Answer:
The answer is C.) Rotation
Step-by-step explanation:
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
<span>Hello! Lets solve this step by step! :)
Okay so we are ganna use the Pythagorean theorem.
</span><span>Since we know that FG = 10 cm, BC = 8 cm, and AB = 9 cm, we can now plug those numbers into our equation. So we take 8 squared + 9 squared = c squared
</span>So thats 81+64=c^2
<span>145=c^2
and √145 =</span><span><span>12.0415945788
Now we round it</span> to the nearest tenth of a centimeter and that gives us 12.04 So thats our answer! :)
Hope this helped if you have any other questions or would like further explanation just let me know!! :)
</span>
Answer:
$2.96
Step-by-step explanation:
3x$2.67=$8.01
3x$2.73=$8.19
5x$3.27=$16.35
$8.01+$8.19+$16.35=$32.55
This makes 11 pounds of trail mix.
$32.55 divided by 11 = $2.9590909 = $2.96