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The area of a parallelogram is A = BH where B = base and H = high so in the problem, B = 14 and H = 12 so our equation would be 14*12 = A and we get our area is 168 or as an equation A = 168 

D is the centroid of △ABC. What is the value of x when BD = 45 - x and BF = 21x?

(I assume that BF is a median of triangle ABC)

BD : DF = 2 : 1

45 - x = 2(21x)

x = 45/43

Look  at  the  graph  here  :   https://www.desmos.com/calculator/2x44zxv4qs

The  first two constraints  form a 10 x 10  square.....the  area  =  100

The  unshaded area  in the constraint region   forms a  triangle   that  has  a base of 10  and a  height of 5

The  area of this triangle  = (1/2) (10)(5)   =  25

But....we  are  interested  in the  shaded area in the  constraint region....

This area =  100  - 25  =  75

The probability  that a  point falls into this   region  is   75 / 100  =   3 / 4

QR  =  2*QW  =  2*25   = 50

RZ  =  sqrt  ( RX^2  + ZX^2 )   =  sqrt ( 40^2  +  9^2)  =  sqrt ( 1681)  =  41

 XS = RX  = 40

ZS  =  RZ  =  41 

WZ   =  sqrt  ( RZ^2  - RW^2)  =   sqrt  ( 41^2  -  25^2)   =

sqrt  ( 1681  - 625)  =  sqrt (1056) = 4sqrt (66) ≈  32.5

Divisors  of  112

1   2    4    7   8    14    16    28    56    112

Let  m  =  16

        n =   56

m + n   =   16  +  56    =    72

Here :   https://web2.0calc.com/questions/help_51506

Unit  cost =   total cost /  total number of  items

So

30  / 24  =   5 / 4   =  1.25    (dollars)

39.60  / 36  =   1.10     (dollars)

Last one

Here again, we  have  a problem....we can only answer  the  "walk"  and "bus"  categories......we would  have to know the central angles of the "bike"  and "car"  sectors  to answer  these......your  teacher  should  recognize this  !!!

Walk  =  ( 120 /360)  * 60  =   (1/3) * 60   =  20

Bus  =  (90 / 360) * 60   =   (1/4) * 60   =    15

All we  can say is  that   60  - 20 - 15    =   25    total  students  ride their bikes or take a car

Second  one -  a little tricky

We  know  that   3960  more women voted  than men

Note  that  the angle of  the   sector  occupied by women  = 360 -125  = 235°

Let  x  be the  number of men who voted

Then x + 3960  =  the number of women who voted

So...we  can set  up  this proportion

x/ 125  = (x + 3960) / 235              cross-multiply

235 x  =  125 ( x + 3960)    simplify

235 x  =  125x  + 495000

235x - 125x  =  495000

110x  = 495000

x  =  495000 / 110  =   4500

Total number of  voters  =

x  +  ( x + 3960)  =

4500  +  (4500 + 3960)  =

12960

ithank you

0  = 5 -  1/2 a t^2     where a is acceleration of gravity   32.2 ft/s

4 out of 7   is   4/7 ths of the total #  students

4/7 * 112 =  64 attended

First  one

a)  1/2  of  the circle show the people over 60

So    (1/2) ( 180)   = 90

b )  cannot  be answered  unless we  know the central  angle  of the  25 - 60 sector   !!!

a / b  =  3  / 4

a =  (3/4)b

Divisors  of 120

1  2  3  4  5  6  8  10  12  15  20  24   30  40   60   120

a  =  30      b  =  40

gcd   =    5

6t > t + 6 + 2t.   simplify

6t   > 3t + 6

6t - 3t >  6

3t >  6

t >   6 / 3

t >  2

Thanks, James

Another  method

We  have  the relationship that

BD / AD  = AD  /  DC

BD / 20  =  20 / 16           cross-multiply

16 BD  =  20 * 20

16 BD  =  400

BD  =  400  /16     =   25

\(CA=\sqrt{20^2+16^2}=\sqrt{656}\)

\(BD^2+20^2=BA^2\)

\(AC^2+BA^2=(DC+BD)^2\) =>\(656+(BD^2+20^2)=(16+BD)^2\)

\(656+BD^2+400=256+32BD+BD^2\)

\(1056-256=800=32BD\)

\(BD=25\)

-8r <  -12  + 2r           rearrange   as

12 <  2r + 8r

12 <  10r

12/10 < r

6/5 <  r       which also  means that    r  >  6/5

Good job, James.....exactly correct   !!!!

First.....find  the altitude, A,   as....  sqrt  (12^2  - 8^2)  = sqrt  [ 144 - 64 ] = sqrt (80) =  4sqrt 5

And  we  have  this relationship

x / A =  A  / 8

x / ( 4sqrt 5)  =  (4sqrt 5)  /  8        cross-multiply

8x  =  (4 sqrt 5)^2

8x  =  80

x  =  80 / 8   =   10

\(\angle N=\angle O=90\)

\(\angle J+\angle H=360-\angle O-\angle N=360-90-90=180\)

I'm not sure about this

Area  =  pi  *  radius ^2  *  ( 40 / 360)   =

pi * 4^2  *  ( 40 / 360)  = 

16 pi  * ( 1/ 9)   =

16pi / 9    cm^2

Unit price  =

11.43 /  9     = 

$1.27

The gcd of a and b is 5.