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 length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).