All Answers 358090 Answers

yeah!sure!but let me think !this ones a lil hard!

I find it funny aswell! On another note, can we maybe focus on the problem at hand? *points at above math problem.* 

Its okay!And isnt it funny , we both have made mistakes at the same time and are apologizing!

And im too sorry for not reading your post correctly !i just thought u posted the same question again and didnt notice it was a  new one!

Nevermind, im happy you'd follow my advice next time!

My appologies!! Ill be sure to do that next time! 

Anonymous , if you couldnt understand the answer properly then instead of making a new post it would be better if you could ask the person who answered your question to explain it a lil more further in the same thread like all others!But im just advising ,you can follow whatever u feel is good!

Correction:sorry i didnt read your question properly and gave u my advice!

actually as this question is much similar to your last one so i just got distracted!sorry !

Let's make a system of equations:

x = cost of sausage sandwiches and y = cost of milkshakes

(1) 3x + y = 8.25

(2) x + 2y = 5.25

We can solve for x or y in either equation and substitute it to the other. 

Let's solve for y in equation(2).

x + 2y = 5.25, subtract x from both sides: 5.25 - x = 2y

Next, solve for y by dividing both sides by 2 = 2.625 - (1/2)x = y. 

Now, substitute this - 2.625 - (1/2)x = y into equation(1) for y.

3x + y = 8.25 --> 3x + 2.625 - (1/2)x = 8.25. Now solve for x.

Collect like terms - 3x - (1/2)x = 2.5x and subtract 2.625 from both sides to obtain: 2.5x = 5.625. Divide both sides by 2.5 to obtain x = 2.25 or $2.25 for the cost of one sausage sandwich.

Substitute the value of x = 2.25 into either equation(1) or (2) to solve for y, the price of one milkshake.

3x + y = 8.25 --> 3(2.25) + y = 8.25 --> 6.75 + y = 8.25. Subtract 6.75 from both sides to obtain y = 1.50 or $1.50 for the cost of one milkshake.

Now, do a check to see if the values for x and y make sense.

3x + y = 8.25 --> 3(2.25) + 1.50 ?= 8.25 --> Yes.

x + 2y = 5.25 --> 2.25 + 2(1.50) ?=5.25 --> Yes.

Therefore, the cost of one sausage sandwich is $2.25 and the cost of one milkshake is $1.50.

Since we are not given a value for the variable, "a", I assume we have to somehow simplify this expression.

tan^2a-1/1+tana = tan^(2a-1) / 1 + tan(a) OR tan^(2a) - 1 / 1 + tan(a) OR tan^(2)a - 1 / 1 + tan(a) OR tan^(2)(a-1) / 1 + tan(a). The first two possiblities are weird because the "2a" is a variable and is included in the power of the tan. The last one is unlikely leaving the third form, which is one that makes the most sense.

tan^(2)a - 1 / 1 + tan(a): Simplifying this is tricky since the "tan^(2)a" and "tan(a)" are both very different. We would need a bit more information such as a value for the variable, "a", or any other extra hints provided.

For g(x)=4^x, notice that we can say y = g(x) = 4^x or y is a function of x. The same goes for y = f(x) = log(5)x. 

For g(x)=4^x: To find the x-intercept, we need to set y = 0 --> y = g(x) = 0 = 4^x or simply, 0 = 4^x. Now, if we plug in any values not includng 0 for x such as x = -5, -4, -3, -1, 1, 2, etc. we get y-values that are NOT 0. Therefore, the x-intercept does not exist. If we graph g(x)=4^x, we notice that as the x-values reach negative infinity, the y-values are closer and closer to the 0 value but never 0. Therefore, there is no x-intercept.

To find the y-intercept, we need to set x = 0 --> y= g(x) = 4^0 = 1. Any number to a power of 0 is equal to 1. Now, notice that if we tried plugging in x = 0 first when we were finding the x-intercept, we would have already found the y-intercept without noticing! Therefore, the y-intercept = 1 at the point (0,1).

f(x)=log(5)x: To find the x-intercept, we need to set y = 0 --> y = f(x) = 0 = log(5)x. Since this is a log function, it is best to observe the behavior of the graph since plugging in points may be a bit too tedious. It is best to use the properties of logs to find the intercept(s). 0 = log(5)x. The log, in this case, is in the log based 10 form (log 10). So by properties of logs, we can do the following: 10^0 = 10^(log10(5)x) --> 1 = 5x [10 to the power of log based 10 cancels out leaving the 5x] --> Now, the algebra is simple and we divide both sides by 5 to obtain x = 1/5 = 0.2. However, by looking at the graph, we notice that the graph is symmteric. Therefore, the x-intercepts would be at 0.2 and -0.2 at the points (0.2, 0) & (-0.2, 0).

To find the y-intercept, we need to set x = 0 --> y = f(x) = log(5)0 = log(0). Notice that we have y = log 0 and there is no x anywhere which means there is no y-intercept since x = 0 becomes log 0 which is a continous function when graphed, the y-value goes to negative infinity because of the nature of the log 0 graph. There is no y-intercept.

The inverse button on this calculator is the "1/x" which is the fourth button on the 1st row. 

For example, if we have 4/5 --> we can just use division to obtain 0.8. Another way to tackle this would be to divide something into 5 equal slices for a total of 100%. Each slice would then be 20% and 20 X 4 = 80% --> 0.8.

If we have 99/100 --> notice that the denominator is 100, so we can just directly do the following: 99.0* --> 0.99 by moving the decimal place two places to the left.

