All categories

3 years ago

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:

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.

You might be interested in

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.

3 0

3 years ago

Find the midpoint (8, -6) (6,5)

andrey2020 [161]

I think it’s (7, -0.5)

7 0

2 years ago

If f(x)=3|x-2|, what is f(5.9)? a: 9 b: 10 c: 11 d: 12

Mice21 [21]

$|a|= \left\{\begin{array}{ccc}a&if&a\geq0\\-a&if&a \ \textless \ 0\end{array}\right\\\\f(x)=3|x-2|\\\\f(5.9)=3|5.9-2|=3|3.9|=3\cdot3.9=11.7$

7 0

3 years ago

Read 2 more answers

When Joycelyn goes to work, she drives at an average speed of 65 miles per hour. It takes about 1 hour and 30 minutes for Joycel

insens350 [35]

Jocelyn has to spend $13.46 on gas.

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.

65 miles per hour * 1.5 hours = 97.5 miles.

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.

97.5 miles / 25 miles per gallon of gas = 3.9 gallons

Now we can determine the cost by multiplying the amount of gallons by the price.

3.9 gallons * $3.45 per gallon = $13.46

4 0

2 years ago

Breakfast at Denny's cost $8.63. You give a 15% tip. What is the total cost?

Nataliya [291]

Answer:

9.92

Step-by-step explanation:

8.63 x 1.15=9.92

3 0

3 years ago