CPhill

Triangles BDA and BDC are under the same height...so....their areas are to each other as their bases

So   area of   BDA =  (1/(1 + 2)) [ABC]  = (1/3) [360] = 120

Note that sin  angle BEA =  sin angle DEA

And  BE = ED

And AE= AE

So

area of  triangle  BEA = (1/2) (BE)(AE) sin (BEA)

area of triangle  AED =  (1/2) (ED)(AE) sin ( DEA)

So  area of  triangle  BEA  = area of trinangle  AED  

So

[AED] + [ BEA ]  = [ BDA ] 

 2 [ AED ] =   120

[ AED ]  =   60

3x^2  + 12x  -  k  =  0

Sum of roots  =  -12/ 3  = -4

So

x + 1/x=  -4

x^2 + 4x + 1 =  0

x^2 + 4x  =  -1          complete the square on x

x^2 + 4x  + 4 =  -1 + 4

(x + 2)^2  = 3        take  both roots

x + 2 =  sqrt (3)             x + 2 = -sqrt (3)

x = sqrt (3) - 2              x =  -sqrt (3) - 2

Product of the roots  =   -k /3

So

(sqrt (3) - 2) (-sqrt (3)  -2)  =  -k/3

- (sqrt (3) - 2) (sqrt (3) + 2)  = -k/3

(sqrt (3) -2) ( sqrt (3) + 2)  = k /3

3 -4  =  k/3

-1  = k/3

k = -3

x^2  + (7)^2  =  100

x^2 + 49 = 100

x^2    =  51             take both roots

x = sqrt (51)          x  = -sqrt (51)

Sum  of x soutions  =   0 

Here :  https://web2.0calc.com/questions/quadratic_28591

floor  [  2pi + 4sqrt (7)  - 5/3 ]  =   15  whole numbers

A + 2  = B -2   →  B = A + 4

A + 2 = C + 2 →  A = C

A + 2 = D - 2 →   D = A + 4

So

A + B + C + D = 36

A + (A + 4)  + A  + (A + 4) =  36

4A  + 8 =  36

4A = 28

A = 7   C  = 7    B =  11     D =   11

ABCD =  7^2 * 11^2  =    5929

Howard's salary =  (10/7) (3500)  =  $5000

If Howard's is decreased by 15%  he makes 85% of what he was making  =   5000 (.85)  =  $4250

Fiona  now makes   4250 (7/10)  =   $2975

We could get an algebraic solution, but a graph seems easier :

The toal length of the drive  ≈  73.54  miles

You are within the transmission range for  ≈ 31.5 miles

So

31.5 /  73.54 ≈ .428  =   42.8%  of the time    (assuming a constant speed)

-5t^2 + 20t + 3 =  13              subtract 13 from  both sides

-5t^2  + 20t  - 10  =  0            divide through by -5

t^2  - 4t + 2  =  0                   

Using the quadratic formula

t =   4 ±   sqrt [ 4^2 - 4 (1) (2) ]                4 ±  sqrt [ 8]       4 ± 2sqrt (2)

       _____________________  =        ___________  =  __________  =

                     2 * 1                                           2                     2

2 ± sqrt (2) =      about .59 sec   and   about 3.4 sec 

Here :  https://web2.0calc.com/questions/geometry_95436