You can put this solution on YOUR website!
f(x) = –3x – 2 is a straight line graph, with y intercept of -2, and slope of -3. It should look like this:



R^2 at SCC

You can put this solution on YOUR website!
This problem would have been a LOT easier to solve if, instead of using the quadratic formula as Checkley suggested you do, you just take the square root of each side:




Now, just subtract 3 from each side:


You were ALMOST correct!! Never mind Checkley's chiding!!

R^2 at SCC

You can put this solution on YOUR website!
The answer you were given to this problem by Checkley is WRONG! YOU WERE CORRECT in saying that this is an irrational number. An irrational number is a REAL NUMBER, but it is one that is NOT rational. That is, it CANNOT be expressed as a quotient of two integers. Irrational numbers include radical expressions that do not come out even, such as , , etc. If the square root happens to be of a perfect square, such as , then it is considered to be rational. Your answer involves the square root of a number, 68, that is not a perfect square. Therefore it is an irrational number.

is a REAL but yet an IRRATIONAL NUMBER.

R^2 at SCC

You can put this solution on YOUR website!
You have to give us a problem. We don't have your book. See my Lesson Plans on Domain and Range in algebra.com or see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, look for "MATH IN LIVING COLOR", "College Algebra", "Chapter 2".

R^2 at SCC

You can put this solution on YOUR website!
A function is a set of points in which no two points have the same x coordinate. It is like a set of points that has a special uniqueness relationship. For example, is you have x=y^2, this is NOT a function because if you let x = a given number, like 4, and you solve for y, you will get TWO values of y (that is, y = 2 or y=-2), so there is NOT a unique value of y.

On the other hand, if you have y=x^2, then this IS a function, since for any value of x, there is ONLY one value of y, so it does have this uniqueness property.

For more on Functions, Domain, and Range, see my Lesson Plan in algebra.com, or go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for "MATH IN LIVING COLOR", "College Alegebra", "Chapter 2", "Functions, Domain, and Range".

R^2 at SCC

You can put this solution on YOUR website!



The hard part of this is the factoring of the trinomial since the coefficient of the a*2 is NOT 1. I call this "Advanced Trinomial Factoring", and I have a Lesson PLan for this topic in algebra.com, or go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for "MATH IN LIVING COLOR", "Basic Algebra", "Chapter 2", "Advanced Trinomial Factoring."



or
or
or

R^2 at SCC

You can put this solution on YOUR website!
(4-t)(-7)=
-7(4-t)
-28 + 7t

R^2 at SCC

You can put this solution on YOUR website!
When an equation has one or more square roots involving a variable, it is necessary to square both sides of the equation one or more times in order to remove the square roots and enable you to solve the equation. The trick however, is that when you square both sides of an equation, you do NOT guarantee that the answers that you get at the end of the problem will solve the original equation. These are called EXTRANEOUS ROOTS and must be rejected!! Therefore, any time you square both sides of an equation, you MUST check the answers! They are NOT guaranteed!!

R^2 at SCC

You can put this solution on YOUR website!
This is the distributive property:
7(t-5) = 7t -35

R^2 at SCC

You can put this solution on YOUR website!


First factor each denominator in order to find the LCD:


The LCD = x(x-1)(x+1), so multiply both sides of the equation by the LCD, makin note that x cannot equal 0, 1, or -1:


When ALL these denominators divide out, this is all that is left:









The answer does NOT make any denominators zero, so it should check okay!
It does, but it's hairy!

R^2 at SCC

PS. Get your math teacher to check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Take a look at, among other pages, my "MATH IN LIVING COLOR PAGES!"

You can put this solution on YOUR website!


It may help to write this in a different format:
DIVIDED BY


Now, you have to get the common denominator before you can subtract the first two fractions:


It's hairy, but this is why your numerator is , over the common denominator (times h, of course).

R^2 at SCC

You can put this solution on YOUR website!
This is much easier than it looks. Joint variation means that the variable varies as the PRODUCT of two or more variables. By the way, was this supposed to be "Z varies jointly as a and b"???
Using k as the constant of proportionality, write an equation that expresses: Z varies jointly as a and b.
Z=k*(ab)
Z=kab

R^2 at SCC

You can put this solution on YOUR website!
You must complete the square on the x and y terms respectively:


You must "complete the square" by taking HALF of the x coefficient, and SQUARE the result, adding this amount to each side of the equation. Repeat by taking HALF of the Y coefficient, SQUARE, and add to each side of the equation. It should look like this:




The center is at x=2 and y=-1, and r^2 = 4.
Therefore, the center is (2,-1) and r=2.

