The product of two rational numbers is ______ rational.

Answers

Answer 1
The product of two rational numbers is ALWAYS rational
Answer 2

The product of two rational numbers is always rational

Proof:

Let a = p/q and b = r/s be two rational numbers. We will have p,q,r,s be integers where denominators q and s are nonzero. We cannot divide by zero.

Multiplying a and b gives

a*b = (p/q)*(r/s) = (p*r)/(q*s)

Due to the closure property of integer multiplication, the expressions p*r and q*s are integers. The result we get is in the form of integer/integer. Basically we have two integers being divided. Furthermore, q*s is nonzero as neither q nor s is zero.

Therefore, if a and b are rational, then a*b is also rational as well.


Related Questions

Which equation represents a proportional relationship that has a constant of proportionality equal to –10? y = x minus 10 y = StartFraction over negative 10 EndFraction y = negative 10 x y = negative 10

Answers

Answer:

The correct answer would be C. y = -10x

Step-by-step explanation: We cam eliminate the first two by common sense, that would leave us with options C, and D. The correct answer would be C, the reason it is not D is because D isn't a proportion, y = -10 is just stating that variable y equals -10, whereas, y = -10x represents a proportion.

Answer: the other guy is correct

Step-by-step explanation: it is C i got a 100%

What is the measure of angle B?

Answers

Answer: 97

Step-by-step explanation:

Answer: 78 Degrees

Step-by-step explanation:

To get the answer you must take 180 (the number of degrees in every triangle) and take away 50, and 52. 180 minus 50 is 130 minus 52 is 78

please help! desperate!

Answers

Answer:

i believe it centimeters

Answer:

I see it now, haha

Radius = 2cm

Step-by-step explanation:

We reverse equation for volume

V=πr2  h/3 becomes r2=  V/( h* 3 *π)

We have height of  6cm  so 6*3 = 18 Then V = 72/18π = 4

We then found the square r2 or ^2 or ^2 they are both same answers Radius = 2   as √4 = 2 and 4/2 also is 2

This radius is squared so we use the root √4cm and find r = 2.

Hope this helps glad you got back to me.

What is the side lengths of volume=343 cm and side lengths of 729 cm

Answers

Answer:

Volume = 343 - Length: 7, Width: 7, Height: 7

Volume = 729 - Length: 9, Width: 9, Height: 9

Step-by-step explanation:

Assuming that the shapes are rectangular prisms.

Graph g(x) = 50 – 6+2.

Answers

Answer:

42

Step-by-step explanation:

sorry if it wrong

I need urgent help plz

Answers

i think the answers a



hope this helps :)

(if you wouldn’t mind can you mark me brainliest?)

what does the polynomial pirate have as a pet



From work sheet called quadratic function transformations

Answers

Answer:

Apparently pirates had a flare for the exotic (who would have thought) and also commonly kept small monkeys. More common type pets, such as cats and dogs, were probably kept on ships too - but they would be expected to earn their keep

Step-by-step explanation:

hope this helps oxox

Solve for x in the equation x2 – 3x+41 = 0

Answers

Answer:

no solution

Step-by-step explanation:

Let's solve your equation step-by-step.

x2−3x+41=0

Step 1: Subtract 41 from both sides.

x2−3x+41−41=0−41

x2−3x=−41

Step 2: The coefficient of -3x is -3. Let b=-3.

Then we need to add (b/2)^2=9/4 to both sides to complete the square.

Add 9/4 to both sides.

x2−3x+

9

4

=−41+

9

4

x2−3x+

9

4

=

−155

4

Step 3: Factor left side.

(x

−3

2

)2=

−155

4

Step 4: Take square root.

x

−3

2

=±√

−155

4

Step 5: Add 3/2 to both sides.

x

−3

2

+

3

2

=

3

2

±√

−155

4

x=

3

2

±√

−155

4

Answer:

No real solutions.

A__ has a regular polygon base and a vertex over the center of the base.
O A. right prism
B. prism
C. regular pyramid
O D. pyramid

Answers

Answer:

C.Regular Pyramid

Step-by-step explanation:

If it has a vertex over the centre of the base,it has to be a pyramid .Also, since the base is a regular polygon,the solid is a regular pyramid

Which of the following expressions can be used to find the perimeter of the square? All sides are the same length. A. 4 x 9. B. 9 x 9. C. 9 + 9 +9 +9. D. 4 + 4 +4 +4.

Answers

Answer:

Step-by-step explanation:

The formula for the perimeter of a square of side length s is P = 4s.

