29. (09.04 MC)

Mathematics

1 answer:

lara [203]3 years ago

7 0

Answer:

The center is located at (-1, -2), and the radius is 5.

Step-by-step explanation:

The general equation of a circle is given as

(x - a)^2 + (y - b)^2 = r^2

where

a and b are the centre of the circle and r is the radius

Given the equation

x2 + 2x + y2 + 4y = 20

add 1 ad 4 to both sides

x2 + 2x + 1 + y2 + 4y + 4 = 20 + 4 + 1

factorise

(x +1)^2 + (y+2)^2 = 5^2

comparing with the general equation

a = -1, b = -2, r = 5 (all measured in units)

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Answer:

See attached image and explanation below.

Step-by-step explanation:

We notice that any quadrilateral abed can be divided into two triangles by drawing one of the quadrilateral's diagonals. See the attached picture where the quadrilateral is noted with a green perimeter, the diagonal is pictured in red, and the triangles that are form are shaded in light blue and beige.

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