Why is the product of negative reciprocals always -1?

Answers

Answer 1

Answer:

please check the explanation.

Step-by-step explanation:

Let suppose we have a number = n  

n≠0    

The negative reciprocal of 'n' = -1/n

Taking the product of 'n' and its negative reciprocal '-1/n':

[tex]n\left(-\frac{1}{n}\right)[/tex]

remove parentheses: (-a) = -a

[tex]=-n\frac{1}{n}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}[/tex]

[tex]=-\frac{1\times \:n}{n}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:n[/tex]

[tex]=-1[/tex]

Canceling the common factor (the number itself) will bring -1.

It proves that the multiplication of any number and its negative reciprocal will always yield -1.


Related Questions

a car travels 55 miles per hour for 2 hours how far does the car travel in 1/2 of a hour 1 1/2 hour

Answers

Answer:

Suppose you travel a distance of 100 miles, and it takes 1 1/2 hours to do it. Your average speed is then 100 miles divided by 1.5 hours which equals 66.67 miles per hour.

Step-by-step explanation:

Answer:

for a half an hour the car travels 13.75 miles

Step-by-step explanation:

please help me with this question ​

Answers

9514 1404 393

Answer:

  D

Step-by-step explanation:

The leading term is of odd degree and negative coefficient. The odd degree tells you the end behaviors will have opposite signs. The negative coefficient tells you the left end behavior will be positive, and the right end behavior will be negative.

  [tex]\textbf{D. }\lim\limits_{x\to -\infty}f(x)=\infty\quad\lim\limits_{x\to \infty}f(x)=-\infty[/tex]

About % of the area under the curve of the standard normal distribution is outside the interval z = [ − 0.12 , 0.12 ] (or beyond 0.12 standard deviations of the mean).

Answers

Answer:

10? I did not learn this yet

Step-by-step explanation:

A company charges an initial fee plus an hourly rate to rent scooters. This table
shows the total cost to rent a scooter for different amounts of time.
Hours
Total Cost
3=$25
5=$35
7=$45
What is the hourly rate (in dollars) that the company charges to rent a scooter?

Answers

Answer:10

Step-by-step explanation: it adds 10 every 2 hours

The hourly rate is $5 per hour that the company charges to rent a scooter.

What is rate?

Rate is a measurement to determine the change in one quantity with respect to another quantity.

Given that,

Company charges initial fees, and hourly rate to rent scooter,

Also given,

Cost of scooter for 3 hours = $25,

Cost of scooter for 5 hours = $35,

And cost of scooter for 7 hours = $45

From the given information,

The cost of scooter for 2 hours = $10

Cost of scooter for 1 hour  = $5

Hourly rate of scooter that company charges to rent a scooter is $5.

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2500 cm are equal to how many meters

Answers

Answer:

25

Step-by-step explanation:

divide the length value by 100.

need help. pls help. i suck at math. math is a no no for me. help me pls.​

Answers

Answer:

A5#A

Step-by-step explanation:

The Magic Carpet charges $90 for installation and $9 per square yard of carpeting. If the total cost to carpet an office is $810, how many square feet is the office?

Answers

Answer:

11.11 square yard

Step-by-step explanation:

Step one:

given data

charges=$90

installation=$9 per square yard

total cost of installation= $810

let x represents the number of square feet

Step two:

The expression for the installation cost is given as

810=9x+90------------1

solve for x, collect like terms

810-90=9x

720=9x

divide both sides by 9 we have

x=720/9

x=11.11 square yard

Solve the equation below for : y.6x – 3y = 36

A. y = 2x – 12
B. y = 12 - 2x
C.y = 1/2 x + 6
D. y= 6 - 2x

Answers

Hi there! :)

[tex]\large\boxed{A. \text{ } y = 2x - 12}[/tex]

6x - 3y = 36

Solve for y:

begin isolating by subtracting both sides by 6x:

6x - 6x - 3y = 36 - 6x

-3y = 36 - 6x

Divide both sides by -3 to solve for y:

(-3y) / (-3) = (36 - 6x)/ (-3)

y = -12 + 2x

Rearrange:

y = 2x - 12, or choice A.

