MATHEMATICS MIDDLE SCHOOL

The product of the slopes of perpendicular lines equals what?

Answers

Answer 1

Answer:

The product of the slopes of perpendicular lines equals -1

Solution:

Need to determine product of slope of perpendicular lines.

Product of slopes of perpendicular lines is always equal to -1.

lets verify this.

let consider following two equation of perpendicular lines

2x – y = 1

x + 2y = 2

Now evaluate slope of each line by representing them in slop intercept form that is y = mx + c

Where coefficient of x represents slope m.

Representing first line in slope intercept form we get

y = 2x – 1

On comparing above equation with slope intercept form we can say that its slope is 2.

Similarly representing x + 2y = 2 equation in slope intercept form we get

$y=-(1)/(2) x+1$

On comparing above equation with slope intercept form we can say that its slope is $(-1)/(2)$

On multiplying slopes of two perpendicular lines we get,

$2 *\left(-(1)/(2)\right)=-1$

Hence product of slope of perpendicular line is -1

Answer 2

Answer:

If two non-vertical lines are perpendicular, then their slopes are opposite reciprocals giving you -1.

:) Hope this helps.

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What is the 89,420 divided by 27

Answers

ok. 89420 / 27= 3,311.851

The answer is 3311.851851851852

Two buses leave towns 948 miles apart at the same time and travel toward each other. One bus travels 10 mi h slower than the other. If they meet in 6 hours, what is the rate of each bus?

Answers

Answer:

Use a d=rt table, find x, and plug it in for the part you need. 74 & 84

Step-by-step explanation:

Create a chart for the 2 buses that shows the distance, rate, & time. Calculate the distance by multiplying the rate and time.

x is the rate of speed of the faster bus

Bus 1: D (6x) = r (x) × t (6 hrs)

Bus 2: D (6x-60) = r (x-10) × t (6 hrs)

We also know the total distance traveled was 948 miles. So 6x-60+6x=948.

Then we combine like terms.

12x-60=948

Now isolate the x term by adding 60 to both sides.

12x=1008

Divide both sides by 12 to isolate the x.

x=84

Finally, plug the x back in to the rates to determine the rate of the buses.

Bus 1 - 84 mph

Bus 2 - 74 mph

Julie spends $ 5.62 at the store. Micah spends 5 times as much as Julie. Jeremy spends $6.72 more than Micah . How much does each person spend?

Answers

Answer:

Julie = $5.62 Micah = $28.10 Jeremy = $34.82

Step-by-step explanation:

5.62 * 5 = 28.1

28.1+6.72=34.82

easy all you have to do is times $5.62 by 5 once you get your answer that will be Micah's price then, add 6.72 then you will get you answer for each of them or

Answer:
Julie: 5.62
Micah: 21.20
Jeremy:27.92

I recommend showing the work because you don't want just the simple answer.

What is the equivalent decimal for 1\2