Let the second side be x
then,
first side = twice the length of the second side
= 2x
third side = 20 feet less than three times the second side
3 (second side ) - 20
= 3 (2x) -20
= 6x - 20
perimete of a triangle = sum of all sides,
substitute the values we know,
and you'll be left with this equation
106 = x + 2x + 6x - 20
106+ 20 = 9x
126 = 9x
126/9 = x
14 = x
so,
measure of second side = x = 14 feet
measure of first side = 2x = 2 (14) = 28 feet
measure of thurd side = 6x - 20 = 6 (14)-20 = 84- 20 = 64 feet.
Answer:
(P, Q) = (-75, 57)
Step-by-step explanation:
The equation will have infinitely many solutions when it is a tautology.
Subtract the right side from the equation:
Px +57 -(-75x +Q) = 0
x(P+75) +(57 -Q) = 0
This will be a tautology (0=0) when ...
P+75 = 0
P = -75
and
57-Q = 0
57 = Q
_____
These values in the original equation make it ...
-75x +57 = -75x +57 . . . . . a tautology, always true
Recall that
where 
is the angle between the vectors 
whose magnitudes are 
, respectively.
We have
Answer:
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Step-by-step explanation:
Answer:
the solutions are these
Step-by-step explanation:
