Prove the following statement directly from the definitions. The difference of any two rational numbers is a rational number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r

Answers

Answer 1

Answer:

- Integers, b ≠ 0 and d ≠ 0.

- r - s = (ad - bc)/bd.

- products and differences of integers are integers.

-  zero product property

- quotient.

Step-by-step explanation:

Rational numbers are integers that can take the form of numerator divided by a denominator, that is to say in the form of 'a/b;. So, we are given from the question or problem to prove and fill in the gap the correct information or data:

For the first part of the question:

The missing data in the gap = Integers; b ≠ 0 and d ≠ 0. That is to say the denominators can not be zero or say that the denominators are non zero. This is one of the properties or let us say one of the ways of identifying a Rational number.

For the second part:

The missing data in the gap = a/b - c/d =  (ad - bc)/bd. This is the representation in  a simplified form.

For the third part:

The missing data or information = products and differences of integers are integers.

For the fourth part:

The missing data or information: zero product property, that is to say the product of the numerators is not equal to zero, or it is non zero.

For the fifth part:

The missing data or information: quotient.  r - s is a quotient of two integers.


Related Questions

Need Help. ( Look at the picture). Will Mark Brainliest. Graph the step function over the interval. And you can just write the steps out also. Working on it now but really need help please asap. ​

Answers

Answer:

x = -3

Step-by-step explanation:

f(x) = x + 3

0 = x + 3

-x = 3

x = -3

PLZ HELP !!
Max deposited $1,300 into an account that pays 4.5% interest, compounded daily. At end of six years he has a balance of ?

Answers

Answer:

The final balance is $1,692.94.

The total compound interest is $392.94.

Step-by-step explanation:

1,300 x 0.045=___ x 6

20 points & will give brainliest

Find the distance between (5,8) and (3,-1)

Answers

Answer:

root 85

decimal 9.21

slope 9/2

Step-by-step explanation:

didnt know which one you wanted fully

6. The store paid $2.50 for a book and sold it for $5.25. What is the profit as a percent?

Answers

7.75 I hope this helps

what does 3 to the -2 power equal

Answers

Answer:

[tex]\frac{1}{9}[/tex]    

Caroline is baking pies to the teachers lunch at her school she plans to give every teacher 1/8 of a pie she decides to bake 12 pies Each pie takes 26.5 minutes to bake if coraline bakes 1 pie at a time how many total minutes is it​

Answers

Multiply the number of pies by the amount of minutes it takes to bake them
12 x 26.5 = 318

Answer:

It will take her 318 minutes.

Step-by-step explanation:

26.5 times 12 equals 318

Given z1 = StartRoot 2 EndRoot (cosine (StartFraction 3 pi Over 4 EndFraction) + I sine (StartFraction 3 pi Over 4 EndFraction) ) and z 2 = (Cosine (StartFraction pi Over 2 EndFraction) + I sine (StartFraction Pi Over 2 EndFraction) ) , what is the value of z1 – z2?

cos(0) + isin(0)
cos(0) – isin(0)
cos(Pi) + isin(Pi)
cos(Pi) – isin(Pi)

Answers

Answer: C. cos(Pi) + isin(Pi)

Step-by-step explanation:

The value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).

What are complex numbers?

A complex number is an element of a number system that includes real numbers and a specific element labeled i sometimes known as the imaginary unit, and which obeys the equation i² = 1. Furthermore, every complex number can be written as a + bi, where a and b are both real values.

How to solve this problem?

We know that cos(π - x) = - cosx, sin(π - x) = sinx, cos(π/4) = 1/√2 = sin(π/4), cos(π/2) = 0, sin(π/2) = 1, cos(π) = - 1, sin(π) = 0.

Given that z₁ = √2[cos(3π/4) + isin(3π/4)] = √2[cos(π - π/4) + sin(π - π/4)] = √2[- cos(π/4) + sin(π/4)] = √2[- 1/√2 + 1/√2] = √2[0] = 0

and z₂ = cos(π/2) + isin(π/2) = 0 + i × 1 = 1

Now, z₁ - z₂ = 0 - 1 = - 1 = - 1 + i × 0 = cos(π) + isin(π)

Therefore, the value of subtraction of two given complex numbers z₁ and z₂ is cos(π) + isin(π).

