Find the possible value of "a" using the distance formula.
(4,-1) and (a,5) with d = 10

Step-by-step explanation:

The distance formula is given by:

We are given the two points (4, -1) and (a, 5). The distance between them is 10.

Let (4, -1) be (x₁, y₁) and let (a, 5) be (x₂, y₂). Substitute:

Solve for a. Square both sides and simplify:

Simplify:

Take the square root of both sides. Since we are taking an even root, we will need plus/minus. Hence:

Solve for a:

So, our two possible points are (12, 5) or (-4, 5).

b

step-by-step explanation:

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.