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 A man walks (12x^2+11x+2) km for (3x+2) hours. What is his speed per hour?

Hello Guest!

\((12x^2+11x+2)\) : \((3x+2)=4x\)+1

  \(\underline{12x^2+8x}\)

                \(3x+2\)

The man walks (4x+1) km per hour.                ??

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See here: A000032 in the OEIS:  The First 10 Lucas' numbers are:

2, 1 , 3 , 4 , 7 , 11 , 18 , 29 , 47 , 76 

Find the sum of the cubes of the solutions of x^2-12x+4=0.

Hello Guest!

\(x^2-12x+4=0\)

\(x=6\pm \sqrt{36-4}=6\pm \sqrt{2^5}\)

\(x_1=6+2^2\sqrt{2}\\ x_2=6-2^2\sqrt{2}\)

\(x_1^3+x_2^3=1584=2^4\cdot9\cdot 11\)

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1 - ( 5760, 6720, 8064, 10080, 13440, 20160, 40320) >>Total = 7 divisors are > 7!

2 - (11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583, 594, 605, 616, 627, 638, 649, 660, 671, 682, 693, 704, 715, 726, 737, 748, 759, 770, 781, 792, 803, 814, 825, 836, 847, 858, 869, 880, 891, 902, 913, 924, 935, 946, 957, 968, 979, 990) = 90 such numbers, which are ALL multiples of 11.

Student tickets are \(\$8.00\ and\ adult\ tickets\ are \)  $15.00. If you sold 167 tickets for a total revenue of $1630, how many of each ticket did you hand sell?

    Hello Guest!

    \(8st+15ad=1630 \)

    \(st+ad=167\)            | * 8

 - \(\underline{8st+8ad=1336}\)    

   \(7ad=234\) 

   \(ad=42\)

   \(st=167-42\)

   \(st=125\)

125 tickets were sold to students and 42 tickets to adults.

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PLease help!

How did you get the second line from the first line?

The length is 25.

Yes!

A few AoPs questions sent from him/her were sent a few weeks ago when it was that weeks homework as well lmao

Glad to help!

Thank you! That's correct!

Ok, so here is my version of the answer to this problem.

We can determine that we can split the balls into the groups 4-0-0-0, 3-1-0-0, 2-2-0-0, 2-1-1-0, and 1-1-1-1. Now we have to count how many ways the boxes can be chosen.

For 4-0-0-0, there are 4 ways we can choose the box that gets all four balls.

For 3-1-0-0, there are 4 ways we can choose the box that gets three balls, then 3 ways we can choose the box that gets one ball.

For 2-2-0-0, there are \(\binom{4}{2} = 6\) ways we can choose the two boxes that get two balls each.

For 2-1-1-0, there are 4 ways we can choose the box that gets two balls, then 3 ways we can choose the box that gets no balls (then the other two boxes get one ball each).

For 1-1-1-1, there is only one way.

The total number of ways is then \(4 + 4 \cdot 3 + 6 + 4 \cdot 3 + 1 = \boxed{35}.\)

Hope this helped! 

1*10^100

The sum of the measures of all the arcs in a circle is  360°

So... looking at the circle in problem #9....we can make the following equation:

61°   +   (5x - 7)°   +   34°   +   (9x - 22)°   =   360°

                                                                                Remove the degree sign from every term.

61   +   5x - 7   +   34   +   9x - 22   =   360

                                                                                Combine like terms.

14x   +  66   =  360

                                   Subtract  66  from both sides of the equation.

14x   =   294

                                   Divide both sides of the equation by  14

x   =   21

Now that we know what  x  is, we can find the measures of all the arcs.

\(\begin{array}{ccccccc} m\stackrel{\large\frown}{GK}& =& (9x-22)^{\circ}& =&(9(21)-22)^\circ&=&167^\circ\\~\\ m\stackrel{\large\frown}{HJ}& =& (5x-7)^{\circ}& =&(5(21)-7)^\circ&=&98^\circ\\~\\ m\stackrel{\large\frown}{HGJ}& =& m\stackrel{\large\frown}{HG}+m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} & =& 61^\circ+167^\circ+34^\circ&=&262^\circ\\~\\ m\stackrel{\large\frown}{GKJ}&=&m\stackrel{\large\frown}{GK}+m\stackrel{\large\frown}{KJ} &=&167^\circ+34^\circ&=&201^\circ \end{array}\)

1 million   =   1 000 000   =   1 * 10^6

To get a number into scientific notation, we want to write it in such a way that the decimal point immediately follows the most significant digit.

In other words, we want to move the decimal point all the way up to right before the most significant (leftmost) digit.

Notice that

4.5  *  10   =   45

So  45  could be expressed as  4.5 * 10

Also...

3.25 * 10 * 10   =   325

So  325  could be expressed as  3.25  *  10²

In the same way.....

1 trillion   =   1 000 000 000 000     =     1  *  10¹²

1 million   =   1 000 000   =   1 * 10^?

Can you fill in the blank? 

Since  Y  is the midpoint of  XZ,  it must be that

the length of  XY   =   the length of  YZ

which means

3a + 1   =   a + 9        Let's solve this equation for a.

                                  Subtract  a  from both sides of the equation.

2a + 1   =   9

                                  Subtract  1  from both sides of the equation.

2a   =   8

                                  Divide both sides of the equation by  2

a   =   4

Now that we know what  a  is,  we can find the length of  XZ.

the length of  XZ   =   3a + 1  +  a + 9

the length of  XZ   =   3(4) + 1  +  4 + 9

the length of  XZ   =   12 + 1  +  4 + 9

the length of  XZ   =   ?

To find the mean, add up all the numbers and divide by the number of numbers in the list.

mean   =   (  5  +  -7  +  12  +  -10  +  15  )  /  5

Just type that into a calculator (such as the one on this website) to get your answer 

_

5000 represents 1/4 of the total cost of the car

   so car + int can cost   20 000

    removing interest   20 000 / (1.01) =  19801.98    I suppose answer C is the closest to true

x   from  -3   to  +3       1/3    would be -2      2/3 would be  +1

y   from  -2  to  +3         1/3 would be   -2 + 5/3 = -1/3      and   2/3 would be  -2 + 10/3 = 1 1/3

 (-2, -1/3)   and   (1,  1 1/3)  

4 + 2⁷ = 132

(4+2)⁷ = 4782969