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stepladder [879]
3 years ago
9

How do you prove theorems behind two parallel lines cut by a transversal?

Mathematics
1 answer:
LenaWriter [7]3 years ago
5 0
The way to do it can be explained like this:
Say AB and CD are the two parallel lines cut by a transversal at E and F respectively.
 Then the pairs of alternate interior angles are:
Angle(AEF) and Angle(DFE)
Angle(CFE) and Angle(BEF)
Now lets prove if this is true:
<span>Angle(CFE) +Angle(DFE) = 180
(linear pair)
Also
Angle(CFE) +Angle(AEF) = 180
(Corresponding angles)
</span><span>Equate the above results:
Angle(CFE) +Angle(DFE) = Angle(CFE) +Angle(AEF)
</span><span>Angle(DFE) = Angle(AEF)
</span>Happens the same with
<span>Angle(CFE) = Angle(BEF)
</span>Hope this is very useful for you

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3 years ago
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What is y=2 plus 4?<br>​
Volgvan

Answer:

y=6

Step-by-step explanation:

all you do is add 4 and 2

5 0
3 years ago
Celinda thought of 89.5 in parts, 80 + 9 + 0.5, and divided each part: 80 ÷ 10 = 8; 9 ÷ 10 = or 0.9; 0.5 ÷ 10 = 0.05. Then she a
Arlecino [84]

Answer:

Dividing each part into 10 and then summing the results up, is equivalent to dividing 89.5 into 10.  

Step-by-step explanation:

This example refers to the Distributive Property of the division, which is valid when the dividend is decomposed.

A simple example could be: 400 ÷ 10 = (200 ÷ 10) + (200 ÷ 10)

In the exposed example we know that 89.5 = 80 + 9 + 0.5.

  • <u>Option 1</u>

(80/10) + (9/10) + (0.5/10) =

8 + 0.9 + 0.05=

8.95

  • <u>Option 2</u>

89.5/10 = 8.95

     

8 0
3 years ago
Ryan spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill. If $759 was left, what was his
musickatia [10]

Step-by-step explanation:

<h3><u>G</u><u>i</u><u>v</u><u>e</u><u>n</u><u> </u><u>Inform</u><u>ation</u><u> </u><u>:</u></h3>

  • Ryan spent 1/3 of his monthly salary for rent and 1/7 of his monthly salary for his utility bill.
  • Remaining money = $759

<h3><u>T</u><u>o</u><u> </u><u>calculate</u><u> </u><u>:</u></h3>

  • His monthly salary.

<h3><u>C</u><u>a</u><u>l</u><u>c</u><u>u</u><u>l</u><u>a</u><u>t</u><u>i</u><u>o</u><u>n</u><u> </u><u>:</u></h3>

Let us assume his monthly salary as x. According to the question,

➝ Money spent on rent + Money spent for utility bill + Remaining money = His salary

\longrightarrow\sf {\dfrac{1}{3}x + \dfrac{1}{7}x + 759 = x} \\

\longrightarrow\sf {\dfrac{7x + 3x + 15939}{21}= x} \\

\longrightarrow\sf {\dfrac{10x+ 15939}{21}= x} \\

\longrightarrow\sf {10x+ 15939= 21x} \\

\longrightarrow\sf {15939= 21x - 10x} \\

\longrightarrow\sf {15939= 11x} \\

\longrightarrow\sf {\cancel{\dfrac{15939}{11}}= x} \\

\longrightarrow\underline{\boxed{\bf {1449= x}}} \\

<u>Therefore,</u><u> </u><u>his</u><u> </u><u>monthly</u><u> </u><u>income</u><u> </u><u>is</u><u> </u><u>$</u><u>1</u><u>4</u><u>4</u><u>9</u><u>.</u>

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andrey2020 [161]
I believe, if I'm not correct but I think the answer would be 8 minutes or less.. Considering the fact that the Harris Family left 12 minutes ahead and the Arlen family is Averaging 55 MPH.. Too the speed that the Arlen's are going make the time for them to catch up to the harris's shorter. The Arlen's are going 15 mph faster sooo.. Yeah.. Tell em if this helps! :D
8 0
3 years ago
Read 2 more answers
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