Assuming that we can have "non-sense" words
We could have a word with an "A" and this letter could appear in any of 4 positions......and we could choose any of the other three consonants to occupy a second positon, then any two of the consonants to occupy a third position, and the last consonant would appear in the last position by default.......so we have
4 * 3 * 2 *1 = 24 words using just the A and the other three consonants
The same result would occur if we just used the "E" and the other three consonants
If we used the "A" and the "E," we would have 24 words using any two of the other consonants......but, we could choose any 2 of the 3 remaining consonants.....so the total "words" would be 24 * (3C2) = 24 * 3 = 72
So....the total number of words would be 24 + 24 + 72 = 120 "words"
We have to get a common denominator in both equations. Let's try to make it positive and the smallest, so it would be 12. Multiplying the left side by 4 would get us (20-4c)/12 and multiplying by -3 on the right side would get us (-6c-6)/12. We can cancel out the denominators by multiply both sides by 1/12 to get 20-4c=-6c-6. Adding 6 to both sides gets us -4c+26=-6c and adding 4c to both sides gets us 26=-2c. Divide by -2 on both sides to get c = -13. Hope this helps!
1. For a triangle XYZ, we use [XYZ] to denote its area.
Let ABCD be a square with side length 1. Points E and F lie on line BC and line CD, respectively, in such a way that angle EAF=45 degrees If [CEF]=1/9, what is the value of [AEF]?
2. A triangle T is separated into two congruent triangles by a straight cut. Which of the following statements are true?
A) T must have two sides with equal length.
B) The cut must be perpendicular to one side of T.
C) T must have two interior angles with the same measure.
D) The cut must go through the midpoint of one side of T.
Type your answer as a list of letters separated by commas. For instance, if you believe that conditions A, B, and C are enough, then type "A,B,C" into the answer box. If you believe none of the options are correct, enter "none."
3. Line PS bisects angle QPR . We can ensure that triangle PQS is congruent to triangle PRS by adding just one more condition. Which of the following statements could be that condition?
C) Angle PQS=Angle PRS
D) Angle PSQ=Angle PSR
Hint: The figure is a kite bisected into two parts from P to S
Type your answer as a list of letters separated by commas. For instance, if you believe that any of the conditions A, B, or C would be enough, then type "A,B,C" into the answer box. If you believe none of the options are correct, enter "none."