Learn more about complex numbers here -

https://brainly.com/question/18643242

#SPJ2

Find three nonzero vectors a, b, and c such that a × b = a × c != 0 but b != c.

Answers

9514 1404 393

Answer:

  a = {1, 2, 3}, b = (2, 4, 7}, c = (-3/14, -3/7, 5/14}

Step-by-step explanation:

For the above vectors, ...

  a × b = a × c = (2, -1, 0)

__

Here, c is found to be a scaled version of (a×(a×b)).

Question 5
Here are four cards.
4 5 0.
Use each card once to make the largest number that is less than 10
Here are four cards.
4 5 0 .
Use each card once to make the largest number that is less than 10​

Answers

Answer:

9 by adding all the three cards

can i plz plz get some help with this

Answers

Answer: -2/6 or -1/3

g Statesville population in 2010 was about 24,700, and was growing by about 1% each year. If this continues, what will Statesville population be in 2018? [Round to the nearest person.]

Answers

Answer:

26,676population

Step-by-step explanation:

Population in 2010 = 24,700

If it grows yearly by 1%, increment per year is expressed as:

1% of 24,700

= 1/100×24700

= 247 populations

After 8years, population increase will be 247×8 = 1976 population

Statesville population in 2018 will be expressed as;

Population in 2010+increase after 8years

= 24700+1976

= 26,676 population

Hence statesville population in 2018 will be 26,676population

What is 3/4 ÷ 1/2 ?​

Answers

Answer: 3/4 divided by 1/2 is 1.5

Pure acid is to be added to a 10% acid solution to obtain 99L of a 20% acid solution. which amounts of each should be used ?

Answers

Answer:

x = amount of 100% acid solution (pure acid, no water)

y = amount of 10% acid solution (acid + water)

both amounts are in liters

Step-by-step explanation:

14/18 in decimal form

Answers

24/18 in decimal form is 0.778

Answer:

.77

Step-by-step explanation:

the 7 is repeating so you can put a dash above the second 7

A serving of rice is 2/5 of a cup. How many servings are there in a 1 3/5-cup bag of rice?

Answers

3 i think i’m not sure tho if u add 2/5 until u get 1 3/5 that might help

7 – 0.2n = -0.8n + 10
What value of n makes this equation true?
Please helpp

Answers

The answer to the equation is [tex]n=5[/tex]

First, you must add 0.8n on both sides.

[tex]0.6n+7=10[/tex]

Then, subtract 7 from both sides.

[tex]0.6n=3[/tex]

Finally, divide both sides by 0.6

[tex]n=5[/tex]

How do you find what p is?

Answers

Answer:

p > -3

Step-by-step explanation:

This is an alternating p-series.  It is absolutely convergent if│an│converges.  1 / nᵖ⁺³ converges if the exponent is greater than 1.

p + 3 > 1

p > -2

The series is conditionally convergent if │an│diverges.  1 / nᵖ⁺³ diverges if the exponent is greater than 0 and less than or equal to 1.

0 < p + 3 ≤ 1

-3 < p ≤ -2

Combining these two, we get p > -3.

The base of a triangle is 12 inches greater than the height. If the area is 80 square inches, find the length of the base
PLEASE HELP

Answers

Answer:

Step-by-step explanation:

Because the area of a triangle you have to divide by 2 and then you get the area right so we multiply 80 x 2 = 160 is the area of the square which you divide by 2 but we are not going to do that. now we have to get 2 lengths with 12 difference so we have to just do trial and error method.

divide 25.84 divide by 4

Answers

i believe it is 6.46

Answer:

25.84 divide by 4 Is 6.46.

Where is the vertex of f(x) = -2x - 3| +6.4?

