CPhill

(2x + 7)  ( x  - 5)   = -43 + jx       simplify

2x^2  + 7x -10x -35  = -43  +jx            rearrange as

2x^2  - 3x  - jx - 35 + 43  = 0

2x^2  - (3 + j)  + 8  =  0

If this has one solution the  discriminant must  =  0    ....so....

(3 + j)^2  - 4(2) (8)   = 0

j^2  + 6j  + 9  -  64  =  0

j^2 + 6j  - 55  =  0       factor

(j + 11)  ( j - 5)   =  0

Setting each factor to 0  and solving for  j

j + 11   = 0                   j - 5  =   0

j  = -11                           j  =  5

So...  j   =   -11,  5

BTW.....when x  = -11,  x  = -2   and when x  = 5, x  = 2

The  length of the leg opposite the 30°  angle = (1/2) (hypotenuse)  = (1/2)(26)  = 13

The length of the  side opposite the  60° angle =   (side opp 30° angle)  * sqrt (3)  = 13sqrt (3)

Sum of sides =   26 + 13 + 13sqrt(3)   =   [39 + 13sqrt (3) ] cm ≈ 61.5 cm

Here are a couple of approaches   (EP's is WAY better than mine  !!!  )

https://web2.0calc.com/questions/if-the-area-of-triangle-abc-is-27-what-is-the-value-of-p

Second one .....this one is a little tougher

Similar to the  first....we have  that

r/2  =  -4        multiply both sides by 2

r  =  -8

Since we have a vertical asymptote at x = 3....we need to solve this

2(3) + t  =0

6 + t = 0

t  = -6

And since  the point (1,0)  is on the graph, we can ignotr the denomiantor and solve

-8(1)   +  s  = 0

-8 + s  = 0

s= 8

Our function is

f(x)  =  -8x  + 8

          _______

             2x  -6 

Graph here  :   https://www.desmos.com/calculator/plavxacf5r

1st one

The horizontal asymptote   will be given  by the ratio  of the  coefficients on the variable x in the numerator and denominator

So      a/1  = -4      implies that  a  = -4

A vertical asymptote  will occur when the  denominator   = 0 

So....when x=  3 we have that     3 + c  = 0    →   c = -3

And since  f(1)  = 0.....this means that

0  = -4(1) +  b

     _________     multiply  both sides  by   x -3

         x - 3   

So we have

0  = -4 + b     →   b =  4

Our  function is

f(x)   =   -4x  + 4

             _______

               x - 3

Here is the graph  :

https://www.desmos.com/calculator/vgpwl6hezj

V (cone)   = ( pi ^ radius^2 * height )  / 3

104.67  = (3.14) * (radius)^2 *  4 / 3

Multiply both sides by 3  and divide both sides by 3.14

104.67 * 3  / 3.14   =  radius^2

The left side  evautes  to  ≈  100

Taking the square root of both sides  gives that

10  =  radius

Double this value to  find the  diameter....

Glad to help  !!!

Do you see why this answer is  correct   ???.....that's the important thing.....

-39  =  6  - 5x      subtract 6 from both sides

-45  =  -5x         divide both sides by  -5

9  =  x

-3.5

Wall space  if no windows  and  no doors (1)  =  9 (10 + 10 + 12 + 12) =  9 ( 44)  = 396 ft^2

Subtract   windows and doors square footage =   2  (3*6  + 3.5 * 6.5)  =  2 ( 18 + 22.75)  = 2 ( 40.75)  = 

81.5 f^2

So

396  - 81.5    =   

314.5 ft^2  =  sq ft to be painted