<h3>
Answer: 80 degrees</h3>
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Explanation:
I'm assuming that segments AD and CD are tangents to the circle.
We'll need to add a point E at the center of the circle. Inscribed angle ABC subtends the minor arc AC, and this minor arc has the central angle AEC.
By the inscribed angle theorem, inscribed angle ABC = 50 doubles to 2*50 = 100 which is the measure of arc AC and also central angle AEC.
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Focus on quadrilateral DAEC. In other words, ignore point B and any segments connected to this point.
Since AD and CD are tangents, this makes the radii EA and EC to be perpendicular to the tangent segments. So angles A and C are 90 degrees each for quadrilateral DAEC.
We just found angle AEC = 100 at the conclusion of the last section. So this is angle E of quadrilateral DAEC.
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Here's what we have so far for quadrilateral DAEC
- angle A = 90
- angle E = 100
- angle C = 90
- angle D = unknown
Now we'll use the idea that all four angles of any quadrilateral always add to 360 degrees
A+E+C+D = 360
90+100+90+D = 360
D+280 = 360
D = 360-280
D = 80
Or a shortcut you can take is to realize that angles E and D are supplementary
E+D = 180
100+D = 180
D = 180-100
D = 80
This only works if AD and CD are tangents.
Side note: you can use the hypotenuse leg (HL) theorem to prove that triangle EAD is congruent to triangle ECD; consequently it means that AD = CD.
Answer: -5.6
Step-by-step explanation:
Simplifying
(4x + -28) = 9x
Reorder the terms:
(-28 + 4x) = 9x
Remove parenthesis around (-28 + 4x)
-28 + 4x = 9x
Solving
-28 + 4x = 9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9x' to each side of the equation.
-28 + 4x + -9x = 9x + -9x
Combine like terms: 4x + -9x = -5x
-28 + -5x = 9x + -9x
Combine like terms: 9x + -9x = 0
-28 + -5x = 0
Add '28' to each side of the equation.
-28 + 28 + -5x = 0 + 28
Combine like terms: -28 + 28 = 0
0 + -5x = 0 + 28
-5x = 0 + 28
Combine like terms: 0 + 28 = 28
-5x = 28
Divide each side by '-5'.
x = -5.6
Simplifying
x = -5.6
Answer:
T(3) = 13
Step-by-step explanation:
If we are trying to find the 3rd term of this <em>specific </em>sequence, then we simply plug in 3 as n.
T(3) = (3)² + 4
T(3) = 9 + 4
T(3) = 13
However, this isn't proper notation for an arithmetic or geometric sequence.
Answer:
(0,-3)
(3,0)
Step-by-step explanation:
The solutions to the system of equations are where the two graphs cross
The first is at x=0 and y=-3
The second is at x=3 and y=0
Answer:
It should be 324.
Step-by-step explanation: