You can put this solution on YOUR website!
The first problem is to FACTOR the numerator and denominator. It's like in the last solution that I posted, but this time the factoring is a LOT harder. You may need some help with what I call "Advanced Trinomial Factoring" and I have a lesson on this if you are interested.




Now, the (3x-2) factors divide out:


The Lesson on Advanced Trinomial Factoring can be found in algebra.com or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Next, click on "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", then in Chapter 2, look for the section about "Advanced Trinomial Factoring." While you are there, check out ALL the sections on Factoring. There are several sections devoted to this important skill.

R^2

You can put this solution on YOUR website!


The first step is to FACTOR the numerator and denominator:


Divide out the factors of (x-2):


R^2

You can put this solution on YOUR website!
The GCF is the largest factor that divides into both terms in this expression. If variables are involved, it will be the LOWEST power of each variable. This would be .

When you take out the NEGATIVE of this common factor, it changes all the signs. What is left is this:


R^2

You can put this solution on YOUR website!
4x – 6y = –30

Get the x term isolated by adding +6y to each side:
4x = 6y-30

Divide both sides by 4. There are two ways to write this:
or
or

R^2

You can put this solution on YOUR website!
Let x = first angle
x+14= second angle

x+x+14 = 90
2x +14= 90
2x=76
x= 38 degrees
x+14= 52 degrees

Check: 38+52 = 90 degrees

R^2

You can put this solution on YOUR website!
Let x= first angle
x+30 = second angle

x+ x+ 30= 180
2x= 150
x= 75 degrees
x+30 = 105 degrees

Check 75+105= 180

R^2

You can put this solution on YOUR website!
Assuming that the earth is located at the point (0,0), find the distance between (0.0) and the satellite at (12 504, 16 050).
Find . Since this is greater than the of the orbit of the other satellite, I would say that it is OUTSIDE the orbit of this satellite.

R^2

You can put this solution on YOUR website!
Percent of increase is always the amount of increase divided by the original amount. In this case you have an increase of 14, but the original amount is ZERO. You can't divide by zero, so the percent of increase is "undefined" or "infinity"!!

R^2

You can put this solution on YOUR website!
Let x = measure of one of the equal angles
2x-36 = third angle

x + x + 2x-36 = 180
4x - 36= 180
4x -36+36= 180+36
4x = 216
x= 54 Degrees = Equal angles
2x-36 = 72 Degrees = Third angle

Check: 54+54+72= 180 degrees

R^2

You can put this solution on YOUR website!
Are you sure you copied this correctly? This particular equation NEVER hits the ground. Maybe you meant to say ??

R^2

You can put this solution on YOUR website!
f(2)=4, f(0)=6

Slope =
RISE = 6-4=2
RUN=0-2=-2
Slope = =.

R^2

You can put this solution on YOUR website!
I apologize for my WRONG answer here!! It was pointed out to me that a trapezoid can have equal diagonals! I completely forgot about these. Diagonals of a quadrilateral being equal does NOT imply rectangularity!! I sincerely apologize for my error!!

R^2

You can put this solution on YOUR website!
This is called "completing the square". Assuming that the coefficient of the x^2 term is 1, you take HALF of the x coefficient, and SQUARE it. In this case, take HALF of 18 (which is 9) and SQUARE (which is 81).

Now you have



The final answer is 81.

R^2

You can put this solution on YOUR website!
According to DeMoive's Theorem

=
=

Now, and
=
=
= or

R^2

You can put this solution on YOUR website!
Let x = votes cast for the loser
x+ 220 = votes cast for the winner
Total votes cast= 810

x + x+ 220 = 810
2x + 220 = 810
2x+220-220= 810-220
2x= 590
x= 295 votes for the loser
x+ 220 = 515 votes for the winner

Check: 295+ 515 = 810 total votes cast

R^2

You can put this solution on YOUR website!
Let x = side of square
4x = 60
x= 15 cm

R^2

You can put this solution on YOUR website!
Multiply the number of people times the number of liters of water per person:

When you multiply numbers like , you add exponents!


Now, change to scientific notation by converting 52.74 to .



R^2

You can put this solution on YOUR website!
Perimeter of a triangle is just the sum of the three sides. So, add up the sides:
x +3x +3x+2= 37
7x + 2 = 37
7x= 35
x= 5
3x = 15
3x+2 = 17

Check: 5 + 15+ 17 = 37 It checks!

See my Lesson Plan in algebra.com, or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for my MATH IN LIVING COLOR PAGES, then go to Basic Algebra, Chapter 1, then look for the section on Word Problems. FREE and in COLOR!! How is that!!!

R^2

You can put this solution on YOUR website!
The formula for Circumference is or . Since you want the radius, take the second equation:




To eliminate the fraction , multiply both sides by the reciprocal of the fraction which is .



Did you notice that 44 divides into 132 exactly 3 times? That may make the calculation easier. Or just use a calculator. It comes out to an even 7*3= 21 yards.

R^2

You can put this solution on YOUR website!
Let x = longer side (length)
x-3 = shorter side (width)

2L + 2W = P
2(x) + 2(x-3) = 54
2x+2x-6=54
4x-6= 54

Add +6 to each side:
4x-6+6=54+6
4x= 60
x=15 Length
x-3= 12 = Width

Check:
2(15) + 2(12 ) = 54
30+ 24= 54
It checks!

R^2

You can put this solution on YOUR website!
This is like working a problem backwards, starting from the answer and ending up with a quadratic equation. Start with
x=5 and x= 12
Write each of these as mini-equations equal to zero.
x-5=0 and x-12=0

Now, write the product of these factors equal to zero:
(x-5)*(x-12)=0

Finally, multiply it all out:


I hope you get this in time for your presentation!!

R^2

You can put this solution on YOUR website!
The answer in simplest radical form is . It's always best, unless instructed to do otherwise, to rationalize the denominator.

R^2

You can put this solution on YOUR website!
The correct answer is -1/3. The other tutor made a small error. Sorry about that.

R^2

You can put this solution on YOUR website!
You asked to factor this trinomial! This trinomial CANNOT be factored! Moreover, this is NOT an equation, so you can't solve it by quadratic formula, as one of the other tutors tried to do. It is INCORRECT to solve something that is NOT an equation to begin with!!

R^2

You can put this solution on YOUR website!
I just want you to know that I got your answer!! Your answer is in simplest radical form, no matter what anyone else may tell you!!!

R^2

You can put this solution on YOUR website!
A function is a set of points such that no two points have the same x coordinate. An example of a function is .

R^2

You can put this solution on YOUR website!
Remember that means that .
Likewise, means that . This is easy to solve!



Subtract 4x from each side:



Subtract 20 from each side:



Check the answer by substituting the value into the original equation:



It checks!!

R^2

You can put this solution on YOUR website!
If the first term is 100, the second term would be 93, and the third term would be 7 less than this which would be 86. Right???

R^2

You can put this solution on YOUR website!
You didn't give us enough information!

R^2

You can put this solution on YOUR website!


First factor the common factor of 4:


Next, you have to factor the trinomial. By the way, this is a problem all in itself! Do you know how to factor these what I call "Advanced Trinomials"? I have a lesson on this if you are interested! Anyway, here is the factored form:


Now, of the factors given above, the 4 factor cannot equal zero, so it does not give you any solutions. However, the other two factors do give solutions:
or

or

R^2 Retired from SCC

You can put this solution on YOUR website!
When you have a product of factors equal to zero, then one of the factors must be zero. That is,
(2y-9)(y+4)(y-5)=0
2y-9 = 0 or y+4= 0 or y-5=0
2y=9
or or

R^2 Retired from SCC