Two angles are said to be complementary, if the sum of the measures of the to angles is equal to 90 degrees.
Thus, given that HFG is complementary to ACB, them mHFG + mACB = 90 degrees.
From the figure, given that the line from point F meats line CE at point P, then HFG = CFP.
But mCFE = 90 degrees and mCFE = mCFP + mPFE
Also PFE = DFH
Thus, mCFE = mCFP + mPFE = mHFG + mDFH = 90 degrees
Recall that mHFG + mACB = 90 degrees
Thus, mHFG + mACB = mHFG + mDFH
Therefore, mACB = mDFH.
Answer:
6561 / 128
Step-by-step explanation:
The nth term of a geometric sequence is:
a = a₁ (r)ⁿ⁻¹
The first term is 3, and the fourth term is 81/8.
81/8 = 3 (r)⁴⁻¹
27/8 = r³
r = 3/2
The eighth term is therefore:
a = 3 (3/2)⁸⁻¹
a = 6561 / 128
<h2>
Answer:</h2>
There are 1757600 possibilities.
<h2>
Step-by-step explanation:</h2>
In a certain state, fishing licenses are in the form of LLL NN
L stands for a letter of the alphabet (a to z)
N stands for a one-digit number from 0 to 9.
Now, for the series LLL, 3 alphabets are placed that can be any from a to z. This means at each place, 26 letters can be placed.
Similarly, for NN, 2 numbers are placed that can be any, between 0 and 9. At each place 0 to 9 can be placed.
Hence, the total possible outcomes will be :
=1757600
Therefore the answer is 1757600 possibilities.