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Hey MHB.... hour hand makes ONE revolution in 12 hours     minute hand makes 12 revs

52 c 5 = 2598960

multiplied by :

26/52   * 25/51  * 24/50 * 23/49 * 22/48             =  65780  ways          ...as MHB posted  .... maybe we are correct.....maybe !

There are 65,780 possible ways to choose all black cards.

Slope =  (11 - 7)  / ( 3 -1)  =   4 / 2  =  2

Equation of line

y = 2(x - 1)  +  7

y  = 2x  - 2  +  7

y  = 2x  +  5

The line intersects  the  x axis  where y = 0 

So

0 = 2x + 5

-5  =  2x

-5/2  =  x    

In triangle ABC, BAC = 72 and ABC = 60. The incircle of triangle ABC touches sides BC, AC, and AB at D, E, and F, respectively. Find angle DEF  in degrees.

∠DEF = 60º

∠EDF = 54º

∠DFE = 66º

The answer is 18, actually.

\(8a+4b+2c+d=(3 \cdot (2)^2 - 5 \cdot (2) + 4)(7 - 2 \cdot (2)) = 6 \cdot 3 = \boxed{18}\)

circumference of hour hand circle  =  2π( 5 cm )  =  10π cm

circumference of minute hand circle  =  2π( 10 cm )  =  20π cm

distance traveled by tip of hour hand  =  2 * 10π cm  =  20π cm

distance traveled by tip of minute hand  =  24 * 20π cm  =  480π cm

20π cm + 480π cm   =   500π cm   =   5π  meters   ≈   15.708 meters

(3x^2  -  5x  +  4)    ( 7  -  2x)

7 ( 3x^2  -  5x  + 4)  =    21x^2  -35x  +  28

-2x ( 3x^2  -5x  + 4)  = -6x^3 + 10x^2  - 8x

Adding like terms  we  get

-6x^2  +  31x^2  - 43x + 28

a = -6       8a =  -48

b = 31      4b = 124

c =  -43    2c  = -86

d =  28

Brett and Derrick had 108 marbles altogether. Brett gave away 1/2 as many marbles as what Derrick gave away. The number of marbles Derrick had left was the same as the number of marbles he had given away. If Derrick had 1/2 as many marbles left as Brett, how many marbles did Derrick have at first?

Let   the  number of  marbles  that  Brett had  =  N

Let  the  number  that  Derrick  had  =  108 - N

Let  the  number  that   Derrick gave  away  =  G

Let  the  number  that  Brett gave away  =  (1/2)G

Derrick    had  the  same number left  as  he  gave  away.....this implies that

( 108 -N )  -  G =  G

108 - N  =  2G

N  =  108 - 2G              (1)

And finally  we  have  this  equation

What Brett  had left   = 2* what  Derrick had  left

[N  - (1/2)G ] =   2 G           (2)

Sub (1)  into (2)

[108 - 2G - (1/2)G ]  =  2 G

108  -  (5/2)G  =  2 G

108  =  (9/2)G

108 (2/9)  = G  = 24

Derrick   started with    

2G  =  2(24)  = 48  

f(-7) = 3       from the definition

f(0)   = 2(0) -3   = -3

f(7) = 7² + 1                                                sum = 50

Hmmm okay. Thank you for your reply! Let me think about it, I'll ask you any questions if I'm having trouble. :)

That is what I posted    it goes   1 - 7     then  backwards to 1    then forwards to 7      then the 2021st bag winds up in box 5   ( by my calcs)

Get y by itself in the first equation

x + y + 3z = 10      →   y =  10 - x - 3z

Substitute this into the second equation and simplify:

-4x + 2y +5z = 7    →   -4x + 2(10 - x - 3z) + 5z = 7   →   -4x + 20 -2x - 6z + 5z  = 7  →  -6x - z = -13  →

6x + z  = 13

So we have this system:

k*x + z = 3

6x + z = 13 

And notice that, if k =6, we would have this system:

6x + z  = 3      and

6x + z  = 13       but this is impossible, because two things added together can't possibly have two different outcomes 

So....as geno found, when k = 6, the system has no solution...!!!

WORD OF CPhill

Sorry I think you misunderstood the problem statement. Thank you for your answer though!

Notice that it doesn't go from 7 to 1, it actually goes back and forth. Once you put a beanbag in box 7, then next beanbag you put will be in box 6, and then box 5, and so on. Once you reach box 1 again, you go to box 2, and so on. It keeps looping...

First pass place 7 bags    each subsequent pass places 6 bags

2021 - 7 = 2014

2014 / 6 = 2014/6 = 335 passes   then   4  bags are left over   

First pass goes from 7 to 1  ( this is the first pass of '6' after the initial 7)

   335th pass goes from 7 to 1

        then 4 more bags   go to boxes     2 3 4 5         I think.

Let  the original radius =  r

Let  the  degree  measure  of  the arc  = θ

arc length  =  r * θ

New  arc length =  (1.20)r  * (  1.35 θ)  =  1.62 r θ     =   62%  increase   (as  EP  found)

        15     27     51

62 %   increase

5 p + 3 m   = 90 + 3 p + 5 m

2 p - 2 m = 90

p - m = 45 cents

pen costs 45 cents mor than marker

Thanks!

\(4x^3*1*1=4x^3\\ 4*x^2*3*x=12x^3\\ 4C3*x*x*x=4x^3\\ total\\ 20x^3\)

I get 20

t = r + 28

 y = r-46

r

r + 28       +   r-46       +  r    =   228

r = 82         t  = 110        ryan = 36

Sorry, but I don't really get it. Could you explain it one more time? Thanks.