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
Answer:
x = -18
Step-by-step explanation:
x - (-5)= - 23
you would do the opposite of -5 which is positive 5 and you would add 5 to the negative 5 to cancel out that -5 and add 5 to the -23 which gives you -18 so x = -18
Hope this helps!
(oﾟvﾟ)ノ
<span>These types of lines are called contour lines. Though the image is flat and on a two dimensional sheet of paper, they suggest the volume of the shape. Such drawings are often done very quickly or with a single hand motion.</span>
Yards per pillow.....yds/pillow....make sure u put the yds over the pillows when dividing
16/12 = 1.33 (or 1 1/3) yds per pillow....this lies between 1 and 2 yds
4.2 = <u>c
</u> 8
<u>
<em /></u><em>multiply both sides by 8
</em>
4.2* 8 = <u>8</u><u>c
</u> 8
<u>
</u> c = 33.6<u>
</u>
