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Triss [41]
3 years ago
11

Stacy rowed across the lake with her friend Rainey (in the same boat) at a rate of 3 mph. Rainey then rowed back at a rate of 2

mph. If the lake is 6 miles across, how long did it take them to complete their trip?
Mathematics
2 answers:
Pie3 years ago
6 0
Velocity in the direction of crossing the river = 3mph
Velocity in the backward direction = 2mph

Net velocity in forward direction = (3-2)= 1mph

Distance = 6 miles

t = ?

Velocity = Displacement/Time
1 = 6/t
t = 1/6 hr
t = (1/6)×60 min

time = 10 minutes
Hope this helps you!
Debora [2.8K]3 years ago
4 0
Multiply then divide
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3 years ago
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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
Sorry for tabs!! I need help in this. Please help me.
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Answer: 11 more i think

Step-by-step explanation:

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Is the absolute value of -8.3, 8.3?
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Answer:

Step-by-step explanation:

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Polygons ABCD and A'B'C'D' are shown on the following coordinate grid:A coordinate grid is shown from positive 6 to negative 6 o
Blababa [14]
<span>A(2, -2), B(4, -2), C(1, -3), D(5, -3).

A'(1, 2), B'(1, 4), C'(2, 1), D'(2, 5)

That looks like a rotation 90 degrees around the origin then a translation.  

Let's do the rotation ABCD->A"B"C"D"

The rotation is (x,y)->(-y,x)

</span>A"(2, 2), B"(2,4), C"(3,1), D"(3,5).

Compare to
 
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we need to translate one unit to the left.

Answer: 90 degree rotation around the origin then translation by (-1,0)

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2 years ago
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