Can someone we this and explain how to do it?
what are the points at which the line y - x = 4 intersects the given circle?

(0, 4) and (- 4, 0)

Step-by-step explanation:

We require the equation of the circle

The equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

The radius is the distance from the centre to a point on the circle

To calculate r use the distance formula

r = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (, - 2)

r =

  = = = 4, hence

x² + y² = 16 ← equation of circle

given y - x = 4 ⇒ y = x + 4

Substitute y = x + 4 into the equation of the circle

x² + (x + 4)² = 16 → distribute and simplify left side

x² + x² + 8x + 16 = 16

2x² + 8x + 16 = 16 ( subtract 16 from both sides )

2x² + 8x = 0

2x(x + 4) = 0

Equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x + 4 = 0 ⇒ x = - 4

Substitute these values into y = x + 4 for corresponding y- coordinates

x = 0 : y = 4 ⇒ (0, 4)

x = - 4 : y = - 4 + 4 = 0 ⇒ (- 4, 0)

The points of intersection are (0, 4) and (- 4, 0)

the image of (6, 9) under a dilation is (4, 6). the scale factor is

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.