R^2 at SCC

You can put this solution on YOUR website!
Assuming that you mean , the first step is to find the LCD, which must contain both factors of x and x+3. This LCD= x(x+3).

The second step is to build each fraction so it's denominator is x(x+3):




The fraction does not reduce.

R^2 at SCC

You can put this solution on YOUR website!
f(x) = -3x + 2

The graph is a straight line, with a y-intercept at 2, and the slope is -3. This means to start with the first point by going UP 2 units on the y-axis. Then, from this point move DOWN 3, RIGHT 1 unit, and put the second point. Connect the two points with a straight line, and it should look like this:


R^2 at SCC

You can put this solution on YOUR website!
Since there are 5 students to choose from, and a "team" consists of 4 players, you are taking a combination of "5 students taken 4 at at time". One way to write this is C(5,4). To find the value of this:

=.

An easier way to do this is to realize that CHOOSING 4 out of 5 to be on the team is EXACTLY the same as choosing 1 out of 5 to NOT be on the team. There are obviously 5 ways to choose 1 person NOT to be on the team, so the answer is 5.

R^2 at SCC

You can put this solution on YOUR website!
Do you need help with negative exponents? If so, I have several Lesson Plans in algebra.com, or you can check out my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for "MATH IN LIVING COLOR", and look in "Basic Algebra" in Chapter 2.




R^2 at SCC

You can put this solution on YOUR website!
The Greatest Common Factor (GCF) is the largest possible number/variable expression that divides evenly into both of the given quantities.

and

The numbers that divide evenly into BOTH 90 and 150 would be
1, 2, 3, 5, 6, 10, 15, and 30. The largest such number is 30.

You also have common factors of m, n, and p. Since m divides evenly into m^2 but NOT viceversa, m is a common factor. Actually, it turns out that when variables raised to different powers are involved, you can just choose the LOWEST POWER each factor. By this way of thinking, you can determine that n is a common factor (when compared to n^3), and also p^2 is a common factor (when compared to p^3).

Therefore, putting it all together, the GCF = .

R^2 at SCC

You can put this solution on YOUR website!
Do you mean to "expand" or "multiply"? If you have a product of two binomials, usually you are asked to multiply the product. This would be what we sometimes call "F OI L". In this case:
(p-3)(p+5)

FIRST times FIRST =
OUTER times OUTER =
INNER times INNER =
LAST times LAST =

Add these terms together and combine like terms:



Now, if you were given this trinomial, you would be asked to "factor it", which is to change this trinomial to a product of two binomials that you started out with.

For more help with this topic, see my Lesson Plans in algebra.com, or my website under "Basic Algebra", "Samples from Basic Algebra: One Step at a Time", "Chapter 2", "Section 2.01."

R^2 at SCC

You can put this solution on YOUR website!
I think you are looking for something that doesn't exist!! Although the great mathematicians have been looking for one for centuries, there is NO pattern of prime numbers, and there is no way to recognize a prime number by looking at the sequence of primes around it. The only way to identify whether is number is prime is by the Sieve of Eratosthenes--that is, to test for divisibility by every prime number up to and including the square root of the number.

R^2 at SCC

You can put this solution on YOUR website!
First of all, let me suggest that you check out my Lesson Plans on Factoring in algebra.com, especially the lessons pertaining to "Advanced Trinomial Factoring." See also my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for "MATH IN LIVING COLOR", then "Basic Algebra", the look for Chapter 2, the topic "Advanced Trinomial Factoring."

Now, has to start off with the First times First to be 3a times a


The Last times Last has to be two numbers whose product is 12. This could be
1*12
2*6
3*4

However, because the middle term is an ODD number, you cannot use an EVEN-EVEN combination of numbers. Start with 3*4.

Because the last term is POSITIVE, you must find an OUTER times OUTER and INNER times INNER combination that will ADD together to give you -13 for the middle term. By trial and error, the combination that works is this:

Notice that the OUTER times OUTER is -9x and the INNER times INNER is -4x, and this adds up to the middle term which is -13x.

