The value of <em>x</em> where by exterior angles theorem, ∠DCO equals 2·x, 69° equals the sum of ∠DCO and x° is <em>x </em>= 23°
<h3>What is the exterior angles theorem?</h3>
The exterior angles theorem states that the exterior angle of a triangle is equal to the sum of the opposite interior angles.
The given parameters are;
Points on the circle are; ABCD
Straight lines = AOBE and DCE
Segment CO = Segment CE
∠AOD = 69°
∠CEO = x°
∠OCD = ∠ODC base angles of isosceles triangle
69° = ∠x° + ∠ODC exterior angle of a triangle
∠DOC = 180 - 2×∠ODC (Angle sum property of a triangle)
180 - 2×∠ODC + x° + 69° = 180° (Sum of angles on a straight line are supplementary)
x° + 69° - 2×∠ODC = 0
∠ODC = 2·x° (exterior angle of a triangle is equal to the sum of the opposite interior angles)
69° = x° + ∠ODC = x° + 2·x° = 3·x° (substitution property of equality)
69° = 3·x°
x = 69° ÷ 3 = 23°
Learn more about angles in a triangle here:
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Answer:
f⁻¹(x) = -(x+4) / 5
Step-by-step explanation:
Given function is :
f(x) = -5x-4
We have to find the inverse of given function.
Step 1. Put y = f(x) in given function
y = -5x-4
Step 2. Add 4 to both sides of above equation
y+4= -5x-4+4
y+4 = -5x
Step 3.Divide by -5 to both sides of above equation
y+4 / (-5) = -5x / (-5)
-(y+4) / 5 = x
Step 4 . Swap sides
x = -(y+4) / 5
Step 5. Put x = f⁻¹(y) in above equation
f⁻¹(y) = -(y+4) / 5
Step 6. replace y with x
f⁻¹(x) = -(x+4) / 5 which is the inverse of f(x) = -5x-4.
Answer:
Step-by-step explanation:
is C -1/2
y=mx+b
2y=6-x
y=-x/2 +3
m=-1/2
Compare 
to 
. Then in applying the LCT, we have
Because this limit is finite, both
and
behave the same way. The second series diverges, so
is divergent.
Answer: -9sinx + 3cosx + 4sec^2x
