Answer:
B.
Step-by-step explanation:
How many values of x are there that are solutions to the equation |x| + 22 = 63
2 answers:
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CE ⊥ CF because m∠ECA + m∠FCA = 90°
Step-by-step explanation:
In ∆ABC
- On the extension of the side BC , draw a line segment CD ≅ CA
- Draw the segment AD
- The line segment CE is the angle bisector of ∠ACB
- The line segment CF is the median towards AD in ∆ ACD
We want to prove that CF ⊥ CE
Look to the attached figure
In Δ ABC
∵ CE is the bisector of angle ACB
∴ ∠ACE ≅ ∠BCE
In Δ ACD
∵ CA = CD
∴ Δ ACD is an isosceles triangle
∵ AD is the median towards AD
- In any isosceles triangle the median from a vertex to its opposite
side bisects this vertex
∴ AD bisects ∠ACD
∴ ∠ACF ≅ ∠DCF
∵ BCD is a straight segment
∵ CE , CA , CF are drawn from point C
∴ m∠BCE + m∠ACE + m∠ACF + m∠DCF = 180°
∵ m∠ACE ≅ m∠BCE
∵ m∠ACF ≅ m∠DCF
- Replace m∠BCE by m∠ACE and m∠DCF by m∠ACF
∴ m∠ACE + m∠ACE + m∠ACF + m∠ACF = 180°
∴ 2 m∠ACE + 2 m∠ACF = 180°
- Divide all terms by 2
∴ m∠ACE + m∠ACF = 90°
∴ EC ⊥ CF
CE ⊥ CF because m∠ECA + m∠FCA = 90°
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Answer:
1) Option B - 25.12 ft
2) Option C - 24.1 ft
Step-by-step explanation:
1) Given : The circular rug has a diameter of 8.2 feet.
To find : Which measurement is closest to the circumference of the rug in feet?
Solution :
The circumference of rug is given by
Where, d is the diameter = 8.2 feet.
The most closest measurement is 25.12 ft.
Therefore, option B is correct.
2) Given : A circle has a diameter of 5.2 feet.
To find : Which measurement is closest to the circumference of the circle in feet?
Solution :
The circumference of circle is given by
Where, d is the diameter = 5.2 feet.
The most closest measurement is 24.1 ft.
Therefore, option C is correct.