All Answers

+118728

aleecia:
is the point of (3,5) the solution to each system of linear equations? Explain.
a) 2x-y=1
3x+4y=29

You have to substitute in x=3 and y=5 into each of the equations and see if it makes both true.
2*3 - 5 = 6-5 = 1 = RHS that one is true
3*3 + 4*5 = 9 +20 = 29 = Right hand side, that one is true to.
So (3,5) is the solution to this system of linear equations.
This means that if you graphed both lines on a number plane they would intersect (cross over) at (3,5)

You can do the next one yourself

MelodyFeb 8, 2014

+118728

Thank you

MelodyFeb 8, 2014

+118728

aleeboo21:
The two largest deserts in the world are the Sahara Desert and the Australian Desert. The sum of their areas is 13 million square kilometeres. The area of the Sahara Desert is 5 million square kilometeres more than the area of the Australian Desert. Write and solve a system of equations to find the area of each desert.

I want you to at least have a go at starting this yourself.
Let the area of the Sahara desert be S million square km and
Let the area of the Australian desert be A million square km

Set up 2 separate equations to describe the 2 facts that you have been given.

(Just an annoyance but there is NO desert called the Australian desert)

Get back to the forum after you attempt this please.

MelodyFeb 8, 2014

(x+6)+ (x-4 ) + x + (x * 3) = 40

I assume you want to know how to solve this equation. First of all, get rid of all the parentheses because you do not need them and change x*3 to 3x. The equation now looks like x+6+x-4+x+3x=40. Next, combine like terms. There are 6 x's, a 6 and a -4. Combine the 6 x's to get 6x and add the 6 and -4 together to get 2. Now the equation looks like 6x+2=40. Next subtract 2 from each side and the equation now looks like 6x=38. Divide 6 to each side and you get x=6 1/3 or 19/3. To see if the answer is correct, in the original equation, substitute x for 6 1/3 or 19/3; I will be using 19/3. The equation will look like (19/3+6)+(19/3-4)+19/3+(19/3*3)=40. Add 19/3 and 6 together and the equation now looks like 37/3+(19/3-4)+19/3+(19/3*3)=40. Now subtract 4 from 19/3 and the equation now looks like 37/3+7/3+19/3+(19/3*3)=40. Now multiply 19/3 and 3 to get the equation looking like 37/3+7/3+19/3+57/3=40. Now add 37/3 and 7/3 together and the equation looks like 44/3+19/3+57/3=40. Now add 44/3 and 19/3 together to make the equation look like 63/3+57/3=40. Now add 63/3 and 57/3 together to get the equation to look like 120/3=40. Next divide 3 from 120 and get 40=40. This proves that x does equal 19/3. Hope this helps.

GuestFeb 8, 2014

#12

+118728

Hi Stu,
I don't quite know where to start and i don't have a lot of time right now.
but
1/2 * 1/3 = (1*1)/(2*3) => 1/6
It is easier to see if the fractions are written upright.
When multiplying fractions multiply straight across the top, then multiply straight across the bottom.
A whole number can be written as a fraction by putting it over 1 so 3=3/1, 2x = (2x)/1 etc.

1/2 + 1/3 = 3/6 + 2/6 = 5/6
Again it is much better (but much more time consuming for me, in the forum) if you write the fractions upright.
Before you can add fractions you have to get a common denominator, preferably the lowest one.
The multiples of 2 are 2,4,6,8,
The multiples of 3 are 3,6,9,12,...
The lowest common one is 6.

Now, when you are getting rid of negative indices you only swap the thing with the negative indice to the other side of the fraction line. NOT everything.
3/4 ^-2 = 3 * 4 ² all over 1 if you like = 48
perhaps you are confusing it with
(3/4) ^-2 => (4/3) ² => 16/9 => 1 and 7/9

Oh, dividing by a fraction.
When you divide by a fraction, you multiply by its reciprocal.
In other words, you turn the second one upside down and change the divide to a multiply.

You may need to work through some mathsisfun units on fractions I think Stu.
Anyway, I hope that this is a good start to helping you out.

MelodyFeb 8, 2014

#11

+1313

re: above, step 3 in last image. Where equal to 36 ^5/3, where do you get ^5/3?

I'm reworking these same problems with the same issues.

StuFeb 8, 2014

+6252

Quote:
Using imaginary numbers, what is the √-16?

i = sqrt(-1)

sqrt(ab)=sqrt(a)*sqrt(b)

-16 =(16) (-1)

sqrt(-16) =sqrt(16)*sqrt(-1)

sqrt(-16) = 4*i = 4i

RomFeb 8, 2014

the ± symbol (I think what you are saying) is a symbol to say that in the algebraic equation you add and subtract either the two real numbers, two variables, one real number and one variable, or one variable and one real number which would result in two answers to the algebraic equation. The only time that happens if you take an even root of a number which will result in two answers. For example: you would think that the √4 is 2 which correct; however, √4 is also -2 because -2 times -2 is 4. You can write √4 is equal to 2 and -2 and you can also write √4 is ±2, which is a cleaner way to write the answer. Hope this answer helps.

To the second part of your question, I know what the symbol integral looks like, ∫; however, I do not know what the symbol means as I have not gotten far enough in my math class at college. Sorry I could not help you with that part of the question.

GuestFeb 8, 2014

uh… A-L-G-E-B-R-A?

GuestFeb 8, 2014

If you do not know the answer, I do not know what to tell you. Anyway the answer is one apple.

