You can put this solution on YOUR website!
I am assuming that the x is NOT in a denominator. If this was NOT your intention, you'll have to resubmit the problem.



The LCD for the denominators of 8, 6, and 3 will be 24, so multiply both sides by 24.







R^2

You can put this solution on YOUR website!
Let x = number of students enrolled in all three classes. Since students are enrolled in at least two classes, there are four categories of students summarized below.

x= Students in all three classes
170 -x = students in math and English but not history
150 - x = students in English and history but not math
300 - x = students in history and math but not English

The sum of these students must equal 500.
x + 170-x + 150-x + 300-x = 500
620-2x = 500
-2x = -120
x=60

R^2

You can put this solution on YOUR website!
You must have mistyped the equation. You have two equal signs. By the way, if the equation is NOT in standard form, your first step is to get it into standard form by setting the equation equal to zero. Try again and repost it, or send me an Email.

By the way, what method were you supposed to use? With these big numbers, it's going to be hard to factor. The quadratic formula will have some big numbers but it's okay. Have you done the completing the square method?

R^2

You can put this solution on YOUR website!
I have a feeling no one is helping you on this because we are all stumped by it too!! I'm retired, and particularly bored today, so I thought I would give it a looksee! I would say first of all, for you to go with your calculator solution!!

I haven't worked with matrices for a VERY long time, but, if your equations are correct and I think they are correct, you need to convert from this system of equations to one in which you have eliminated coefficients to leave 0s and 1s. You may have to try a few times and I must admit that I didn't get the calculator answers the first time. This is what I did. First, reduce the equations to smaller numbers:
10a + 4b + 12c = 120 (Divide by 2)
11a + 77b + 0c = 220 (Divide by 11)
4a + 1b + 16c = 80

5a + 2b + 6c = 60
a + 7b + 0c = 20 (Mult by -4 and add to eq #3)
4a + 1b + 16c = 80

5a + 2b + 6c = 60
a + 7b + 0c = 20 (Mult by -5 and add to eq #1)
0a - 27b + 16c = 0

5a + 2b + 6c = 60
0a - 33b + 6c = -40
0a - 27b + 16c = 0

Next, eliminate the b coefficients by multiplying Eq #2 times -27 and Eq #3 times 33 and add together. (The first two equations remain the same!)
5a + 2b + 6c = 60
0a - 33b + 6c = -40
0a + 0b + 366c = 1080


Next, divide the Eq #3 by 366:
5a + 2b + 6c = 60
0a - 33b + 6c = -40
0a + 0b + 1c = 1080/366

So, c= 1080/366 = 2.9508 approximately, which is the calculator value that I got. I'm sure you can finish this now. By the way, my other calculator values were a=7.759 and b= 1.7486 approximately.

Good luck!!

R^2

You can put this solution on YOUR website!
Just add +8 to each side of the inequality:



R^2

You can put this solution on YOUR website!
If Steven can mix 20 drinks in 5 minutes, then in 1 minute he can mix 4 drinks.
If Sue can mix 20 drinks in 10 minutes, then in 1 minute she can mix 2 drinks.
If Jack can mix 20 drinks in 15 minutes, then in 1 minute he can mix 20/15 =4/3 drinks.

Let x = time it will take all 3 mixing drinks together to mix 20 drinks.
Then in 1 minute, all will be able to mix 20/x drinks.

Now, number of drinks of Steven in 1 minute + no drinks by Sue in 1 minute + no drinks by Jack in 1 minute = Number of drinks by all in 1 minute.




Multiply both sides of the equation by the LCD which is 3x:



minutes (approximately)


R^2

You can put this solution on YOUR website!
Since the leading coefficient is 1, the possible rational roots must be factors of the constant term, which is -6. Therefore, the possible rational roots are +1,-1, +2, -2, +3, -3, 6, and -6.

R^2

You can put this solution on YOUR website!
Since the leading coefficient is 1, the possible rational roots must be factors of the constant term, which is -6. Therefore, the possible rational roots are +1,-1, +2, -2, +3, -3, 6, and -6.

R^2

You can put this solution on YOUR website!
(x^4 -1)
(x^2-1)(x^2+1)
(x-1)(x+1)(x^2+1)

R^2

You can put this solution on YOUR website!


Domain requires that denominators must NOT equal zero! In this case, x canNOT equal 2 or -2. Domain therefore is all values of x except 2 and -2.
In interval notation: (-inf, -2) U (-2,2) U (2, inf).

R^2

You can put this solution on YOUR website!
x^2=180


or

R^2

You can put this solution on YOUR website!
Let x = the number

1x -5 = -3
x-5+5 = -3+5
x= 2

R^2

You can put this solution on YOUR website!
Please state the problem???

R^2

You can put this solution on YOUR website!
Since the cars are moving towards each other, you can ADD their speeds together. The distance between them is closing at a rate of 55 + 70 miles per hour, or a total of 125 mph. The TIME it takes to close the distance of 20 miles is given by the formula , so
hours.


That probably doesn't mean very much to you, so convert this to minutes by multiplying by 60. That would be
t= 0.16 hours * 60 = 9.6 minutes.

Keep that in mind the next time you decide to drink and drive!!!

R^2

You can put this solution on YOUR website!
Is this your problem? ???
If so, multiply the radicands (inside the square roots!) together to get


Sort out the perfect squares by forming two square roots:


Simplify the square root that is a perfect square:


If you need resources and explanations that PLATO does NOT provide, then you need to see my website!! Click on my tutor name, "rapaljer" anywhere in algebra.com, and then take my first main link on my homepage which is "Basic, Intermediate, and College Algebra: One Step at a Time." Go to Basic Algebra, Chapter 5, and you will find the ENTIRE chapter on Square Roots, complete with explanations, examples, exercises, and answers in a Discovery Method format, a LOT easier to understand than PLATO, and UNLIKE PLATO, IT's ALL FREE!!!!

