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defon
3 years ago
8

The equation of four lines are given. Identify which lines are perpendicular.

Mathematics
2 answers:
PilotLPTM [1.2K]3 years ago
7 0

Answer: A.) Lines 2 and 4 are perpendicular

Step-by-step explanation:

Two lines are said to be perpendicular if the product of their slope gives - 1 . That is , if m_{1} is the slope of the first line and  m_{2} is the slope of the second line , if the two lines are perpendicular , then :

m_{1} m_{2} = -1  , which can also be written as ;

m_{1} = -1 /  m_{2}.

The equation of line in slope intercept form is given as :

y = mx + c , where m is the slope and c is the y - intercept.

Line one : y = - 1 , comparing with the equation of line in slope intercept form , it means line one has no slope

Line two : y = -1/2x - 2 , it has a slope of - 1/2

Line 3 : x = -4 , has no slope

Line 4 : y + 3 = 2 ( x - 2 )

Writing this in slope intercept form , we will make y the subject of the formula.

y + 3 = 2x - 4

y  = 2x -4 - 3

y = 2x - 7

This means that the slope of line 4 is 2.

Comparing line two and line four to check if they are perpendicular

- 1/2 x 2 = - 1 , surely , it obeys the perpendicularity rule , this means that line 2 and 4 are perpendicular

Bumek [7]3 years ago
6 0
Lines 2 and four r perpendicular I think
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Last question please
MatroZZZ [7]

Let's try an make a formula to make things easy.

_________________________________________________

Look at Andrew's pattern, it goes up 6 every time. Lets look at the 6 times table

6 times table:           6, 12, 18, 24, ...

____________________________________

First think, how would you work out the <u>7</u>th term in the <u>6</u>th times table?

You would do <u>6</u> times <u>7</u>.

So the formula for the 6th times table is:

6n     (where n is the term you want to find out)

_______________________________________

So to get the 9th term in the 6 times table, you would replace the n with 9, like so:

9th term in 6 times table = 6 x 9 = 54

______________________________________

Now lets compare the 6 times table to Andrew's pattern:

6 times table:           6, 12, 18, 24,

Andrew's pattern:     3, 9, 15, 21,

_____________________________________

If you look, you can see that Andrew's pattern is the 6 times table minus 3!

So what would be the formula for Andrew pattern?

---> it would be:  6n - 3   (since it's the 6 times table but minus 3)

_____________________________________

We can use this formula to easily work out the 20th term in Andrew's pattern!:

20th term = 6 x 20 - 3 = 120 - 3 = <u>117</u>    (remember, replace the n with 20)

______________________________________

Now let's make a formula for Ben's pattern!

Ben's pattern goes up in 5s, so lets compare it to the 5 times table:

5 times table:       5, 10, 15, 20

Ben's pattern:       3, 8, 13, 18,

The formula for the 5 times table is 5n, and Ben's pattern is the 5 times table but minus 2.

So the formula for Ben's pattern is: 5n - 2

__________________________________

<u>Now swap out the n for 20</u>  (to get the 20th term):

20th term = 5 x 20 - 2 = 100 - 2 = <u>98</u>

_________________________________________

So Andrew's 20th term is <u>117</u>, and Ben's 20th term is <u>98</u>.

All we do now is subtract them to find the difference:

117 - 98 = <u>19</u>

- - - - - - - - - - - - - - - - - - - - - - - - -

Answer:

Ben's 20th term is smaller by 19!

- - - - - - - - - - - - - - - - - - - - - - - - - -

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3 years ago
PLEASE HELP URGENT!! What single rigid transformation maps ABC onto A'BC'?
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3 years ago
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<h2>it is (-3,-2)...........</h2>

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so the thousanth odd number is 2(1000)=2000
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