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Here :  https://web2.0calc.com/questions/pls-help_114

Thanks!

f(5) = 18.

g(x) = -6x^^4 + 9x^3 - 3x^2.

 2xy + 3y^2 - 9y^2*z + 18y^3

y ( 2x  + 3y  - 9yz  + 18 y^2)

Triangles  AGE  and  CGD are similar

Since  AE = (1/3)AB

Then AE  = (1/3) CD

So AG  = (1/3) CG

CG = GH  + HC

And triangles  CHF and  AHB  are  similar

Then  CF  = (1/4)CD  = ( 1/4) AB

So  HC  = (1/4) HA

HC =  (1/4) ( GH  + AG)

AG  = (1/3)CG

AG =  (1/3) (GH  + HC)

3AG = GH + HC

HC  =  3AG - GH

Therefore

    HC  =  HC    so

3AG  - GH  =  (1/4)(GH +AG)

3AG - GH  =  (1/4)GH  + (1/4)AG

(3 - 1/4)AG  =  ( 1 + 1/4) GH

(11/4)AG  = (5/4)GH

11AG  = 5GH

AG  = (5/11)GH

And HC =  (1/4)(GH + AG)  =  (1/4)  [GH  + (5/11) GH ]   =  (1/4)(16/11)GH  =  (16/44)GH = (4/11)GH

So

AG   : GH  :  HC    =

(5/11)GH : GH : (4/11) GH   =

5GH   :  11 GH  :  4GH   = 

5  :   11   :   4

Thank you!

Second  one  :

Since  AB = AD   angles ABD  and BDA   are equal  = 72

So  angle BAD  = 180  -  ABD - BDA  =  180 - 72 - 72  =  36

And  since BA =  BC  then angle  BCA  =  angle BAD   =  36  =  angle BCD

So....by  the exterior agle Theorem angle BDC  =  angle ABD + angle BAD  =  72 + 36 =  108

So...angle  DBC  =  180  - BDC - BCD  =  180  - 108 - 36  =  36

So  angles  DBC  and BCD  are  equal...so   DC  =  BD...so  .....BCD is isosceles

First  one

Angle CDA  = 90 

Since DEF is equilateral, then  angle  EDF  =  60  =  angle DEF

So  since CDF is  a straight  line,  then  angle ADE  =  180 - CDA - EDF  =    180  - 90 - 60  =  30

And  AD = AE  so angle  AED  = angle  ADE

So....angle AEF  =  angle  AED + angle DEF  =   60  + 30  =  90

Common diiference   = 1  - 2/3  =  1/3

8th  term =  (2/3)  +  (1/3)  (8 - 1)   =    

2/3  + (1/3) * 7  =

2/3  +  7/3   =

9/3  = 

3

note 1 = 3/3

2/3, 3/3, 4/3 etc.

(2 + 7*1)/3 = 9/3 = 3

This problem is controversial. The shape isn't even a parallelogram, so none.

There are 100 odd numbers in the interval    sum = 100/2 (301 + 499) = 40 000

Thank you, catmg! :)

301 + 303 + 305 + 307 + … + 497 + 499

301 * 100 + 2(1+2+3+4+…+98+99)

30100 + 2(99)(100)/2

30100 + 9900

40000

Nice :))

I got sniped. 

=^._.^=

6! / (1! 2! 3!) = (6*5*4)/(2)=6*5*2=60

Original side length 36/4 = 9 in

PYTHAG THEOREM TO FIND NEW SIDE LENGTH = sqrt ( 4.5^2 + 4.5^2 ) = sqrt 40.5  in

New perimeter = 4 * sqrt 40.5 inches

x  =  1  +  sin (pi * t)

3/2  =1 + sin (pi * t)

3/2  -1  = sin (pi * t)

1/2  =  sin (pi * t)

Note  that   for  the  correct  values of t ,  y  must  also  = 3/2....so.. the  sine  must be  positive  in both cases.....so...t  must produce  a first  quadrant  angle  in both cases

This  happens  when     t   =   (1/6)     t   =  (1/6) + 2    t =  (1/6) + 4    t  =(1/6)  + 8

So

t  =   (1/6)   ,  (13/6)   , ( 25/6)   and  (37/6)

We  have  two  cases

Let   x  be positive  and  - x  be  negative

If    x is  an integer  then    floor (x)  = x      and  floor  (-x)  = -x

So   x  +  - x   =   0

If  x is NOT  an integer, then    floor (x)  = a  where  a  is  a positive integer   and   floor (-x)  =    -a  -  1

So  a  + ( - a - 1)   =  -1

So.....all  possible  values  of  the  sum  of  the floor functions =  - 1  ,  0

Try to measure everything in terms of the circle. 

The area of the parallelogram is equal to the area of the circle. 

The height of the paralleogram is equal to the raduis of the circle. 

The base of the parallelogram is half the circumfrence of the circle. :))

=^._.^=

150-23 = 127 people brought pies.

75 + 89 = 164 total pies.

If everyone brought 1 pie, 37 pies are left, so 37 people must've brought another pie. 

75 - 37 = 38 people only brought pumpkin pies. 

=^._.^=

See  the  graph here  :  https://www.desmos.com/calculator/ehqpfxhrwz

Note  that no matter  what  t  is, we  can never  make  x  =  0  (we can get close, but  never 0 )

So.....this curve  never  intersects  the  y  axis   at all

So....no closed  curve  is  formed  by  this  curve  and the  y axis

Thank you so much for looking at my problem, but I don't think your solution is correct. Would you mind taking another look at it if it's not too inconvenient?

Well....let's  see

70%  of  the  aritmetic  questions correct  =  7  correct

50% of the algebra  questions correct  =  15 correct

50%  of  the  geometry  questions correct  =  10  correct

Total correct =  32

To  get  60%, he needs   60 * .60   =  36  correct

So.....4  more  correct  answers