Let f(x) = x2 + 3x − 4 and g(x) = x + 5. find f(x) ⋅ g(x). a) x3 + 3x2 + 16x − 20 b) x3 + 5x2 + 14x − 20 c) x3 + 8x2 + 11x − 20 d) x3 + 9x2 + 19x − 20

   [C]:    " x³ + 8x² + 11x − 20 " .

Step-by-step explanation:

Given:      "  f(x) =  x² + 3x − 4 " ;   and

                " g(x) =  x + 5  "  ;

Find:         "  f(x) ⋅ g(x) "  :

    f(x) ⋅ g(x) =

     " (x² + 3x − 4) (x + 5) " ;

     ↔  " (x + 5) (x² + 3x − 4) " ;

Note:  " (a + b) (c + d + e)  =  ac + ad + ae + bc + bd + ae " ;

 →  " (x + 5) (x² + 3x − 4)

             =  (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;

             =  (x³) + (3x²)  + (-4x) + (5x²) + (15x) + (-20) ;

             =   x³  + 3x² − 4x + 5x² + 15x − 20 ;

 →  Combine the "like terms" :

          + 3x² + 5x²  =  + 8x²  ;

           − 4x + 15x   = + 11 x ;

 → And rewrite:

        →   "  x³ +  8x²  +  11x  − 20 " ;

       →  which is:  Answer choice:  [C]:   " x³  +  8x²  +  11x  −  20 " .

     Hope this helps!

        Best wishes!

Step-by-step explanation:

f(x) = x^2 + 3x − 4

g(x) = x + 5

To find f(x) * g(x) we multiply f(x) with g(x)

First multiply each term in f(x) and multiply with x+5

x^2 times x+5 becomes

3x times x+5 becomes

-4 times x+ 5 becomes -4x -20

so f(x) * g(x) =

Combine like terms

f(x) * g(x) =

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2