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dybincka [34]
2 years ago
11

Find the volume of the prism

Mathematics
2 answers:
frozen [14]2 years ago
8 0

Answer:

96 in^3

Step-by-step explanation:

Anarel [89]2 years ago
5 0

V = 96" cubed

4*4=16

16*6=96

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42:28
gogolik [260]

Answer:

The statements about arcs and angles that are true in the figure are;

1) ∠EFD ≅ ∠EGD

2) \overline{ED}\cong \overline{FD}

3) mFD = 120°

Step-by-step explanation:

1) ∠ECD + ∠CEG + ∠CDG + ∠GDE = 360° (Sum of interior angle of a quadrilateral)

∠CEG = ∠CDG = 90° (Given)

∠GDE = 60° (Given)

∴ ∠ECD = 360° - (∠CEG + ∠CDG + ∠GDE)

∠ECD = 360° - (90° + 90° + 60°) = 120°

∠ECD = 2 × ∠EFD (Angle subtended is twice the angle subtended at the circumference)

120° = 2 × ∠EFD

∠EFD = 120°/2 = 60°

∠EFD ≅ ∠EGD

∠ECD = 120°

∠EGD = 60°

∴∠EGD ≠ ∠ECD

2) Given that arc mEF ≅ arc mFD

Therefore, ΔECF and ΔDCF are isosceles triangles having two sides (radii EC and CF in ΔECF and radii EF and CD in ΔDCF

∠ECF = mEF = mFD = ∠DCF (Given)

∴ ΔECF ≅ ΔDCF (Side Angle Side, SAS, rule of congruency)

\\ \overline{EF}\cong \overline{FD} (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)

∠FED ≅ ∠FDE (base angles of isosceles triangle)

∠FED + ∠FDE + ∠EFD = 180° (sum of interior angles of a triangle)

∠FED + ∠FDE = 180° - ∠EFD = 180° - 60° = 120°

∠FED + ∠FDE = 120° = ∠FED + ∠FED (substitution)

2 × ∠FED  = 120°

∠FED = 120°/2 = 60° = ∠FDE

∴ ∠FED = ∠FDE = ∠EFD =  60°

ΔEFD  is an equilateral triangle as all interior angles are equal

\\ \overline{EF}\cong \overline{FD}\cong \overline{ED} (definition of equilateral triangle)

\overline{ED}\cong \overline{FD}

3) Having that ∠EFD = 60° and ∠CFE = ∠CFD (CPCTC)

Where, ∠EFD = ∠CFE + ∠CFD (Angle addition)

60° = ∠CFE + ∠CFD = ∠CFE + ∠CFE (substitution)

60° = 2 × ∠CFE

∠CFE =60°/2 = 30° = ∠CFD

\overline{CF}\cong \overline{CD} (radii of the same circle)

ΔFCD is an isosceles triangle (definition)

∠CFD ≅ ∠CDF (base angles of isosceles ΔFCD)

∠CFD + ∠CDF + ∠DCF = 180°

∠DCF = 180° - (∠CFD + ∠CDF) = 180° - (30° + 30°) = 120°

mFD = ∠DCF (definition)

mFD = 120°.

5 0
3 years ago
Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef fo
olasank [31]
You can solve this by using the system of equations.
Jan - 4.95 = 2H + 3C
Wayne - 5.45 = 3H + 2C

Use elimination.
-3(2H + 3C = 4.95)
2(3H + 2C = 5.45)

Solve. And you'll get:
-6H + (-9C) = -14.85
6H + 4C = 10.9

Cross out -6H and 6H because they cancel out. And you're left with:
-9C = -14.85
4C = 10.9

Add -9C with 4C, and -14.85 with 10.9.
-5C = -3.95

Divide each side with -5.
C = $0.79

Now to figure out what H is, just substitute the C in one of the equations with 0.79.
5.45 = 3H + 2(0.79)
5.45 = 3H + 1.58
-1.58            -1.58
3.87 = 3H
3.87/3 = 3/3(H)
1.29 = H

Finished!
7 0
3 years ago
Read 2 more answers
How do I make a table for x = 2
postnew [5]
What kind of table?
Because for every the x would be 2
3 0
3 years ago
What is the volume of the sphere shown below with a radius of 3? ​
garri49 [273]

Answer: 113.1

Step-by-step explanation: v=4/3(pie)r^3=4/3•(pie)•3^3= 113.09734

3 0
3 years ago
Is this Statement true or false?
nikitadnepr [17]

Answer:

True

Step-by-step explanation:

Yes, this is True because dotted lines are not part of the solution on a graph.

Sorry! Can't be explained more than this!

3 0
3 years ago
Read 2 more answers
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