Is the equation y=2x-2 is proportional or non-proportional?​

Answers

Answer:

i believe their proportional

Step-by-step explanation:

cause they have a linear function

The diagram shows two straight lines.
Not drawn accurately
136°
Х
Work out the value of x.

Answers

Answer:

x = 136º

Step-by-step explanation:

This is true because of the vertical angles rule. With vertical angles, they always equal each other.

There is a elephant shaped weather vane at the top of a corn dryer tower that is 45 m high. If the weather vane weighs 190 N, wjat is the potential energy that the wether vane has?

Answers

Solution :

Given :

Height of the tower , h = 45 m

Weight of the weather vane, mg = 190 N

So the potential energy possessed by the weather vane is given by

E = m x g x h

where, E is potential energy

           m is mass

           g is acceleration due to gravity (taken as 10 m/s2)

           h is height

Therefore,

E = m x g x h

E = (mg) x h

E = 190 x 45

E = 8550 J

Two students are pulling an object with ropes. One student pulls with a force of 40 pounds at an angle of 30° above the ground, and the other student pulls with a force of 35 pounds at an angle 45° above the ground. What is the direction of the resultant force?

approximately 37.33° above the ground
approximately 42.27° above the ground
approximately 47.73° above the ground
approximately 53.13° above the ground

Answers

Answer: A. approximately 37.33° above the ground

Step-by-step explanation:

edge2020

The the direction of the resultant force is A. approximately 37.33° above the ground.

What's a resultant force?

A resultant force simply means the single force that has same effect as two or more forces that are acting together.

In this case, a student pulls with a force of 40 pounds at an angle of 30° above the ground, and the other student pulls with a force of 35 pounds at an angle 45° above the ground.

The direction of the resultant force is 37.33° above the ground.

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The figures are similar find x for both

Answers

First one is x=10 and second one is x=9

PLEASE HELP I WILL BRAINLIEST, MY GPA RELIES ON THIS!! IM BEGGING HERE


1. The base of the prism is a trapezoid whose bases are 24 cm and 10 cm, and the shorter ones are 13 cm and 15 cm. Calculate the area and volume of the prism if its height is equal to the height of the trapezoid?​

Answers

Step-by-step explanation:

it's so much work, here's the first half untill i do the rest

i added the rest, i hope i helped somehow good luck!! :)

If x = 0 and y < 0, where is the point (x, y) located?

Answers

It’s 0 hope this helps(:

Need help with these types of questions

Answers

Answer:

i think it should be B...

Answer:

I’m brainly tester and this is a testing answer

Step-by-step explanation:

Test test tedt

Is this statement true or false? *
If an odd number is less
than 15, then it is prime.

Answers

Answer: That is false

Step-by-step explanation: 9 is odd but not prime

The statement "If an odd number is less than 15, then it is prime" is false because the number 9 is not prime.

What is the number?

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

If an odd number is less than 15, then it is prime.

As we know,

The prime number is the number that has factors only 1 and itself the number.

The odd number is less than 15.

The odd number is less than 15 = {13, 11, 9, 7, 5, 3}

The statement "If an odd number is less than 15, then it is prime" is false

Because the number 9 is not prime.

Thus, the statement "If an odd number is less than 15, then it is prime" is false because the number 9 is not prime.

Learn more about the number here:

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solve x-15% of x= Rs.170​

Answers

[tex]170 - ( \frac{15}{100} \times 170)[/tex]

Please answer this question correctly for me, I'm doing 30 points for all my questions.

Answers

Answer:

B

Step-by-step explanation:

5) Mary drives 33 miles in 3/5 of an hour. After 6 hours of traveling, 1 point

how far will she drive? (Hint: Not just 1 hour, but 6 HOURS!) Don't

forget to include appropriate units with your answer, no

abbreviations please. *

Answers

Answer:

330 miles

Step-by-step explanation:

speed of marry  = distance traveled /time taken

=33/3/5 = 55 miles/hr

therefore distance travelled by marry in 6 hours = 55*6 = 330 miles.

Linda made $24 for making 8 baskets . If she made 12, baskets, how much money would she make? Use a model to explain your answer. Upload your model below.

Answers

it’s 36 dollars ....

What is the answer? Or how can I solve this.

