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gogolik [260]
3 years ago
7

Given lines appearing parallel are parallel, ∠7=30°, and ∠10=80°, find the measure of the following angles.

Mathematics
1 answer:
elixir [45]3 years ago
8 0

<7 = 30

<7 = <5  vertical angles

<5 = <3 alternate interior angles

<3 + <2 = 180 straight line

30 + <2 = 180

<2 = 180 -30

<2 = 150


<10 = <12  vertical angles

<11 + <12 = 180

<11 + 80 = 180

<11 = 100

<7+<13+<12 = 180   it forms a triangle

30 + <13 + 80 = 180

110 +< 13 = 180

< 13 = 180-110

< 13 = 70



<13 = <15  vertical angles

< 15 = <17 alternate interior angles

< 17 = <19 vertical angles

< 19 = 70


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If the height of a 60 inch  T.V. is 32 inches, what is the width.

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3 years ago
What is 4log1/2^w(2log1/2^u-3log1/2^v written as a single logarithm?
IrinaK [193]
Given:

4log1/2^w (2log1/2^u-3log1/2^v)

Req'd:

Single logarithm = ?

Sol'n:

First remove the parenthesis,

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Simplify each term,

Simplify the 4 log 1/2 (w) by moving the constant 4 inside the logarithm;
Simplify the 2 log 1/2 (u) by moving the constant 2 inside the logarithm;
Simplify the -3 log 1/2 (v) by moving the constant -3 inside the logarithm:

 log 1/2 (w^4)  + 2 log 1/2 (u) - 3 log 1/2 (v) 
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We have to use the product property of logarithms which is log of b (x) + log of b (y) = log of b (xy):

Thus,

Log of 1/2 (w^4 u^2) - log of 1/2 (v^3) 

then use the quotient property of logarithms which is log of b (x)  - log of b (y) = log of b (x/y)

Therefore, 

log of 1/2 (w^4 u^2 / v^3)

and for the final step and answer, reorder or rearrange w^4 and u^2:

log of 1/2 (u^2 w^4 / v^3)  
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