A. 4 x 9.   Incorrect.  There are 4 sides, not just 2.

B. 9 x 9.    Incorrect.  There are 4 sides, not just 2.

C. 9 + 9 +9 +9.    This would be the perimeter of a square of side length 9.

D. 4 + 4 +4 +4.      This would be the perimeter of a square of side length 4.

Determine the interval(s) on which the function is (strictly) increasing. Write your answer as an interval or list of intervals. When writing a list of intervals, make sure to separate each interval with a comma and to use as few intervals as possible. Click on "None" if applicable.

Answers

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Each of the 17 guinea pigs needs its cage cleaned. If it takes 1 hour to clean 4 cages, how many hours will it take to clean all 17 cages? It will take hours to clean all the cages.

Answers

Answer:

Time taken to clean all 17 cages = 4.25 hours

Step-by-step explanation:

Total number of Guinea pig cage = 17

Time taken to clean 4 cage = 1 hour

So,

Time taken to clean 1 cage = [tex] \frac{1}{4} [/tex] hour = 15 minutes

Therefore,

Time taken to clean 17 cages = 17 × 15 minutes = 255 minutes

= [tex] \frac{255}{60} [/tex] hours

= 4.25 hours

Answer:

Time taken to clean all 17 cages = 4.25 hours

Step-by-step explanation:

A serving tray is the shape of a rectangular prism without a top the dimentions of the tray or 8" by 10" by 2" what is the surface area of the tray

Answers

Answer:

it's8

Step-by-step explanation:

What is h(x) = 7 + 10x + x2 written in vertex form? h(x) = (x – 25)2 – 18 h(x) = (x – 5)2 + 32 h(x) = (x + 5)2 – 18 h(x) = (x + 25)2 + 32

Answers

Answer:c

Step-by-step explanation:

20 points for this one but please with the explanation

Answers

Answer:

∠DGE = 48°

Step-by-step explanation:

∠DGE = 48° (arc is equal to the angle)

I'm not so sure on how to find GF



Javier wants to prove that triangle MNP is similar to triangle RSP.


What missing piece of information does Javier need to prove that triangle MNP is similar to triangle RSP by the Angle-Angle Similarity Postulate?

A. Javier needs to know the measure of angle P.

B. Javier needs to know the measure of angle M.

C. Javier needs to know the measure of angle S.

D. Javier needs to know that segment MN is parallel to segment SR.

Answers

Answer:

Step-by-step explanation:

In triangles MNP and RSP, if there are two pairs of corresponding angles that are congruent or equal, it means that

triangle MNP is similar to triangle RSP. The corresponding angles in both triangles are

P corresponding to P

M corresponding to R

N corresponding to S

Therefore, the missing piece of information that Javier needs to prove that triangle MNP is similar to triangle RSP by the Angle-Angle Similarity Postulate is

A. Javier needs to know the measure of angle P.

Answer:

D. Javier needs to know that segment MN is parallel to segment SR.

Step-by-step explanation:

(I know this is old, but I wanted to answer if anyone else comes to this.)

If Javier does not know if segment MN is parallel to segment SR, he would not be able to prove that the two triangles were similar.

Using the drawing below, find the inequality statement that it represents AND choose all of the numbers that would be part of that solution.



A
m > −5
B
m ≥ −5
C
m < −5
D
m ≤ −5
E
−5
F
−8
G
0
H
3

Answers

Answer: A, B, E

Step-by-step explanation:

You have to choose the awnsers that would be apart of the awnser

Iris wants to buy sneakers at $15 each and high heels at $30 each. Write an algebraic expression to find the total cost of the shoes if she buys x sneakers and y high heels. Write your answer in the form “ax + by” where a and b are positive or negative constants.

Answers

Answer: 30y + 15x

If x is for sneakers, and y is for high heels, plug 15 in for a and 30 in for b. This means that x is how many sneakers she buys, and y is how many high heels she buys. The equation altogether represents the total amount of her purchases.

The intercepted arc of an inscribed angle is ______ the measure of the inscribed angle.

Answers

The intercepted arc of an inscribed angle is (half) the measure of the inscribed angle.
The intercepted arc of an inscribed angle is HALF the measure of the inscribed angle.

Rivers created a model of her school building.
1 in
5 in.
3 in.
What is the surface area of the model Rivers made?

A. 9 squares inches
B. 31 squares inches
C. 46 squares inches
D. 52 squares inches

Answers

Answer:

46 square inches

Step-by-step explanation:

Using the formula: 2(w l+h l+h w)

Answer:

its C

Step-by-step explanation:

Amy is putting money into a savings account. She starts with $650 in the savings account, and each week she adds $70 .