See my Lesson Plans and website for additional explanations.

R^2 at SCC

You can put this solution on YOUR website!
This is an EXCELLENT question! When you solve the quadratic equation if the discriminant is POSITIVE, then there will be TWO distinct real roots. If is NEGATIVE, then there will be NO real roots. If is ZERO, then there will be only ONE real root, of multiplicity 2.


Now, if you graph the quadratic function , the ROOTS of the quadratic equation described in the previous paragraph correspond to the ZEROS (that is, the x-intercepts) of the graph of the quadratic function.


Likewise, the NUMBER of roots in the quadratic equation corresponds to the NUMBER of x-intercepts of the quadratic function.


If the discriminant of the quadratic function is POSITIVE, then there will be TWO x-intercepts. For example: , the discriminant is POSITIVE, since . There are TWO x-intercepts at x= 2 and at x= -2.
.

If the discriminant of the quadratic function is NEGATIVE, then there will be NO x-intercepts. For example: , the discriminant is NEGATIVE, . Notice that there are NO x-intercepts, since the graph does not touch or cross the x-axis.
.


If the discriminant is ZERO, then there will be only ONE x-intercept, and it will be of multiplicity 2. For example: , the discriminant is ZERO . There is ONE x-intercept at x= 0, and it has a multiplicity of 2.
.

R^2 at SCC

You can put this solution on YOUR website!
It sounds like your problem is this, which is NOT a SQUARE root! It is a CUBE root!


This means the cube root of . This means basically, "What number would you have to cube in order to end up with . Before you begin a cube root problem, you must know your perfect cubes:





It might be helpful to break this up and write it this way:
=
The numerator of the answer must be -2, and the denominator must be 3. Therefore, the answer is or

R^2 at SCC

You can put this solution on YOUR website!
factors into . Either factor will do, either the factor (x-6) or the factor (x+1). If you need extra help on factoring trinomials, see my Lesson Plans on this topic in algebra.com. Also, go to my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, look for "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time," "Chapter 2". Also see my topic called "MATH IN LIVING COLOR" and click on Basic Algebra, the Chapter 2.

R^2 at SCC

You can put this solution on YOUR website!


Simplify the fraction inside the square root first. Maybe good things will happen to you!! Remember that when you divide, you must subtract exponents!


Good things DID happen!! Notice that everything inside the square root sign is a perfect square!! Remember, when you take a square root of variables with exponents, you divide the exponents by 2!



R^2 at SCC

You can put this solution on YOUR website!
Let x = amount invested at 5%

The rest of the money would be 25000-x. This is invested at 2% interest.
The total interest for the year is $980.

.05x + .02(25000-x) = 980
.05x + 500 - .02x = 980
.03x+500 -500 = 980-500
.03x= 480


x= $16000 at 5%
25000-x = $9000 at 2%

Check:
.05*16000 = $800
.02* 9000 = $180
Total Int: $980 it checks!!

R^2 at SCC

You can put this solution on YOUR website!
Do you mean y = |x| + 3 ?? These vertical lines mean absolute value. What you posted was brackets [x], which in math means something completely different.

They want you to make a table of values.

Let x=3, then y = |3| +3 = 6
Let x=2, then y = |2| +3 = 5
Let x=1, then y = |1| +3 = 4
Let x=0, then y = |0| +3 = 3
Let x=-1, then y = |-1| +3 = 1+3=4
Let x=-2, then y = |-2| +3 = 2+3=5
Let x=-3, then y = |-3| +3 = 3 +3=6

Notice that the points "turn around" at x= 3. The graph looks like this:


R^2 at SCC

You can put this solution on YOUR website!
You need to post a problem or two. I'm not even sure what your topic is.

R^2 at SCC

You can put this solution on YOUR website!




You really need to see my own explanations of this topic of square roots. Click on my tutor name "rapaljer" anywhere in algebra.com, and look for "MATH IN LIVING COLOR". Then select "Basic Algebra", "Chapter 5". See if that help!!

R^2 at SCC

You can put this solution on YOUR website!
First, I'm not familiar with your book, so I don't know what property 2 is. Secondly, I'm not sure what you mean, as with several problems that I just posted solutions for.

If you meant , then this cannot be simplified.

R^2 at SCC