Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths. tiles x2 + y2 − 2x + 2y − 1 = 0 x2 + y2 − 4x + 4y − 10 = 0 x2 + y2 − 8x − 6y − 20 = 0 4x2 + 4y2 + 16x + 24y − 40 = 0 5x2 + 5y2 − 20x + 30y + 40 = 0 2x2 + 2y2 − 28x − 32y − 8 = 0 x2 + y2 + 12x − 2y − 9 = 0 sequence
x = 9
this shape is a 30-60-90 triangle, which means that the angles of the triangle are each 30°, 60° and 90°. given that the measures of the angles of the triangle are known, as well as one side, we can find the measures of all the other sides (example attached). a 30-60-90 triangle is special because of the relationship of its sides. the hypotenuse (directly across from the 90° angle) is equal to twice the length (2x) of the shorter leg, in this case labeled 'x' and directly across from the 30° angle. the longer leg, across from the 60° angle, is equal to multiplying the shorter leg (x) by √3 or x√3.
since the measure of the hypotenuse is given at 18, we can set the expression of that side equal to 18 and solve for x:
2x = 18 or x = 9
on edgen its a.) 7 3/4
answer: -23 -19 -8 5 14
negative numbers are on the opposite side of a line