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I got Ravenclaw...

Thanks for the answer :)

Melody,Cphill, can you confirm that? ;)

You're explanation was very helpful! My apologies if my example wasn't very clear... I have another question that's similar to the example I did beforehand:

Given this pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?

\({3 \over n}\),\(-{7 \over 2}\)

If I cross multiply, the parallel slope is \(n = -{6 \over 7}\), is that right?

As for perpendicular... how would I solve for that?

Hi Dom, lets see if i can help you cure your hyperbola ebola.    

\(y^2-9x^2-4y+18x-14=0\\ y^2-4y-9x^2+18x=14\\ (y^2-4y)-9(x^2-2x)=14\\ (y^2-4y+4)-9(x^2-2x+1)=14+4-9\\ (y^2-2)^2-9(x-1)^2=9\\ \frac{(y^2-2)^2}{3^2}-\frac{(x-1)^2}{1^2}=1\\ \)

Now it is in standard equation form for a hyperbola with a vertical transverse axis.

For the rest see here.

The equation \(24x^2+25x−47ax−2=−8x−3−53ax−2\)

is true for all values of x≠2a, where a is a constant.

What is the value of a?

I believe there is an error in your question.

x is squared on one side and not on the other.

No matter what a is they can not be equal for more than 2 values of x

Since the base of 25,111 itself mod 31 = 1, it, therefore, follows that any N from N=1 to infinity will always give a remainder of 1. So, the smallest positive integer is 1.

You would use the "Formula for falling bodies" :

d =1/2 x G x t^2, where d = distance fallen, G=Acceleration due to gravity =32.2 ft/s^2, t=time taken.

144 = 1/2 x 32.2 x t^2

144 = 16.1 x t^2       divide both sides by 16.1

8.944 = t^2               take the square root of both sides

t = sqrt(8.944)

t = 2.99 = ~3 seconds - time it takes the pine cone to hit the ground.

1_2 + 10_2 + 100_2 + 1000_2 +10000_2 +100000_2 + 1000000_2 + 10000000_2 + 100000000_2=?

=111111111_2 . Count the number of 1s from right to left and you get 9 "1s", from 0 to 8 as powers of 2 as follows. Start from left to right:

2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 =

256 + 128 + 64 +  32   +   16  +  8   +  4   +   2   +   1  =511 in base 10. And since:

511 = 7 * 73. As you can see, the largest prime that will divide 511 is 73.

Since we know it is an upside down parablola, the two points where it crosses the x axis (where y=0) will define the width

so

y = 0 = -0.2 x  (x-20)       means   x = 0    and x = 20   are the places where it crosses the x-axis (ground level)

distance between 0 and 20 = 20 ft

nvm got it!

area of stone path in sq ft   =   16x  +  8x  -  x²

area of stone path in sq ft   =   24x - x²        Plug in  80  for the area of the stone path.

80  =   24x - x²        Add  x²  to both sides of the equation

x² + 80   =   24x      Subtract  24x  from both sides.

x² - 24x + 80   =   0       What two numbers add to  -24  and multiply to  80  ?  -20  and -4 .

(x - 20)(x - 4)   =   0       Set each factor equal to  0  and solve for  x .

x - 20  =  0         or        x - 4  =  0

x  =  20              or        x  =  4

The width of the paths must be less than the lengths of the sides of the big rectangle,

so  x  must be less than  16 , and  x  must be less than  8 .

Since  20  is too large for the width of the paths, the only solution is  x  = 4

63_7  +  66_7  = 162_7

6_7    -   3_7   = 3_7

Note: The first base I tried was base 7. I converted 162_7 to base 10 = 93. Then I tried 2 numbers that add up to 93. I tried 45 + 48 = 93. Then I converted 45 to base 7 =63. And similarly, converted 48 to base 7 = 66. Then added 63 + 66 (base 7) =162_7. That is how I arrived at the answer above.

What are the dimensions of the rectangles? 18 ft x ? ft (can't read the depth on RHS).

If they do not have to be grouped into what office they are running for, just listed..... there are 18 candidates

18 * 17 * 16 *15.......* 3 * 2 *1 =  18 P 18   = 18! = 6.40237370573 x 10^15  possibilities.

First digit cannot be 5 so yo have   4 * 5 * 5 possible numbers = 100

    2 out of 5 will be even as 2 and 4 are the only evens     2/5 x 100 = 40 possibilities.

I think only "Moderators" can tag such questions as "Advanced" ........etc.

Let's consider properties of integers that fit the following conditions.

• Even three-digit number
• Less than 500
• Comprised of the digits 1 to 5

It is probably easiest to consider the possibilities for the final digit first. Because one criterion is an even number, the final digit must be either a 2 or a 4. 

Eliminating possibilities for the first digit is relatively simple, as well. The numbers must not exceed 500, so the first digit of this three-digit integer cannot be a 5 because it would violate the aforementioned criterion. Otherwise, though, no restriction exists for the beginning digit, so the numbers 1 to 4 are all candidates for the first digit

Excluding the digit restriction, the middle digit cannot affect the ability for a number to qualify for any of the predetermined conditions. Therefore, 1 to 5 are all possibilities. 

There are 4 possibilities for the first digit, 5 possibilities for the middle digit, and 2 for the last digit. The product is the number of integers that satisfy the preset conditions. \(4*5*2=40\text{ total possibilities}\)

Because Rachel is replacing the card back into the deck, then she has:

52 ways of drawing the 1st card x 52 ways of drawing the 2nd card x 52 ways of drawing the 3rd card=

52^3 =140,608 ways.

Suppose I have 6 shirts, 4 ties, and 3 pairs of pants. If an outfit requires a shirt and pants, and can either have a tie or not have a tie, how many outfits can I make?

1) 6 shirts x 3 pants x No ties = 18 outfits without a tie.

2) 6 shirts x 3 pants x 4 ties    = 72 outfits with tie

Total outfits =18 + 72 = 90 - with and without tie.

Permutations of 9 flower pots taken 4 at a time:

nPr = 9P4 = 3,024 - displays possible when order of flower pots matters.

Set up your chart as 2 simultaneous equations as follows:

3x + 150y = 217.50
2x + 112y =148, solve for x, y

x = $60 - charge per day

y =$0.25 - charge per mile

So, now that we know the daily charge and cost per mile, we can easily figure out the cost of renting a mid-sized car for 5 days and drive 250 miles as follows:

5x + 250y =

(5*$60) + (250 *$0.25) =

$300     +    $62.50

=$362.50 - Cost of renting a car for 5 days and drive 250 miles.

p sure you can delete your own posts

EDIT: why the thumbs down? ;-;