topic of "Factoring" from Basic Algebra. See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color".

I have a lot of resources for whatever book or curriculum you may be using, and they are all free on my website.

R^2

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

You can put this solution on YOUR website!
The first step is to write it in descending order:
z^2 -34z + 289

It starts out
(Z____)(Z____).

Next, look at the last term. You need to find two numbers whose product is +289, that will add to give you the middle term which is -34z. This would be 17 times 17. Because the last term is positive, the signs must be the same, but in order for this to add up to -34z, you need to use -17 times -17.

(z-17)(z-17)
(z-17)^2

For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials" and also "Difference of Squares and Perfect Square Trinomials". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color".

R^2

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

You can put this solution on YOUR website!
The first step is to write it in descending order:
m^2 -m - 56

It starts out
(m____)(m____).

Next, look at the last term. You need to find two numbers whose product is -56, that will add (or in this case subtract!) to give you the middle term which is -1m. This would be -8 and +7, so write it this way:

(m-8)(m+7)

For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Factoring Trinomials". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color".

R^2

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

You can put this solution on YOUR website!
What is the question? Why don't you restate the problem and resubmit it.

R^2

You can put this solution on YOUR website!
You may not have recognized this, but it is a perfect square trinomial:
(4x-13)(4x-13)
(4x-13)^2

R^2

You can put this solution on YOUR website!
I'm not exactly sure what your "5 step method" is, but MY "5 step method is this:

STEP 1: Identify the variable.

Let x = first side
x+2 = second side
x+4 = third side

STEP 2: Write the equation.




STEP 3: Solve the equation.



Set the equation equal to zero:



This factors into
(x-6)(x+2)=0
x=6 or x= -2

STEP 4: Answer the question.
Reject the negative value since x is a side of a triangle.

x=6
x+2=8
x+4=10

STEP 5: Check.
You can do this.

Let me know if MY five step rule is the same as YOUR 5 step rule.

R^2

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

You can put this solution on YOUR website!
Because this equation is in STANDARD form, it is easiest to graph with the TWO INTERCEPT method.

4x+y=-4
Let x=0, then 4*0+y=-4
y=-4

4x+y--4
Let y=0, then 4x +0=-4
4x=-4
x=-1

Graph these two points, and you should have this graph:


For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 4, and look for "Graphing and Slope of a Line". I also did a video of me teaching this lesson. Look on my home page for "Rapalje Videos" and select "Basic Algebra."

R^2

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

You can put this solution on YOUR website!
You are correct! Both of these are VALID, although INCORRECT conclusions. As you mentioned, when you incorrect hypotheses (premises!), you get incorrect conclusions. However, are VALID.

R^2

You can put this solution on YOUR website!
First, you have to set this equation equal to zero:

10x^2 +100x = 0

Next factor the common factor which is 10x:
10x(x+10)=0

Solve this in TWO parts!
10x=0
x=0

x+10=0
x=-10

For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Solving Quadratic Equations". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color".

R^2

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

You can put this solution on YOUR website!
-2.7 is a rational number, since it is expressed as a terminating decimal. It is NOT a natural number, whole number, integer. It is NOT an irrational number. It is also a REAL number, but that was not one of the choices.

R^2

Dr. Robert J. Rapalje
Seminole State College
Florida

You can put this solution on YOUR website!
First you have to place the terms in descending order:
4n^2 + 13n - 12

Since the middle term is 13n which is an ODD number, the factoring CANNOT be an EVEN times EVEN combination. It is necessary therefore to begin with 4n*n
(4n_____)(n_____)

Next, the LAST times LAST must be 12 with OPPOSITE signs. It CANNOT be 6*2 since these numbers are both EVEN. My best guess will be 3*4:

(4n__3)(n__4), with opposite signs.

Let's try
(4n-3)(n+4), which checks out because the middle term is 16n-3n, which is 13n.

This is a classic problem!! For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 2, and look for "Advanced Trinomial Factoring". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 2. There I have a lot of problems like this solved in "Living Color".

R^2

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

You can put this solution on YOUR website!
Did you state this problem correctly? It doesn't sound right to me.

R^2

You can put this solution on YOUR website!
Let x = width of the rectangle
2x+4= length of the rectangle

2W + 2L = P
2(x) + 2(2x+4) = 38
2x + 4x +8 = 30
6x + 8= 38
6x=30
x=5 Width
2x+4 = Length
2*5+4 = Length
10+4 = 14 Length

Check: 2*5 + 2 * 14 = 10 + 28 = 38 Perimeter

For additional help with this type of problem, please see my own website by clicking on my tutor name anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time." Select "Basic Algebra", Chapter 1, and look for "Word Problems". See also my page called "MATH IN LIVING COLOR", again, Basic Algebra, Chapter 1. There I have a lot of problems like this solved in "Living Color".

R^2

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

You can put this solution on YOUR website!
Subtract x from each side:
14x-x = x-x
13x=0

Divide both sides by 13:



R^2

You can put this solution on YOUR website!
There are three basic methods of graphing a straight line:

1. Point plotting. Select two or three values of x, find the corresponding value of y, plot the points, and connect the dots!

2. Slope-intercept method. Recommended for equations written in the form y=mx+b.

3. Two intercept method. Recommended for equations written in the form ax+by=c.

For additional explanation, see my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the link on my homepage "Basic, Intermediate, and College Algebra: One Step at a Time", select "Basic Algebra" and look for Chapter 4. The entire explanation is available at this link and it's all free.

For a video of me explaining this topic, on my homepage, look for "Rapalje Videos", select "Basic Algebra", and look for "Graphing and Slope of a Line." Again, it's all FREE!!

Send me an Email if you need help finding anything.

R^2

Dr. Robert J. Rapalje
Seminole State College
Altamonte Springs, FL 31714