Aline and a circle intersect at the points a and b.
use the equations below to find the coordinates of the points of intersection a and b.
y =x+4
(x−3) ^ 2 + (y−5) ^ 2 = 34
can i have a step by step explanation because im so confused

  A = (-2, 2)

  B = (6, 10)

Step-by-step explanation:

The points of intersection on the graphs of these equations are the values of (x, y) where both equations are satisfied. There are several ways to find those points. One of my favorite is to use a graphing calculator. (See attached)

Quite often it is reasonable and feasible just to use the expression given for y to substitute into the second-degree equation. Doing that gives ...

  (x -3)^2 +((x+4) -5)^2 = 34 . . . . . . . x+4 is substituted for y

  x^2 -6x +9 +x^2 -2x +1 = 34 . . . . . eliminate parentheses

  2x^2 -8x -24 = 0 . . . . . . . . . . . . . . collect terms, subtract 34

  x^2 -4x -12 = 0 . . . . . . . . . . . . . . . . divide by 2

  (x -6)(x +2) = 0 . . . . . factor

  x = 6 or -2 . . . . . . . . values of x that satisfy this equation*

Corresponding values of y are ...

  y = x+4 = 6+4 = 10 . . . for x=6

  y = -2+4 = 2 . . . . . . . . for x = -2

The points where the graphs intersect are ...

  {(6, 10), (-2, 2)}

Which is A and which is B is unknown (and probably doesn't matter). Above, they are listed with the smallest x-coordinate first.

the correct answer is 5 6 and 7

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.