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:
p = -4, q = -3
Step-by-step explanation:
y = -2x +4 ... (1) perpendicular bisector of AB, slope = -2
slope of AB = 1/2
Line AB pass (8,3): (y-3) / (x-8) = 1/2
AB equation: y-3 = 1/2(x-8) y = 1/2x - 1 ... (2)
(2)-(1): 5/2 x = 5 x = 2
y = 0 (2,0) intercept of bisector and AB, it is midpoint of A (8,3) and (p,q)
(8+p)/2 = 2
<u>p = -4</u>
(3+q)/2 = 0
<u>q = -3</u>
Answer:
5 weeks
Step-by-step explanation:
We know that she works at a rate of $12 an hour, she also works 20 hours a week.
The total amount she makes per week is $240 (12 x 20). However, that is without deductions. We have to subtract $34 from the $240.
$240 - $34 = $206.
$206 is the amount she makes in a week and she wants to save $950. How many weeks does she have to save? Well, let's divide.
$950 / $206 = 4.6 weeks. However, if we have to round up to 5 weeks.
A. It describes guidlines for moral behavior.
