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Liula [17]
3 years ago
10

6 is what percent of 8

Mathematics
1 answer:
mars1129 [50]3 years ago
3 0
6/8 = 0.75
0.75 x 100 = 75%
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each batch of mrs.claus toffee makes 14 pieces of toffee if the elves need 8 dozen pieces of toffee how many batches does mrs.cl
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Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters
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Answer:

" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* <em>Look to the attached figure </em>

- There are three lines intersected at point D

- We need to find the missing in step 3

∵ Line FA intersects line EC at point D

- The angles formed when two lines cross each other are called

 vertical angles

- Vertical angles are congruent (vertical angles theorem)

∴ ∠ADC and ∠FDE are vertical angles

∵ Vertical angles are congruent

∴ ∠EDF ≅ ∠ADC

∴ m∠EDF ≅ m∠ADC

∵ m∠EDF = 120° ⇒ given

∵ m∠ADC = m∠ADB + m∠BDC

∴ m∠ADB + m∠BDC = 120°

∵ m∠ADB = (3x)° ⇒ given

∵ m∠BDC = (2x)° ⇒ given

∴ 3x + 2x = 120 ⇒ add like terms

∴ 5x = 120 ⇒ divide both sides by 5

∴ x = 24

Column (1)                                                     Column (2)

m∠EDF = 120°                                               given

m∠ADB = 3 x                                                 given

m∠BDC = 2 x                                                 given

∠EDF and ∠ADC are vertical angles           defin. of vert. ∠s

∠EDF is congruent to ∠ADC                        vertical angles are      

                                                                        congruent  

m∠ADC = m∠ADB + m∠BDC                        angle add. post.

m∠EDF = m∠ADC                                          defin. of cong.

m∠EDF = m∠ADB + m∠BDC                         substitution

120° = 3 x + 2 x                                               substitution

120 = 5 x                                                         addition

x = 24                                                              division  

∴ The missing reason is " vertical angles are congruent "

- From the explanation above ∠ADC and ∠FDE are vertical

 angles then they are congruent according to vertical angle

 theorem

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ana has the same WHOLE amount, but in BIGGER pieces because she has an amount less than 8.

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