Send me an Email if you need more help!!!

R^2

You can put this solution on YOUR website!
The correct answer is F, since by Principle Value Definition of square root, it is required that x be greater than or equal to zero.

R^2

You can put this solution on YOUR website!
1. Was the problem stated: ???
If so, the answer is . I think that would be B, but you forgot to close the parentheses in the numerator.

2. Looks correct!

3.
=
=
=
R^2

You can put this solution on YOUR website!
2(x+1)^2+14(x+1)+20=0

Factor out the common factor of 2, or, better yet, divide both sides by 2:
(x+1)^2+7(x+1)+10=0

This factors into
((x+1) +5)*((x+1) + 2)=0
(x+6)(x+3)=0
x=-6 or x= -3

I don't see the correct answer here. Did you copy the multiple choices correctly??? Also, there are other methods to solve this, in case I confused you with this solution.

ALTERNATE SOLUTION (for anyone who did not understand the above solution!)




This trinomial factors into the product of two binomials:

x= -6 or x = -3

Different method, same solution!! I KNOW this is correct!! The given answers are WRONG!!

R^2

You can put this solution on YOUR website!
Let x= points scored by team B,
x-12 = points scored by team A.

x+ x-12 = 144
2x=144 + 12
2x= 156
x=78 points scored by team B
x-12 = 66 points scored by team A

The correct answer is A.
You can check this by adding 66 + 78 = 144

R^2

You can put this solution on YOUR website!
Divide both sides by -4, and you get
|k| = -3

There is no real solution, since the absolute value of a number cannot equal a negative.

R^2

You can put this solution on YOUR website!
You have to state the problem. We don't have your book!!
R^2

You can put this solution on YOUR website!
The previously posted answer to this problem is WRONG!! You can't build a wall that BIG with 113 bricks!! I worked the problem in feet. The height of the wall is 6 feet. If the bricks are laid with lengthwise, the height of each brick would be 8 inches or of a foot.

divided by
bricks high

If the length of the wall is 200 feet, and the length of each brick is 16 inches or feet, then the length of the wall is
divided by
bricks long.

The number of bricks needed is 9 * 150 = 1350 bricks, not allowing for any wasted bricks.

The previously posted answer is INCORRECT because of the most common error perimeters, areas, and volumes!! When a conversion was made from FEET to INCHES, it was noted that there are 12 INCHES in 1 FOOT! HOWEVER, in this problem you are dealing with AREA, so you must use SQUARE INCHES and SQUARE FEET!! This should have been 144 SQUARE INCHES in 1 SQUARE FOOT! In fact, if you multiply the WRONG ANSWER times 12, you get approximately the CORRECT ANSWER (except for the round off error that occurred!!

So, that's my FINAL ANSWER: 1350 BRICKS!!

R^2

You can put this solution on YOUR website!
I solved this one last night, but before I could get it posted, they pulled the plug on Algebra.com, and I couldn't post it. Here is my solution in addition to the one you already received.
Let's see if I understand your notation here. Did you mean ??
If so, you must simplify the square roots first


Simplify the perfect square square roots (divide the exponents by 2!):



I don't know if it is necessary, but you can factor this by taking out a common factor of :


You may want to get some extra explanation on square roots at my website. Click on my tutor name "Rapaljer" anywhere in algebra.com, and take the first main link on my homepage which is "Basic, Intermediate, and College Algebra: One Step at a Time." Then look for Basic Algebra, Chapter 5. A complete explanation is given there with examples, exercises, and answers. Also, I have a page with solutions to a number of problems that are solved "in LIVING COLOR!!" If you ever want to find my website from the "outside world", then do a Google search for "MATH IN LIVING COLOR". I should be the first link on the Google list.

R^2

You can put this solution on YOUR website!
You have to recognize that this is the formula for the DIFFERENCE of sines.
sin(140-50) = sin 90 = 1

R^2

You can put this solution on YOUR website!
There is not enough information to find the value of sec 2x. Was this the one where sin x and cos x were given to be 3/5 and 4/5???

R^2

You can put this solution on YOUR website!
Presumably you mean that sin x = 3/5 and cos x = 4/5.

Then,





Now,

R^2

You can put this solution on YOUR website!




, where and

Now, ,



R^2

You can put this solution on YOUR website!




, where and

Now, ,



Please note, I haven't taught trig in about 20 years!! I'm a bit rusty I'm afraid!!

R^2

You can put this solution on YOUR website!
According to the simple interest formula I= Prt, in this problem, the Interest is the inflow which is $9000 PER YEAR, which means that the Time is 1 year, and the principle is $48000

I = Prt
9000= 48000*r*1

Divide boths sides by 48000 (got a calculator??):

%, which is greater than the desired rate of return!! Pretty good investment, considering my bank pays less than 1% on savings accounts!!

R^2

You can put this solution on YOUR website!
2L +2w=4(L-w+7)
2L + 2w = 4L - 4w + 28

In order to solve for the variable L, you must get all the L terms to one side. I recoommend to subtract 2L from each side, leaving
2w = 2L - 4w + 28

Next add +4W and -28 to each side:
2w + 4w - 28 = 2L
6w - 28 = 2L

Finally, divide both sides by 2:
L = 3W - 14

R^2

You can put this solution on YOUR website!
The perimeter of a rectangle just happens to be 2L + 2w, so translate the sentence
"Perimeter IS L-w + 7, the result multiplied times 4."


Solving this equation will be the other problem that you posted!

R^2