Answers

(-2x-19.2) I think that is the answer :(

Compare: -7 -4


PLEASE HELP ME!

Answers

-11? What do u mean compare

Jesse is driving to a town that is 210 miles away with a speed of 60 miles per hour. If he makes no stops, how long will the trip take?

Answers

Answer: The trip should take 3.5 hours.

Step-by-step explanation: To find the time, divide the distance by the rate. In this case, 210/60 = 3.5.

Answer:

3.5 hours or specifically, 3 hours and 30 minutes

Step-by-step explanation:

We know that the car can be driven 60 miles per hour. The goal is 210 miles. If you divide 210 miles by 60, the result is 3.5. The whole number 3 in 3.5 will represent the hours taken which means 3 hours. The 0.5 will also represent the minutes. 0.5 = 1/2, 1/2 of an hour = 30 minutes.


$11000 is compounded semiannually at a rate of 8% for 19 years. What is the total amount in the compound interest account?

Answers

Answer:

all really all you have to do is do 8 divided by 19 and then whatever that number that you get from that attractive from your highest number that you have in your question which is 11000

When Alexander moved into a new house, he planted two trees in his backyard. At

the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each

year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per

year. Let A represent the height of Tree At years after being planted and let B

represent the height of Tree Bt years after being planted. Write an equation for each

situation, in terms of t, and determine which tree is taller after 3 years.

Answers

Answer:

The equations for each situation are

A = 36 + 6t

B = 21 + 9t

After 3 years, Tree A is taller.

Step-by-step explanation:

From the question,

Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and

Tree A grew by 6 inches per year and Tree B grew by 9 inches per  year after planting.

For Tree A,

Given a period of t years after planting, the height would have increased by 6t

A = 36 + 6t

For Tree B,

Given a period of t years after planting, the height would have increased by 9t

B = 21 + 9t

To determine, which tree is taller after 3 years,

t = 3

For Tree A

A = 36 + 6t

A = 36 + 6(3)

A = 36 + 18

A = 54 inches

For Tree B

B = 21 + 9t

B = 21 + 9(3)

B = 21 + 27

B = 48 inches

Hence, After 3 years, Tree A is taller.

show that 5x²+2x-3
can be written in the
form |x+1/5| < 4/5 Hence, solve
the inequality
5x²+2x-3< 0

Answers

5x² + 2x - 3 < 0

5x² + 2x < 3

x² + 2/5 x < 3/5

Complete the square on the left side:

x² + 2/5 x + 1/25 - 1/25 < 3/5

(x + 1/5)² - 1/25 < 3/5

(x + 1/5)² < 16/25

Take the square root of both sides, keeping in mind that √(x²) = |x| for all x.

√((x + 1/5)²) < √(16/25)

|x + 1/5| < 4/5

This means

-4/5 < x + 1/5 < 4/5

-1 < x < 3/5

Given f(x) = 5x + 1, find f(-3).
I need help ASAP

Answers

Answer:

take a look ...........

Hassan predicted that he would sell 178 postcards. He actually sold 142 postcards. What are the values of a and b in the table below?

Percent Error

Item
Approximate value
Exact value
Error
Absolute error
Ratio
Percent error
Postcards
178
142
a
b


a = negative 36; b = negative 36
a = negative 36; b = 36
a = 36; b = negative 36
a = 36; b = 36

Answers

Answer:

its b

Step-by-step explanation:

took the test on edge

Giving out brainlst to whoever can answer this

Answers

100 - 5d + 10d = 130

5 x 20 = 100
5 x -d = -5d

Write each fraction as a percent. Use a model if needed. V-2
7/10

21/25

3/5

18/25​

Answers

7/10 = 70%
21/25 = 84%
3/5 = 60%
18/25 = 72%
7/10 is 70%
21/25 is 84%
3/5 is 60%
18/25 is 72%

4 tens + 14 ones = 5 tens + ___ ones

Answers

Answer:

4 becuase 40+14 = 54 so 50+4= 54 too

Step-by-step explanation:

HOPE THIS  HELPS :)
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