Use Pythagorean Theorem:
a² + b² = c²
"a" is one side of the right triangle.
Its length is: radius of larger circle minus radius of smaller circle: (11 - 3 = 8)
The distance between the center of the circles creates the hypotenuse (17)
8² + b² = 17²
b² = 225
b = 15
Answer: the length of the common external tangent is 15.
5x^2 - (2x - 3)^2 =
5x^2 - ((2x - 3)(2x - 3)) =
5x^2 - (4x^2 - 6x - 6x + 9) =
5x^2 - (4x^2 - 12x + 9) =
5x^2 - 4x^2 + 12x - 9 =
x^2 + 12x - 9 <===
X will equal 40.
EXPLANATION: since they’re parallel and these are opposite angles, add them together to equal 180.
x+(20)+3x=180.
add common variables.
4x+20=180
subtract 29 from both sides
4x=160
divide each side by 4 so isolate x
x=40
If the dimensions are "nice" factors of the quadratic, and if y > -3, we have
.. area = (y +3)(y +5)
y+5 is greater than y +3, so we take the width to be ....
.. width = y+3