Let S represent the total amount of money in the savings account (in dollars), and let W represent the number of weeks Amy has been adding money. Write an equation relating S to W . Then use this equation to find the total amount of money in the savings account after 17 weeks.

Equation:

Total amount of money after 17 weeks: $


Answers

Answer:

$1,840

Step-by-step explanation:

S + (70 × W)

650 + (70 × 17)

650 + 1190

1, 840

Please help! You don’t have to show work

Answers

Answer:

It is Number 1 A

Step-by-step explanation:

Find the area of the shape shown below.

Answers

Answer:10 is the area

Step-by-step explanation:

A milk container is in the shape of a rectangular prism. The width is 26 centimeters, the depth is d centimeters,
and the height is d + 24 centimeters. Write a polynomial that represents the volume (in cubic centimeters) of the
milk container.

Answers

Answer:

Step-by-step explanation:

The milk container has the shape of a rectangular prism. We would determine its volume by applying the formula for determining the volume of a rectangular prism which is expressed as

Volume = length × width × height

From the information given,

Length = height = d + 24 meters

Width = 26 meters

Height = depth = d meters

The polynomial that represents the volume (in cubic centimeters) of the

milk container is

Volume = (d + 24)26d

Volume = 26d² + 624d

An electric motor pumps water into a pool at a rate of 500 liters per hour. After a tune
up, its rate increases by x liters per hour. If the motor now takes 3 hours 19 pump
1800 liters, in which equation does x represent the increase in speed after the tune
up?
A, 500(2+3) 1800
B, 3(500) +2 1800
C. 5002 +3 1800
D, 3(500 + 2) 1800

Answers

Answer: 3(500+x)=1800

The segments shown are dilations of each other about the origin. Which statement could be true? The coordinate (1, 0) is from a dilation using the scale factor of One-fifth. The coordinate (5, 0) is from a dilation using the scale factor of 4. The coordinate (1, 0) is from a dilation using the scale factor of 5. The coordinate (5, 0) is from a dilation using the scale factor of One-fifth.

Answers

Answer:

the first one The coordinate (1, 0) is from a dilation using the scale factor of One-fifth.

Answer:

the first one

Step-by-step explanation:

Thomas is building rectangular boxes. The table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long. Choose the function that represents the data. f(x) = x2 + 2x f(x) = 2x2 f(x) = 2x

Answers

Answer:

c

Step-by-step explanation:

A function assigns the values. The correct option is C, f(x)=2x².

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

Given that the table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long. Now, the function that can represent this table can be found by substituting the values in the function and checking if the two sides are equal or not.

A.) f(x)= x²+2x

f(1) should be equal to 2.

f(x)= x²+2x

f(1)= 1²+2(1) = 3

Thus, this is not the correct function.

B.) f(x)= x²/2

f(1) should be equal to 2.

f(x)= x²/2

f(1)= 1²/2 = 0.5

Thus, this is not the correct function.

C.) f(x)=2x²

f(1) should be equal to 2.

f(x)=2x²

f(1)= 2(1)² = 2

Also, f(2) should be equal to 8.

f(x)=2x²

f(1)= 2(2)² = 8

Thus, this is the correct function.

D.) f(x)=2x

f(1) should be equal to 2.

f(x)=2x

f(1)= 2(1) = 2

Also, f(2) should be equal to 8.

f(x)=2x

f(1)= 2(2) = 4

Thus, this is the correct function.

Hence, the correct function that represents the area of the box is f(x)=2x².

The complete question is,

Thomas is building rectangular boxes. The table shows the area in square feet, f(x), of the bottom of a box when one side of the box is x feet long.

x    1  2  3   4  5

f(x) 2 8 18  32 50

A.)  f(x)= x²+2x

B.)  f(x)= x²/2

C.)  f(x)=2x²

D.)  f(x)=2x

Learn more about Function:

https://brainly.com/question/5245372

#SPJ5

Hello I really need help and it’s a quick easy multiple choice answer I just don’t know if I’m right! Pls help

Answers

Answer:

The solutions

Step-by-step explanation:

Solving for x gives the solutions

There are 48 girls and 60 boys who want to participate in 6th grade intramural sports. Each team must
have the same number of girls and the same number of boys,
I. What is the GREATEST number of teams that the coach can create to participate in intramurals?
II. How many girls and boys will be on each team?
Use what you know about the GCF to solve this problem. Explain how you know you found the GCF.

Answers

I. 12

II. 4 girls and 5 boys

WORTH 20 POINTS + BRAINLIST
I know this but I can’t remeber some one please help me out!

Answers

Answer:

C- 115

Step-by-step explanation:

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