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.

24

step-by-step explanation:

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9