*Note that the example does not explicitly state 99.0 but 99 is the same as 99.0. The decimal point is just invisible.

48/[(-8+6)-(10--4)] 

Step 1: 48/[(-2) - (14*)]

*(10--4) = (10 + 4) = 14

Step 2: 48/(-16)

*(-2 - 14) = (-16)

Step 3: Divide to get -3. Make sure you have the negative sign.

So we'd solve this like

as out here we are given the values of x and y so im placing thise values instead of the variables and then sloving this expression!so heer we go

$$36x-8y^2$$

$$=36*3 - 8*(-6)*(-6)$$   (now we will multiply the two parts and then subtract)(out here in the second part which is like 8*9-6)*(-6), first we will multiply the two -6's and then it gives us 36 which we then multiply by 8 )

$$=108-288$$   (now we will simply just subtract them)

$$=-180$$  $$ANSWER$$

I hope uve understood by now but if not then pls be free to ask!

i hope this helps!

To solve this, we first need to turn the percent into a decimal, otherwise we would get a weird answer.

62.5% written as a decimal would be 0.625. You basically just move the decimal over two places to the left and take away the percent sign.

Now we have:

$${\mathtt{800\,000}}{\mathtt{\,\times\,}}{\mathtt{0.625}}$$

Multiply it out

$${\mathtt{800\,000}}{\mathtt{\,\times\,}}{\mathtt{0.625}} = {\mathtt{500\,000}}$$

So our answer is 500,000.

Heron's formula can be used when you just know the length of each side. This says

Area = √[s*(s-a)*(s-b)*(s-c)]  where a, b and c are the lengths of the sides and s = (a+b+c)/2.

Here: s = (5+12+9)/2 = 13, so:

$${\mathtt{Area}} = {\sqrt{{\mathtt{13}}{\mathtt{\,\times\,}}\left({\mathtt{13}}{\mathtt{\,-\,}}{\mathtt{5}}\right){\mathtt{\,\times\,}}\left({\mathtt{13}}{\mathtt{\,-\,}}{\mathtt{12}}\right){\mathtt{\,\times\,}}\left({\mathtt{13}}{\mathtt{\,-\,}}{\mathtt{9}}\right)}} \Rightarrow {\mathtt{Area}} = {\mathtt{20.396\: \!078\: \!054\: \!371\: \!139\: \!3}}$$

Area ≈ 20.396

The rotation vector (rot) is e^i*pi/4

e^i*pi/4 = cos(pi/4)+i*sin(pi/4) = 1/√2 + i*1/√2 = 0.7071 + i*0.7071

Then vrot = v*rot = 

(2 + 3i)*(0.7071 + 0.7071i) = 2*0.7071-3*0.7071 +i*(2*0.7071 + 3*0.7071) = -0.7071 +i*5*0.7071 = -0.7071 + 3.5355i

Thank you

$$\\Area\;\; of\;\; circle =\;\;\pi r^2\\
\mbox{Now let's look at the area of this sector}\\\\
\begin{array}{rlll}
64\pi&=&\dfrac{\frac{\pi}{16}}{2\pi}\pi r^2\\\\
64\pi&=&\frac{\pi}{16}\times \frac{1}{2\pi}\times \pi r^2\\\\
64&=&\frac{1}{16}\times \frac{1}{2}\times r^2\\\\
64&=&\frac{1}{32}\times r^2\\\\
64\times 32&=&r^2\\\\
r^2&=&64\times 32\\\\
r^2&=&64\times 16\times 2\\\\
r&=&8\times 4\times \sqrt2\\\\
r&=&32\sqrt2\;inches\\\\
\end{array}$$

This is exactly the same question that I just did only here you used a and in the last one you used x.

They are the same.

Sat 26/7/14

♬                                        ♬ ♬ MELODY ♬ ♬

Rosala's Contribution - Always a crowd pleaser   

web2.0calc.com/questions/last-laugh

@@ End of Day Wrap :  Fri 25/7/14      Sydney, Australia     Time 12:35 am   (Really Saturday morning)   ♬

Hi all,             

Great answers were provided today by Alan, DevikaAnand Heureka, CPhill, AzizHusain, Stu, Zegroes, Rosala, Kitty3, NinjaDevo and DragonSlayer554.  Thank you all.  

Ninja has completed his first draft of 'Great Answers to Learn From' and he is looking for comments and input from other members.  

You may want to suggest that another thread be included.

You may want to suggest that a thread be moved from where Ninja has put it to somewhere else. Remember, Ninja has not done a lot of these topics so it is possible that some things are not in the best places.

You may have something else on your mind that I have not thought of.

I am very pleased with the thread that Ninja has put together.  It is very nicely presented and over the course of time I feel sure that it will be well used.

Ninja, On behalf of web2.0 forum I offer you a very big thank you.  Rosala might have some roses for you if you are really lucky.  

Thanks for the advice !but......................the apple we are talking about out here is rotten and im sorry i cant enjoy the taste of  a rotten apple!

x²-2x-4≥0

first solve   $$x^2-2x-4=0$$

NO factors are jusmping out at me so you couold solve it usingthe quadratic formula

a=1,  b=-2 and c = -4

Thank you Melody!

$$f(x)=17-x^2$$

The domain is all the possible values of x (they must have a corresponding f(x) value)

Any positive x will work

Any negative x will work

x=0 works

so domain is All real x        

Domain:     $$\{x:x\in Z\}$$   

I'm am not sure about set notation but I think this is how you write x is in the set ot real numbers.