Answer:
x = 29
y = 93
Step-by-step explanation:
Angles 1 and 3 are vertical angles and congruent.
3x = 87
x = 29
Angles 2 and 3 are a linear pair and supplementary, so their measure have a sum of 180°.
y + 87 = 180
y = 93
Answer:
well we have the equation d = r * t
(d stands for distance, r for rate, and t for time)
So, plug in our values:
d = 55 *4
And, d = 220
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
12-x
Let x = 5
12-5
7
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:
36 boys are at the camp
Step-by-step explanation:
