Answer:
2r (1 + √3)
Step-by-step explanation:
Circle O₁ is tangent to AB. Let's call the point of intersection point D. If we draw a radius from the center O₁ to D, we know this forms a right angle.
△ABC is an equilateral triangle, so we know m∠A = 60°. If we draw a line from A to O₁, we know that bisects the angle, so m∠DAO₁ = 30°.
So △DAO₁ is a 30-60-90 triangle. We can find the length AD:
AD = r √3
Now on the other side, circle O₃ is tangent to AB. Let's call the point of intersection point E. We know it's the same triangle we found earlier, so:
EB = r √3
And finally, we can draw a rectangle connecting O₁, O₃, E, and D. The distance between O₁ and O₃ is 2r, so:
DE = 2r.
Therefore:
AB = r√3 + 2r + r√3
AB = 2r√3 + 2r
AB = 2r (1 + √3)
Here's a graph showing the steps. Hopefully this helps, let me know if you have questions!
desmos.com/calculator/hgaonfzxsm
(5,7) is the answer to the question, you can also use (-1,-5)
Answer:
B. Dodecahedron
Step-by-step explanation:
It has more of a hectagon shape, instead of a triangular one.
Each tweet would cost between 1 and 140 pennies you can write that as an inequality [1 ≤ x ≤ 140] Since you can't tweet 0 characters or above 140.
if you want to change it to pounds divide by 100.
A) 1 ≤ x ≤ 140
B) Each character costs a penny, you can't tweet less than 1 character or above 140.
Answer:
units
Step-by-step explanation:
If we draw a perpendicular from point (6,2) on the line 6x - y = - 3, then we have to find the length of the perpendicular.
We know the formula of length of perpendicular from a point 
to the straight line ax + by + c = 0 is given by
Therefore, in our case the perpendicular distance is
units. (Answer)
