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nirvana33 [79]
3 years ago
7

On a coordinate plane, line K L goes through (negative 6, 8) and (6, 0). Point M is at (negative 4, negative 2). Which point cou

ld be on the line that is parallel to line KL and passes through point M? (–10, 0) (–6, 2) (0, –6) (8, –10)
Mathematics
2 answers:
erica [24]3 years ago
8 0

Answer:

The point that lies on the line parallel to line KL would be ( 8, - 10 )

Step-by-step explanation:

Line KL passes through the points ( - 6, 8 ) and ( 6, 0 ) while it's respective parallel line passes through point M, ( - 4, - 2 ).

Our approach here is to first determine the slope of KL such that the slope of it's parallel line will be the same, and hence we can determine a second point on this line.

Slope of KL : ( y₂ - y₁ ) / ( x₂ - x₁ ),

( 0 - 8 ) / ( 6 - ( - 6 ) ) = - 8 / 6 + 6 = - 8 / 12 = - 2 / 3

Slope of respective Parallel line : - 2 / 3,

Another point on Parallel line : ( 8, - 10 )

How can we check if this point really belongs to the parallel line? Let's take the slope given the points ( - 4, - 2 ) and ( 8, - 10 ), and check if it is - 2 / 3.

( y₂ - y₁ ) / ( x₂ - x₁ ),

( - 10 - ( - 2 ) ) / ( 8 - ( - 4 ) ) = ( - 10 + 2 ) / ( 8 + 4 ) = - 8 / 12 = - 2 / 3

And therefore we can confirm that this point belongs to line KL's parallel line, that passes through point M.

vlabodo [156]3 years ago
6 0

Answer:  ( 8, - 10 )

Step-by-step explanation:

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2 years ago
7. Jennifer is 6 years older than Sue. In 4 years, she will be twice as old as Sue was 5 years ago. Find their ages
makvit [3.9K]

Answer: Sue is 20 and Jennifer is 26

Step-by-step explanation:

Let's say that J=Jennifer's age now and S=Sue's age now.

We know that:

J=S+6

Because Jennifer is 6 years older than Sue.

We also know that when Jennifer is 4 years older (J+4), she will be twice as old as Sue was 5 years from now (S-5).

So we get the following equation from that information:

J+4=2(S-5)

So we have the two equations:

J+4=2(S-5)

J=S+6

Let's substitute J=S+6 into the first equation (note that RHS means Right Hand Sie and LHS means Left Hand Side):

(S+6)+4=2(S-5)

S+10=2S-10 [Add 6+4 on the RHS, and distribute on the LHS]

S=2S-20 [Subtract 10 from both sides]

-S=-20 [Subtract 2S from both sides]

S=20 [Divide both sides by -1]

So we know S, which is Sue's age, is 20. So Sue is no 20 years old.

Finding Jennifer's age now is simple. We know Jennifer is 6 years older than Sue, and Sue is 20, so Jennifer is 26 years old.

4 0
2 years ago
A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessi
Elza [17]

Question:

A cinema can hold 270 people at one performance 5/9 of the seats were occupied of the occupied seats 40% we occupied by concessionary ticket holders.

What is the number of seats occupied by concessionary ticket holders?.

Answer:

60 seats

Step-by-step explanation:

Given

Number of seats = 270

Occupied Seats = 5/9

Concessionary ticket holders = 40% of occupied Seats

Required

The number of seats occupied by concessionary ticket holders

First the number of occupied seat has to be calculated.

Occupied\ Seats = \frac{5}{9} * 270

Occupied\ Seats = \frac{1350}{9}

Occupied\ Seats = 150

Next is to determine the number of seats occupied by concessionary ticket holders.

Number = 40\%\ of\ occupied\ seats

Number = 40\%\ of\ 150

Convert percentage to decimal

Number = 0.4 * 150

Number = 60

<em>Hence, 60 seats were occupied by concessionary ticket holders.</em>

5 0
2 years ago
The values in the table represent a linear function. What is the common difference of the associated arithmetic sequence
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Answer: 17

21-4=17


4+17=21
21+17=38 and so on..
7 0
3 years ago
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