CPhill

OK, man....glad to help where I can....

Since (x - 7) is a factor   then 7 is a zero

Using a little  synthetic  division to find the  remaining polynomial we have that

7  [ 1    -14       61      -84   ]

               7      -49       84

     ______________________

       1      -7      12        0

The remaining polynomial  is

x^2   -7x  +  12

Set to  0  and factor and we have that

(x - 3) (x - 4)  =  0

Setting each factor to 0  and solving for x  gives the other two roots  (zeroes)  of  x = 3  and  x = 4

The red area is the difference in the area of the sector less  the area of the isosceles triangle  with the radius as its equal sides

Area of sector  =   pi * r^2 * (68.9  / 360)  =   pi *(9.28)^2* (68.9  / 360)     (1)

Area  of triangle  = (1/2) (r^2 )  sin (68.9°)  =  (1/2) (9.28)^2 sin (68.9°)   (2)

So.....the red area = (1)  - (2)  =

[ pi *(9.28)^2* (68.9  / 360) ] - [  (1/2) (9.28)^2 sin (68.9°)  ]  =

        51.78     -   40.17     ≈

            11.6  cm^2

F  =  (9/5) ( C ) + 32   subtract  32  from both sides

F - 32  =  (9/5) C          multiply both sides  by (5/9)

(5/9) [ F - 32 ]  = C

(5/9) [ 41 - 32 ] =  C

(5/9) (9)  = C

5°  =  C

We can use Heron's  formula here

s = the semi-perimeter   = [9 + 4 +7 ]  / 2 =  20/2  =  10

The Area  is

√ [ s  (s - a) (s - b) (s - c)  ]         where a,b,c  are  the sides of the triangle

So we have

√ [ 10 * ( 10-9) (10 -4) (10 - 7) ]  =

√ [  10 * 1 * 6 * 3  ]  =

√ 180  =

√ [36 * 5 ] = 

6√5   units^2

We  have  something like this

                                B

                25                        25

A                           30                            C

Using the Law of Cosines

30^2  = 25^2 + 25^2  - 2(25*25)  cos ABC

cos (ABC) =   [ 30^2 - 25^2 - 25^2 ] / [ [ -2 (25 * 25) ]  

cos (ABC)  =   7/25

So.....  sin (ABC)  =     sqrt (25^2 - 7^2]  / 25  =    sqrt [ 625 - 49 ] /25  = 

sqrt [ 576 ] / 25  =

24  / 25

Area of  sector  =  (1/2) r^2  ( theta in radians)

So we  have

Area of sector  = (1/2) * 7^2  *  ( 4pi/15)     =   98 pi

                                                                        _____    [ in^2 ]

                                                                          15

No prob  !!!!

Formula  for arc length

Arc length  =  r * (theta in radians)    

So we  have that

18 . 4   = r  *  (13pi  /18)        multiply both sides by  (18/  [ 13 pi])

18.4 *  18 / [13pi ]     =  r  ≈  8.1  inches

xy  =  30

x + y = -13   ⇒    y =  -13  - x     sub this into  the first equation

x ( -13 - x)  = 30    simplify

-13x -x^2 =   30     rearrange   as

x^2  + 13x  +  30  =   0     factor  as

(x  + 3) ( x + 10 )  =  0

Set  each factor to 0  and solve for x  and we get that    x =   -3  or x =  -10

We only need to consider either one of these

And when x  = -3    then

y = -13 - (-3)  =   -10

So....the  two   integers are

-3  and   -10