Answer:
The answer to your question is: AC = 20
Step-by-step explanation:
Data
AB = 2x - 4
BC = 4x
AC = 2x + 12
AC = ?
AB + BC = AC
2x - 4 + 4x = 2x + 12
6x - 4 = 2x + 12
6x - 2x = 12 + 4
4x = 16
x = 16/4
x = 4
AB = 2(4) - 4 = 8 - 4 = 4
BC = 4(4) = 16
AC = 2(4) + 12 = 8 + 12 = 20
4 + 16 = 20
20 = 20
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:
14
Step-by-step explanation:
4% of 350 is 14 so he only sold 14
Answer:
G.
Step-by-step explanation:
Since the y-int is (0, 4), you know you have to have an equation that has a +4 in it. When you calculate for the slope, you should get 4/3, and so the only equation that has those 2 is G.
Answer:
17 inches
Step-by-step explanation:
The original square had sides of 4.5 (18/4)
To get a perimeter of 10, we know that two sides would already equal 9 (4.5+4.5). That means we only have 1 inch for the other two sides, so they are each 1/2 inch.
That leaves the second rectangle with a length and width of 4.5 and 4.
2(4.5) + 2(4) =
9+8=
17
