Determine whether lines bt and mv are parallel, perpendicular, or neither. you must show all of your work to earn full credit. b(1,-4), t(5,12), m(-8,3), v(-4,2)

BT ⊥ MV

The direction vector BT is ...

... T - B = (5, 12) - (1, -4) = (4, 16)

The direction vector MV is ...

... V - M = (-4, 2) - (-8, 3) = (4, -1)

One is not a multiple of the other, so the lines are not parallel.

The dot-product of these direction vectors is

... (4, 16)•(4, -1) = 4·4 + 16·(-1) = 0

When the dot-product is zero, the vectors are perpendicular.

the lines are perpendicular

to determine which case is true we require the slope m of the lines

Parallel lines have equal slopes

Perpendicular slopes are the negative inverse of each other

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = B(1, - 4 ) and (x₂, y₂ ) = T(5, 12 )

= = = 4

repeat with

(x₁, y₁ ) = M(-8, 3 ) and (x₂, y₂ ) = V(-4, 2 )

= = -

4 and - are negative inverses, hence

BT and MV are perpendicular to each other

answer:

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

−−−−−−  

so technically the answer is  

→

$

72.6

(

1

+

20

100

)

=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

87.12

(

1

+

8

100

)

=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

20% tip  

20

100

×

$

72.60

=

$

14.52

−−−−−−  

←

add

$

87.12

tax  

8

100

×

$

87.12

=

$

6.97

−−−−−  

←

add

$

94.09

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