Let $f(x) = 3x^2 - 4x$. find the constant $k$ such that $f(x) = f(k - x)$ for all real numbers $x$.

4/3

Step-by-step explanation:

We are given f(x) = 3x^2 - 4x, and so

                       f(k - x) = 3(k - x)^2 - 4(k - x)  

                                  = 3(k^2 - 2kx + x^2) - 4(k - x)  

                                  = 3k^2 - 6kx + 3x^2 - 4k + 4x  

                                  = 3x^2 + (-6k + 4)x + 3k^2 - 4k.

The polynomials f(x) and f(k - x) are the same if and only if their corresponding coefficients are the same. Comparing the coefficients, we obtain the system of equations:  

                                                 -6k + 4 &= -4,  

                                                 3k^2 - 4k &= 0.

From the first equation, k = 4/3. This value of k also satisfies the second equation, so the answer we seek is k = 4/3.

22, 28, 34, 40, 46

b)   f(n) = 6n + 16

n = what is the number of the row ( 22 would be row 1) so if we replaced n with 1, we would get 22

c)   the 14th row will have 100 seats

(1)   (2)   (3)   (4)   (5)   (6)   (7)   (8)   (9)   (10) (11) (12) (13) (14)

22 | 28 | 34 | 40 | 46 | 52 | 58 | 64 | 70 | 76 | 82 | 88 | 94 | 100

the answer is 15.50 for one mile

b) is slope: 0   y- intercept 15.5