What is the radius of a circle whose equation is x2 + y2 + 8x – 6y + 21 = 0?

 The required center of the given circle is 2 units.

Step-by-step explanation:  We are given to find the radius of a circle with the following equation:

The standard equation of a CIRCLE with radius 'r' units and center at the point (h, k) is given by

From equation (i), we have

Comparing the above equation with the standard equation (i), we get

radius, r = 2 units  and  center, (h, k) = (-4, 3).

Thus, the required center of the given circle is 2 units.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

which expression can be used to convert 80 us dollars (usd) to australian dollars (aud)?

1 usd = 1.0343 aud

1 aud = 0.9668 usd

step-by-step explanation:

sorry just need the points