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Sedaia [141]
3 years ago
9

What is three fifths times 2 and five sixths

Mathematics
1 answer:
MrRissso [65]3 years ago
8 0
Three fifths times 2 and five sixths is 1.7
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Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD.
galben [10]

Answer:

∠EFD ≅ ∠EGD ⇒ A

Arc ED ≅ arc FD ⇒ C

m arc FD = 120° ⇒ E

Step-by-step explanation:

Let us revise some facts

  1. Equal chords subtended equal arcs
  2. The measure of an inscribed angle is one-half the measure of the central angle which subtended by the same arc
  3. The measure of a central angle is equal to the measure of its subtended arc
  4. If one angle of an isosceles triangle measure 60° then the triangle is equilateral
  5. The sum of the measures of the interior angles of any quadrilateral is 360°

In the quadrilateral  CDGE

∵ m∠G = 60°

∵ m∠GDC = m∠GEC = 90°

- By using the 5th rule above

∴ m∠G + m∠GDC + m∠DCE + m∠GEC = 360°

∴ 60 + 90 + m∠DCE + 90 = 360

∴ 240 + m∠DCE = 360

- Subtract 240 from both sides

∵ m∠DCE = 120°

In circle C

∵ ∠DCE is a central angle subtended by arc DE

∵ ∠DFE is an inscribed angle subtended by arc DE

- By using the 2nd rule above

∴ m∠DFE = \frac{1}{2} m∠∠DCE

∵ m∠DCE = 120°

∴ m∠DFE = \frac{1}{2} (120)

∴ m∠DFE = 60°

- That means ∠EFD ≅ ∠EGD because their measure is 60°

∴ ∠EFD ≅ ∠EGD

In Δ EFD

∵ EF = FD

∵ m∠DFE = 60°

- By using the 4th rule above

∴ Δ EFD is an equilateral triangle

∴ ED = FD = FE

In circle C

∵ Side ED subtended by arc ED

∵ Side FD subtended by FD

∵ Side ED ≅ side FD ⇒ proved

- By using the 1st rule above

∴ Arc ED ≅ arc FD

∵ m∠ECD = 120°

∵ ∠ECD is a central angle subtended by arc ED

- By using the 3rd rule above

∴ m∠ECD = m arc ED

∴ m of arc ED = 120°

∵ Arc ED ≅ arc FD

∴ m arc ED = m arc FD

∴ m arc FD = 120°

5 0
3 years ago
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How is a debit card like a check?
madam [21]
Erm I would say it comes from the same money pot (account) but not 100% sure what your tryin to ask
5 0
3 years ago
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<img src="https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B1%7D%20%3D2x%2B2" id="TexFormula1" title="\sqrt[3]{x+1} =2x+2" alt="\sqrt
Lina20 [59]
The answer is down below

4 0
2 years ago
Write your answer as a whole number or a decimal
Lynna [10]

Answer:

minutes/mile

minutes=7.5-2.5

=55

55/10

5.5 minutes per mile

5 0
2 years ago
If E = [9, -6], what is the length of E.
Marrrta [24]

Answer:

16

Step-by-step explanation:

Interval E contains (9,8,7,6,5,4,3,2,1,0,-1,-2,-3,-4,-5,-6)

so the numbers of the interval equals 16

3 0
3 years ago
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