Order is important in ratios so in this one, it says the ration from GIRLS to BOYS.
We know there are 12 girls and 9 boys so the ratio is B. 12:9
Answer:
a) 12xy
b) 30pqr
Step-by-step explanation:
multiply the numbers and since x and y are not common terms then keep them as xy multiplied with 12
same goes with b)
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
I choose B. 20.93 kilometers
Answer: 20/12
Step-by-step explanation: In order to get a 12 in the denominator
of 5/3, we multiply top and bottom of 5/3 by 4 to get 20/12.
So 20/12 is an equivalent fraction.