GuestFeb 8, 2014

It depends on what kind of calculator you are using. Some calculators only do basic math: adding, subtracting, multiplying and diving, some calculators do basic math and some algebra which are called a scientific calculator and some do all that and graph called a graphing calculator. Whatever calculator you are using, if you are not familiar with what the buttons do, you may have a problem. I will not say that you will flunk the test; however, if a lot of the math problems on the test require you to use the calculator that you are not familiar with, it may take you longer to complete the test. Good luck,

GuestFeb 8, 2014

+6252

Quote:
What is ln(8.66×10⁻⁷ / 3.61×10⁻¹⁵)

log(ab) = log(a) + log(b)

log(a/b) = log(a) - log(b)

ln(a) = log(a)/log(e) where ln(e) = 1

so first find

log(8.66×10⁻⁷ / 3.61×10⁻¹⁵) = (log(8.66) + (-7)) - (log(3.61) + (-15)) =

0.38 + (15-7) = 8.38

Now we convert to natural log ln by finding

8.38 / log(e) = 19.30

RomFeb 8, 2014

+1313

Am moving on to this<>http://www.youtube.com/watch?v=YFXKu16kWd0
Ukmc lectures on Trig. Very nicely explained.

Can also view the side bar at youtube or search to help problem solve this. (or google calculators with explanations. Try at mathsisfun.)
http://www.mathsisfun.com/area.html < here is the basic equation.
http://www.mathsisfun.com/algebra/trig-area-triangle-without-right-angle.html < here is trig equations. Coupled with the youtube video should be enough.

StuFeb 8, 2014

Feb 7, 2014

#10

+1313

140208 more indices (1).JPG
Please explain steps 4,5,6 to achieving 3a ^5/3 to 9a10/6.

I don't see how to get to 10/6.
If so, I don't see difference of when we apply the exponent of a brack (in this instance to the power 2) before or after calculations. And have seen it done in both ways.

Firstly, ^{1/2 * 1/3 = 2/6} right? And if Squaring it = ^2/6 * ^2/1 then we can't rightfully square it again in step 5 which wouldn't = ^10/6. And if we do square the exponent at step 5 how do you get to 10/6 the answer of 5/3 x 5/3 = 25/9. But I just don't see the links.
------------------------------------
Next -> 140120 negative indices latex info.JPG

I was shown to flip everything. I am pretty sure. In the questions I have been given to solve negative indices is as follows,
eg) 3/4 ^-2
=4 ²/3 =12/3 =4 (confirmed in the answers.) So please outline what are the difference of application of what you told me and what I am shown.
-----------------------------------
Next -> 140206 neg indices (1).JPG

Ho do you go from division to multiplication. Has the equation been shifted around? I can't see it, except you're now got left over x ³ and right under y ².

I guess I need to still know this flexibility of equations from / to * and + to - etc.

StuFeb 7, 2014

+1313

I don't understand the reduction at step 7 of *t ⁿ. Simply because it is only the sum of the top half of the fraction at 8, and if it were t ⁿ on the bottom would it apply the same principle? Am comfortable with the others now.

StuFeb 7, 2014

One of the rules of logs states that log(a/b) = log(a) - log(b). Thus, in your case:
log(9) - log(3) = log(9/3) = log(3).

GuestFeb 7, 2014

+6252

Quote:
a bag of skittles contained 13 reed, 15 yellow, 44 brown, 12 orange, and 9 green candies. What percent of the candy was red?

divide the number of red skittles by the total number of skittles and then multiply by 100 to get percent.

RomFeb 7, 2014

+118728

I just did this for Stu so I thought I would tack it in here as well.

140208 more indices.JPG

MelodyFeb 7, 2014

+118728

The title is (In Albanian)
I want to teach mathematics

duu tw regjistrohm

These words do not translate into English. Are you sure your spelling is correct.
--------------------------------------------------------------------------------------------------------------
Përkthyer nga anglishtja mbrapa
Titulli është (Në gjuhën shqipe)
Unë dua të mësojnë matematikë

duu tw regjistrohm

Këto fjalë nuk do të përkthehet në gjuhën angleze. Jeni te sigurte drejtshkrimi juaj është e saktë.

MelodyFeb 7, 2014

+118728

Stu:
Sure. I will use "sup" now. I didn't know what it was or see it. Thanks for pointing it out. Btw, some answers are wrong from the page I am working on, which I only just proved to be correct. Therefore I have left them out.

Here is the questions.
(2x^1/2 3x^1/3)² =

(12a^1/2 / 4a^1/3)² = (my answer =36x) a simplify website gave 36x(^-10). What is the (^-10)?

(2t^-1)³ / 6t² = (i got 2t³)

4t^-6 3t³ = fraction? How and why do we solve to a fraction?

MelodyFeb 7, 2014

+1313

Always easy when you know how. lol, that's what I'm learning. Just got to get the know how. Nice explanation = logic.

StuFeb 7, 2014

+1313

Not for the top of classes, as you see I'm behind in foundations and was clearly in as a NY12.

Really a great help and supportive. > back to learn maths, moving on to trigonometry lectures @youtube. Also I found an awesome site Mathsportal.org.
Maths portal and this site will become my lifeline.

P.s don't you think there needs to be a sticky in the forum telling people to name the posts better? "then it can be a useful site not only to find info relating to your' field of learning, but attract the people who can answer the specific types of question. It really should happen I think. No time to scour every post, or leave it just to a few to answer, respectively.

StuFeb 7, 2014

+1313

Sure. I will use "sup" now. I didn't know what it was or see it. Thanks for pointing it out. Btw, some answers are wrong from the page I am working on, which I only just proved to be correct. Therefore I have left them out.

Here is the questions.
(2x ^1/2 3x ^1/3) ² =

(12a ^1/2 / 4a ^1/3) ² = (my answer =36x) a simplify website gave 36x( ^-10). What is the ( ^-10)?

(2t ^-1) ³ / 6t ² = (i got 2t ³)

4t ^-6 3t ³ = fraction? How and why do we solve to a fraction?

StuFeb 7, 2014

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