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Hi anonymous,

You have solve the queston but you have done it by substitution. 

The question stipulated 'elimination method'.

But I am really glad that you answered.  I like people to get involved.   

The circle that forms the wheel of fortune from Beijing in China has a perimeter of 621.72 meters. What is the area of the circle of the wheel of Fortune? Consider π = 3.14

$$P=2\pi r\\\\
621.72=2\times 3.14\times r\\\\
r=\frac{621.72}{6.28}\\\\
r=99 \mbox{ metres}$$

$$A=\pi r^2\\\\
A=3.14\times 99^2$$

And you can finish it!  

x=y-5

(y-5) + 2y=13

3y=18

y=18/3=6

x+12=13, so x=13-12

x=1

y=6

1/2=2.5/5

-1/5-2.5/5=-3.5/5=-0.7

Yes - Spooky

In how many ways can a committee consisting of faculty members and students be formed if there are faculty members and students eligible to serve on the committee?

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Well.......that's a tough one to answer !!  We'd have to know three things:

1.  What is the composition of the committee??

2.  How many faculty members are there to be chosen from??

3.  How many students are there to be chosen from??

I can give you an abstract aswer. Let's suppose that we have a committe composed of "f" faculty members and "s" students. And we have "F" faculty members to choose from and "S" students to choose from. Then the total ways the committee can be formed is just C(F, f) * C(S,s), where C (n,r) means the total unordered sets that can formed by selecting r things from n things and r ≤ n.

I wondered about this....when I was answering the question - or, at least, what I thought was the question - there wasn't any website address below it !!

Weird !!!

Re: Find a possible solution to the equation sin(3x+13)=cos(4x).

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Using the fact that sine and cosine are co-functions,

Note that ....[3x + 13] + [4x] = 90

7x + 13 = 90

7x = 77

x = 11

check

sin[3(11) + 13]° = cos [4(11]]°    ???

sin[46]° = cos [44]°    ???

0.719339800339 = 0.719339800339  √

All of anything is 100%

If you decreade it by 73% then you must want 100-73=27%

27%of 900 = 27/100*900 = 243 

Hi Chris,

The web address contained the actual question - I guess that is why my answer seemed a bit strange to you. 

per means divide

So you take the number of miles you have traveled and divide it by the number of hours that it has taken.

that will give you the average speed in miles per hour ( miles/hour)

another notation is

$$^{13}C_4$$    You can get the answer straight from your calculator.

CPhill is right.

THE INVERSE OF A FUNCTION IS THE EQUATION OF THE FUNCTION'S IMAGE WHEN IT IS REFLECTED ABOUT THE LINE Y=X     (This is important to know)

I just swap the letters around right from the beginning and then rearrange

y=5x+6 becomes

x=5y+6

$$y=\frac{x-6}{5}\\\\
f^{-1}(x)=\frac{x-6}{5}\\\\$$

Talking about right and left always confuses me.

If it is a big number the power is positive.

If it is a little number (less than 1) then the power is negative.

Easy Peazy

70,000 is definitiely a big number!

You might find it easier if you replace the x² with y

then you have y²+3y+2

You need two numbers that multiply to 2 and add to 3. they'll be 2 and 1

(y+2)(y+1)    but y=x²

(x²+2)(x²+1)

It will be 85 million cents

1 million has 6 zeros

85,000,000 cents

put the decimal point in to change it to dollars - just take away 2 of the zeros.

$850000.00 = $850,000

All fractions can be written as terminating or recurring decimals.

Any number that can be written as a fraction,  $$\frac{p}{q}$$  , is a rational number.

$$\pi$$ is an IRRATIONAL NUMBER.  This means it cannot be written exactly as a fraction or as a terminating or as a recurring decimal.  The numbers just keep going forever and they never form a pattern!

Re: what is 85million times one cent equal

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85,000, 000 x $(1 / 100) = $850, 000

2(x-1)-6>-6+(x+3)-4x

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Let's simplify this first......we have

2x - 2 - 6 > -6 + x + 3 - 4x

2x - 8 > -3 - 3x        Let's get the "x's" on the left and the "integers" on the right.... so we have

5x > 5    and

x > 1

In "interval" notation, we have (1, ∞)

To check that this is correct, pick two points on either "side" of 1......any values less than 1 should make the original inequality false, and any points greater than 1 should make it true.

$${\frac{{\mathtt{\pi}}}{{\mathtt{e}}}}$$

Re: If x and y are positive integers, what are all the solutions (x,y) of the equation (3*x) + (2*y) = 11

-------------------------------------------------------------------------------------------------------------------------- What we have here is a line with the following equation.

y = (-3/2)x + 11/2  

It has  a y-intercept of (0, 11/2) and an x intercept of (11/3,0) ≈ (3.66, 0) Since you specified that x  and y must be positive integers, we're looking for any x values that lie between 1 and 3, inclusively.

So we have:

x = 1,   y = 4  

x = 2,   y = 5/2

x = 3,   y = 1

So, the only things that "work" are (1,4) and (3,1)  

Rewrite this as x = (11 -2y)/3

Now 2y is an even number, so 11 - 2y must be an odd number.  So we just look at odd numbers below 11 that are exactly divisible by 3.  We quickly see that there are only two, namely 3 and 9.

When 11 - 2y = 3 we must have x = 1, so y = 4

When 11 - 2y = 9 we must have x = 3, so y = 1

Elimination. How do i solve this?

x+2y=13

-x+y=5

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Let's just add the equations together.......that will eliminate "x"

So we have

3y = 18      Divide both sides by 3 and we find that y = 6. Using either one of the equations - I'll pick the second one - substitute 6 for y to find x.  Thus, -x +6 = 5. Subtract 6 from both sides, and we get that -x = -1. Therefore, x = 1.

Make sure you check to see that both answers "work" in the first equation....I think they will...

WHAT IS THE DECIMAL OF 510%

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Drop the % sign, move the decinal two places to the left. Thus, 100% becomes 1.00.....60% is .60, etc.

I think you can do it now.......

Volume scales as length cubed, surface area scales as length squared, so the length scaling here is the cube root of (125/27), which is 5/3 (as (5/3)³ = 125/27). so area scales as (5/3)² = 25/9.  Therefore the surface area of the larger solid is 36*25/9 = 100cm²