Answer:
22
Step-by-step explanation:
n² - m =
-5² - 3 =
25 - 3 = 22
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-Chetan K
If these are terms of a geometric sequence, they have a common ratio. That is, ...
... (k -1)/(2(1 -k)) = (k +8)/(k -1)
... (k -1)² = 2(1 -k)(k +8) . . . . . multiply by the product of the denominators.
... k² -2k +1 = -2k² -14k +16 . . . eliminate parentheses
... 3k² +12k -15 = 0 . . . . . . . . put in standard form (subtract the right side)
... 3(k +5)(k -1) = 0 . . . . . . . . . factor
Possible values of k are ... -5, +1. The solution k=1 is extraneous, as it makes the first two terms 0 and the third term 8. (It doesn't work.)
The value of k is -5.
_____
The three terms are 12, -6, 3. The common ratio is -1/2.
Answer:
Since their corresponding angles are congruent and the corresponding sides are in proportion
Step-by-step explanation:
For ABD,
Sin (B) = (AD ÷ AB) =1
∴ AD = AB
and if AD = AB
⇒ AD = AC (since AD 1 CB).
From triangle ACD,
Sin(C) = (AD ÷ AC)
Since AD = AC , Hence Sin (B) = Sin (C) = 1
Also From definition of similar triangles ABD and ACD are Similar (i.e their corresponding angles are congruent and the corresponding sides are in proportion)
Answer:
∠QTR = 44°
Step-by-step explanation:
Given ∠PTQ = ∠RTS = 35°, then
∠PTQ + ∠QTR + ∠RTS = ∠PTS ← substitute values
35 + ∠QTR + 35 = 114, that is
70 + ∠QTR = 114 ( subtract 70 from both sides )
∠QTR = 44°
