<u>Let's consider the facts at hand</u>:
- By Vertical Angle Theorem ⇒ ∠BCE = ∠DCF
- ∠BEC = ∠DFC
- Sides BE = DF
<u>Based on the diagram, triangles BCE and triangles DCF are similar</u>
⇒ based on the Angle-Angle theorem
⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC
⇒ the two triangles are similar
Hope that helps!
<em>Definitions of Theorem I used:</em>
- <u><em>Vertical Angle Theorem: </em></u><em>opposite angles of two intersecting lines must be equal</em>
- <u><em>Angle-Angle Theorem:</em></u><em> if two angles of both triangles are equal, then the given triangles must be similar</em>
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The answer is B) 1/4.
There are 2 outcomes in his tree that have all coins with the same side up: HHH and TTT. There are 8 total outcomes. This makes the probability 2/8 = 1/4.
<span>2 ln 8 + 3 ln y simplifies to ln 8^2 + ln y^3, which in turn simplifies to
ln 64/y^3, or ln {64*y^3}</span>
Hello! So the formula for compound interest is P(1 + r)^t, where r = rate, P = principal, and t = time (years). C is out, because you multiply the rate and principal together to get the price, not add. You raise the decimal to a certain power, based on the amount of years. You add 1 to the rate. 5% in decimal form is 0.05 and you must add 1 to the amount, which eliminated B. The only answer that works is A, because it shows the correct formula. The answer is A.
Assume that pi is approx. 3.14. Then 86.92 = approx. 27 2/3 times pi, or
86.92 is approx. equal to 83pi/3.
