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1) At the Good dog Obedience School, dogs can learn to do three tricks: sit, stay, and roll over. Of the dogs at the school:

50 dogs can sit & 17 dogs can sit and stay |

29 dogs can stay & 12 dogs can stay and roll over |

34 dogs can roll over & 18 dogs can sit and roll over |

9 dogs can do all three & 9 dogs can do none.

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If I'm not mistaken (again :)) there are 84 dogs.

Slope of given line  is   4

Parallel slope = 4

(-10- -1) / (3-j)  = 4      You should be able to now solve for 'j'

1/9 = 3^-2 

27 = 3³ 

So we have   3^-2 = (3³)^(2x+1)     or  3^-2 = 3^3*(2x+1)

We can equate powers:   -2 = 3*(2x + 1)

Can you take it from here?

"Can an infinite set be placed into a one-to-one correspondence?"

Yes.  For example:

1, 2, 3, 4, 5, .....

|   |   |   |   |   .....

2, 4, 6, 8, 10, ....

The natural numbers are in one-to-one correspondence with the positive even integers.

This is a case of of 4 distinct balls into 3 identical boxes: Case 1 uses “Stirling Numbers of the 2nd kind”. Case 2 uses “Bell numbers”

Case 1:
If we consider that ALL the Boxes Should have Balls, the Solution is:  = 6 ways

Case 2:
If we consider that Boxes Can be left Empty, then the Solution is: 

=0 + 1 + 7 + 6 = 14 ways

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For the community: Please don't submit solutions to this problem. This is a homework problem for an online course that does not allow students to search for answers to specific problems outside of the school.

For the original poster: We realize that homework can be challenging. If you wish to receive help from the staff or other students, we encourage you to use the resources that the online classes provide. Please don't ask or search online for homework help. We understand that it's common in today's information age to look for resources online, and in some contexts, that's a great thing! However, it's against our Honor Code. You can ask for help on the message boards, and you can learn from the official solution after you submit your answer.
 

A^-1v  rotates v clockwise by 36degrees to a.

B^-1v  reflects to d.

C^-1v  goes to b, which seems to be identical to v.

D^-1v  shrinks v to c.

That is incorrect sorry

Substitute n = 1 into each of a,b,c and d.  It is clear that a, b and c then resut in a number which is not -39.  On the other hand, d does result in -39, so d is the right answer.

To find a perpindicular slope, you need to remember that it's negative, then reciprocal. In this case:

3 => -3 => -1/3

*** typo fixed ***

1/28 =1 / [F + 4D]

1/180 = 1 /[F + 12D], solve for D, F

F = -48  and  D= 19

First term =1 /-48. The harmonic sequence looks like this:

1/-48,  1/-29,  1/-10,  1/9,  1/28,  1/47,  1/66,   1/85,   1/104,  1/123,  1/142,  1/161,  1/180.....etc.

First find the slope:

Change in y = 2 - (-4) = 6

Change in x = -1 - (-3) = 2

Remember to subtract in the correct order... if you use y₁ - y₂, then you have to do x₁ - x₂.

Another note, the order in which you subtract (y₁ - y₂ or y₂ - y₁) does not matter.

The slope: 6/2 = 3

To find a parallel slope, you need to remember that it's negative, then reciprocal. In this case:

3 => -3 => -1/3

Draw a V enn diagaram and complete it to find 81 dogs in the school

-(324 / 12)^1/3 = - 3 This is the common ratio.

12 / -3 = -4 This is the first term.

The sequence looks like this from 1st term to 9th term

-4,  12,  -36,  108,  -324,  972,  -2916,  8748,  -26244  

9th term =-26244

The first term is -4/11.

The right ordering is c, d, b, a.

Multiply by 12xy to remove all denominators

12y+12x=xy

So we have xy-12x-12y=0

Add 144

xy-12x-12y+36 = (x-12)(y-12)=144

Note that we can't have 12*12 but we can have 16*9

So x-12 = 16 and y-12 = 9 and x=28, y = 21.

x+y=49

You are very welcome!

:P

I would look at 4 different regions

x<= -7

-7 < x <= 3

3< x <= 10

x>10

I would find f(x) for each of these regions.  You can get rid of the absolute values.

each time f(x) will be a line.

If the gradient is negative then   f(the biggest x) will be the minimum sum for that region.

If the gradient is positive  then   f(the smallest x) will be the minimum sum for that region.

[Graph them and you will see what I mean]

Determine the 4 minimums and then take the lowest minimum value

If you need more help you can ask (be specific about your problem) 

but please no one else jump in before hand

The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?

x = (7.5 - 2.1) / 2

Find the equation of the parabola that passes through (4,-7) and has vertex (1,-6)

Hello Guest!

\(P_{v}(1,-6)\\ P_1 (4,-7) \)

Because of the symmetry

\(P_2(-2,-7)\)

\(\large y=ax^2+bx+c \)

\(c=-6\ (vertex)\)

  \(-6=\ a\ +\ b\ -\ 6\)      | \(\times 4\)

\(-24=4a+4b-24\)     | subtr.

  \(\underline{-7=16a+4b-6}\)

   \(17=12a+18\\ \ a\ =\frac{17-18}{12}\)

     \(a=-\frac{1}{12}\)

  \(-6=-\frac{1}{12}+b-6\)

      \(b=\frac{1}{12}\)

  \(The\ equation\ of\ the\ parabola\ is\)  \(y=-\frac{1}{12}x^2+\frac{1}{12}x-6\)

  !

Are you just being lazy dragonsXayer?

You're asking a lot of questions, sometimes 2 at once, which is greatly discouraged.

And this one is super easy so why did you ask it?

It does not take long to determine this foe yourself.

Unless perhaps you do not know how to write down the rows of Pascal's triangle.