Answer:
The correct option is
The origin is included in the shaded region and the shaded area is below the line.
Step-by-step explanation:
Y>3/2x + 2
Put x=0
Y= 2
(0,2)
Put y=0
X= -4/3
(-4/3,0)
See attached picture for the sketch
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Answer:
7 of the angles measure 144 degrees each and one angle measures 72 degrees
Step-by-step explanation:
Let
x -----> represent the measures of the seven same-size angles,
x/2 ----> represent the measure of the one that is "two times smaller."
we know that
The sum of internal angles of a polygon can be calculated as:
where
n is the number of sides of the polygon
In this case
n=8 (octagon)
substitute
so
The linear equation that represent this problem is
solve for x
so
therefore
7 of the angles measure 144 degrees each and one angle measures 72 degrees
According to given conditions, m+n is equal to 409.
Consider the diagram below.
In the hexagon ABCDEF, let
AB = BC = CD = 3;
DE = EF = FA = 5;
Arc BAF is equal to one-third of the circle's circumference.
Hence, ∠BCF = ∠BEF = 60°;
Similarly, ∠CBE = ∠CFE = 60°;
Let the point of intersection of BE and CF be P, BE and AD be Q and CF and AD be R.
∴ Δ EFP and Δ BCP are equilateral, and so Δ PQR is also equilateral.
Also, ∠ BAD and ∠ BED subtend the same arc and so do ∠ ABE and ∠ ADE.
∴ Δ ABQ is similar to Δ EDQ
Also,
and
On solving these simultaneous equations, we get AD = 360/49
∴ m + n = 409.
To learn more about similarity of triangles, refer to this link:
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