Answers

Answer:

61.5 degrees

Step-by-step explanation:

A triangle has to add up to 180 degrees total

PLEASE MARK BRAINLIEST
Answer: 61.5

Explanation: A triangle adds to 180 degrees. All you need to do is subtract 57 from 180 and you should get 123. 123 divided by 2 is 61.5. Now, you should know that it’s 61.5 for for the other two angles because the little line that goes through the triangle on each side indicates that those two sides are congruent. If you want to check just add 61.5 + 61.5 + 57 and you should get 180. Hope this helps. :)

10x=6x-24

help!!!! me pleasee!!​

Answers

Answer:

x = -6

Step-by-step explanation:

10x = 6x - 24

Subtract 6x from both sides.

4x = -24

Divide both sides by 4.

x = -6

Solve for c.

a (b – c) = d


a) c= d - ab/a

b) c= ab – d/b

c) c= ab – d/a

d) c= ab + d/а

Answers

The answer is c) c=ab-d/a

Answer:

C) c=ab-d/a

Step-by-step explanation:

just took the test

I NEED HELP ON THIS

Answers

Answer:

L'(-1,1)  M'(1,2)  N(1,-1)

Step-by-step explanation:

Now you just need to plot the 3 points and link them with lines and you will find the new triangle.

Your host has the following configuration:

IP Address 192.168.44.65

Subnet Mask 255.255.255.224

Which of these addresses are on your same subnet? (Select all that apply)

192.168.44.76

192.168.44.96

192.168.44.56

192.168.44.86

Answers

Answer:

yes

Step-by-step explanation:

yes yes

yesyesyeay yes

This graph shows a proportional relationship between time (m) and water used
(g). Find the constant of proportionality and use it to write an equation in the
form g=rm, wherer is the constant of proportionality. *
Water Use
50
40
30
Water used (gal)
20
10
o
2 4 6 8 10
Time (min)

Hurry pls and, thank you :)

Answers

Answer:

Use dezmos

Step-by-step explanation:

Sarah started 3 miles below the rim of the canyon and hiked until she was 8 miles above the rim. Her brother Sam said she hiked 5 miles. Sarah said she hiked 11 miles.
Who is correct and why?
A. Sam is correct because |3 – 8| = 5.
B. Sam is correct because |–3 – 8| = 5.
C. Sarah is correct because |–3 + 8| = 11.
D. Sarah is correct because |–3 – 8| = 11.

Answers

Answer:

D

Step-by-step explanation:

We can assume that the rim of the canyon is 0. Sarah started 3 miles below, so -3, BUT distance can never be negative, so it's considered 3 miles. Then, she went 8 miles above zero. So the 3 miles she went before reaching the rim plus the 8 miles she went after reaching the rim equals 11 miles.

So now we know that Sarah is right, but how do we know which equation is correct? Well, if we look at option C:

[tex]|-3+8|=11[/tex]

When solving absolute value, we solve everything within the absolute value before applying the absolute value. This means that we add -3+8 first, which equals 5, and then apply absolute value, which still equals 5. This equation is not correct.

I hope this helps!

Answer:

The answer is D

Step-by-step explanation:

I took the quiz.

If Josiah’s speed, in miles per minute, is constant, what is the constant of proportionality?

Answers

Answer:

the constant of proportionality is 1 mile

Step-by-step explanation:

if you can explain it best, and answer them you'll get a brainliest

Answers

Answer:

11. -3 - (-8) = 5

12. -10 + (-25) = -35

13. -11 - (-10) = -1

14. 12 + (-5) = 7

15. -9 (9 + (-9) = 0)

Step-by-step explanation:

I don't really know how to explain it. For 11 I just found found the difference kind of. It's easier if you draw out a number line. 12 is self - explanatory, you just add the two negative numbers and it will be a negative. I look at 14 as just another minus equation.

Answer:

11. 5

12. -35

13. -1

14. 7

15. -9

Step-by-step explanation:

11. -3-(-8)

= -3 + 8 (double negative is positive)

= 8-3

= 5

12. -10 + (-25)

= -10 -25 (positive negative is negative)

= -35

13. -11 - (-10)

= -11 + 10

= -1

14. 12 + (-5)

= 12 - 5

= 7

15. 9 + x = 0

x = 0 - 9

x = -9

PLS GIVE BRAINLIEST

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