Use the tables to answer the question.

Question

x −x^2+5x
0 0
1 4
2 6
3 6
4 4
5 0
x −x+5
−1 6
k 4
3 2
5 0
7 −2 What value of k in the table will be a solution to the equation −x2+5x=−x+5 ?(1 point)
Responses

−6
negative 6

4
4

1
1

0

Answer 1

To solve the equation −x^2+5x = −x+5, we need to set the two expressions equal to each other:

−x^2+5x = −x+5
Now, we can simplify the equation:

0 = x^2 - 6x + 5
This equation can be factored into:

0 = (x - 1)(x - 5)
Setting each factor equal to zero gives us the solutions x = 1 and x = 5.

Looking at the table, we see that the value of k that corresponds to x = 1 in the second table is 4. Therefore, the value of k that will be a solution to the equation is:

k = 4