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Vera_Pavlovna [14]
2 years ago
6

X - 37 ≤ -1 13/14 solve

Mathematics
1 answer:
seropon [69]2 years ago
7 0

Answer:

405/14

Step-by-step explanation:

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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
Read 2 more answers
Can someone please help me with this proof?!
Elza [17]

Answer:

because AC and BD bis => AX = XC; BX = XD

ΔAXD ≅ ΔCXB (SAS) because: AX = CX

                                                    DX = BX

                                                    m∠AXD = m∠BXC ( 2 opposing angles)

because ΔAXD ≅ ΔCXB (SAS)

=> AD = BC and m∠DAX = m∠BCX

because m∠DAX = m∠BCX => AD//BC

ABCD has AD = BC and AD//BC => ABCD is a parallelogram

Step-by-step explanation:

4 0
3 years ago
Determine the temperature of 2.6 moles of gas contained in a 5.00-L vessel at a pressure of 1.2atm.
strojnjashka [21]

Answer:

28.108 K.

Step-by-step explanation:

Given: Pressure (P)= 1.2atm

           Number of moles (n)=  2.6 moles

           Volume (V)= 5.00-L

Now finding the temperature (T).

Formula; T= \frac{P\times V}{n\times R}

R is a constant factor which makes other factors work together.

There is a numerical value for R which we use is 0.0821 \times \frac{L.atm}{mole.K}

∴ Temperature (T)= \frac{1.2\times 5}{2.6\times 0.0821 \frac{L.atm}{mol.K} }

⇒ Temperature (T)= \frac{6}{0.21346} = 28.1083\ K

∴ Temperature is 28.108 K

8 0
3 years ago
Which expression shows 2x² + 18 factored completely
Lerok [7]

Answer:

2(x^2+9)

Step-by-step explanation:

2x^2 +18

Factor out a 2

2(x^2+9)

3 0
3 years ago
Which points are on the graph of f(x)=(1/3)^x?
frutty [35]

Answer:

(0,1)

Step-by-step explanation:

4 0
3 years ago
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