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almond37 [142]
3 years ago
11

Is the line through points P(0, 1) and Q(5, 0) parallel to the line through points R(–4, 3) and S(–5, 4)? Explain.

Mathematics
1 answer:
ale4655 [162]3 years ago
8 0

Answer:

No

Step-by-step explanation:

Let's find the slope of both lines and then compare these slopes:

From (-4,3) to (-5,4) entails a decrease of -1 in x and an increase of 1 in y.  Thus, the slope is m = rise / run = 1/(-1) = -1.

From (0,1) to (5,0) entails an increase of 5 in x and a decrease of 1 in y.  The slope here is m = rise / run = -1/5.

For these lines to be parallel, their slopes must be the same.  That is not the case here, so NO, the lines are not parallel.



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Solve for x and y:<br> 3/x -1/y =13/10<br> 1/x + 2/y =9/10
harkovskaia [24]

Answer:

  (x, y) = (2, 5)

Step-by-step explanation:

I find it easier to solve equations like this by solving for x' = 1/x and y' = 1/y. The equations then become ...

  3x' -y' = 13/10

  x' +2y' = 9/10

Adding twice the first equation to the second, we get ...

  2(3x' -y') +(x' +2y') = 2(13/10) +(9/10)

  7x' = 35/10 . . . . . . simplify

  x' = 5/10 = 1/2 . . . . divide by 7

Using the first equation to find y', we have ...

  y' = 3x' -13/10 = 3(5/10) -13/10 = 2/10 = 1/5

So, the solution is ...

  x = 1/x' = 1/(1/2) = 2

  y = 1/y' = 1/(1/5) = 5

  (x, y) = (2, 5)

_____

The attached graph shows the original equations. There are two points of intersection of the curves, one at (0, 0). Of course, both equations are undefined at that point, so each graph will have a "hole" there.

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3 years ago
Find the midpoint (8, -6) (6,5)​
andrey2020 [161]
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If f(x)=3|x-2|, what is f(5.9)? a: 9 b: 10 c: 11 d: 12
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To find this, you first have to determine the number of miles she drives. You can find this by multiplying the speed by the travel time.

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Now that he have the amount of miles she drives, we can find the amount of gas she spends. In order to do that we'll divide the distance by the rate.

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