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8_murik_8 [283]
3 years ago
8

ONE, MANY, OR NO SOLUTION1. 4x + 13 = 3x + 15​

Mathematics
1 answer:
Svetllana [295]3 years ago
5 0

Answer:

one solution

Step-by-step explanation:

4x + 13 = 3x + 15

subtract 3x from both sides:

x + 13 = 15

subtract 13 from both sides:

x = 2

one solution

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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
2 years ago
Who ever answers ths is 52 minutes will get brainlyeiest
Klio2033 [76]

Answer:

-6r+6

Step-by-step explanation:

Let us expand the expression:

8-(6r+2)=

8-6r-2=

6-6r

OR

-6r+6

<em>I hope this helps! :)</em>

4 0
2 years ago
Read 2 more answers
Help on numbers 1 and 2<br> any question, 1 or 2.
geniusboy [140]
For #2 you would count how many where the red dashed line is! Which is 3! Then you would count where the blue dashed line is! Which is 4! So then it would be 4/3(4 over 3) For the slope! Hope this helps! :)
6 0
3 years ago
Name a number that has a prime factorization with three distinct factors
yanalaym [24]
210 Has 3,5,7 As Prime Factors

5 0
2 years ago
3. Multiply: 7(-12) <br><br> help
Gnoma [55]

Answer:

Your answer is -84 hope this helps

Step-by-step explanation:

brainlest?

6 0
2 years ago
Read 2 more answers
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