Let a and b be rational numbers. Is a – b rational or irrational?

Answers

Answer 1

Answer:

Rational

Step-by-step explanation:

Since a and b are rational, a - b has to be rational because we are not dividing them. 2 rational numbers subtracted from each other is always a rational number.

Example: 34 (rational) 23 (rational)

34 - 23 = 11 (rational)


Related Questions

William and
Debra
Pierce are celebrating their
20th anniversary by having a reception at a local reception hall. They have budgeted
$2,000 for their reception. If the reception hall charges a
$50 cleanup fee plus
$36 per​ person, find the greatest number of people that they may invite and still stay within their budget.

Answers

Answer:

54

Step-by-step explanation:

i put in the calculator 50+36×54= and got this 1,994

A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 marks

Answers

Answer:

7/40 is the fraction filled with water

Step-by-step explanation:

Here we start by calculating the volume of the cylindrical tank.

Mathematically, that would be;

V = π * r^2 * h

From the question

r = 80 cm = 80/100 = 0.8 meters

h = 1.4 meters

π = 22/7

Plugging these values into the volume equation, we have;

V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3

But mathematically;

1 m^3 = 1000 liters

So 2.816 m^3 = 2.816 * 1000 = 2816 liters

So the fraction filled with water will be;

492.8/2816 = 0.175 = 175/1000 = 7/40

1. In a right triangle, the lengths of the legs are a and b. Find the length of a hypotenuse, if: a=1, b=1; 2. In a right triangle, the length of a hypotenuse is c and the length of one leg is a. Find the length of the other leg, if: c=5, a=3;

Answers

Answer:

1. [tex]c = \sqrt{2}[/tex].

2. b = 4.

Step-by-step explanation:

To solve these two questions, keep the Pythagorean Theorem in mind: [tex]a^2 + b^2 = c^2[/tex]. Also remember that measurements cannot be negative, so we will disregard the negative answers.

1. a = 1, and b = 1. c = ?

[tex]1^2 + 1^2 = c^2[/tex]

[tex]1 + 1 = c^2\\[/tex]

[tex]c^2 = 1 + 1\\c^2 = 2\\\sqrt{c^2} = \sqrt{2}\\c = \sqrt{2}[/tex]

2. a = 3, c = 5. b = ?

[tex]3^2 + b^2 = 5^2\\9 + b^2 = 25\\b^2 = 16\\\sqrt{b^2} = \sqrt{16}\\b = 4[/tex]

Hope this helps!

Write each expression using a positive exponent. ("/" means division)("^" means to the power of) 9^-4

Answers

Answer:

[tex]\frac{1}{9^4}[/tex].

Step-by-step explanation:

[tex]9^{-4}[/tex]

= [tex]\frac{1}{9^4}[/tex]

= [tex]\frac{1}{9 * 9 * 9 * 9}[/tex]

= [tex]\frac{1}{81 * 81}[/tex]

= [tex]\frac{1}{6561}[/tex]

= 0.0001524157903.

Hope this helps!

During summer vacation, Wesley read, on average, 20 pages per night. Now that he has returned to school, he is averaging 65% fewer. How many pages per night is Wesley averaging now?

Answers

Answer:

He is currently reading 7 pages per night

Step-by-step explanation:

We can simply the question a little by finding what percent of the original Wesley is currently reading. Instead of saying 65% fewer, we can say he is reading 35% of what he used to read

Now we need to set up a proportion to solve the problem.

35% of 20

35/100=x/20

Cross multiply

35x20=700

700/100=7

He is currently reading 7 pages per night

Solve |2x+3/4 |=5 1/2 Please help!!!!

Answers

Answer:

=2x+3/4=5.50

x=19/8 or 2 3/8

hope this helps

Step-by-step explanation:

How to do this question plz answer me step by step plzz plz ​

Answers

Answer:

20π cm

Step-by-step explanation:

The circumference (C) of a circle is calculated as

C = 2πr ( where r is the radius )

Here r = 10 , thus

C = 2π × 10 = 20π cm

Answer:

hope it helps

Step-by-step explanation:

circumference of a circle = 2*pi*r = 2*pi*10 =20picm

scott can deliver 10 pizzas per hour and kenneth can deliver 12 per hour how mnay hours will it take them to deliver 110 pixzas

Answers

Answer:

5 hours

Step-by-step explanation:

Scott's delivery rate = 10 pizzas per hour

Kenneth's delivery rate = 12 pizzas per hour

Combined delivery rate

= Scotts delivery rate + Kenneth's delivery rate

= 10 + 12

= 22 pizza's per hour  (take reciprocal to find the rate in "hours per pizza")

= 1/22 hours per pizza

Given that they both deliver 110 pizzas combined, the will take

= 1/22 hours per pizza x 110 pizzas

= (1/22) x 110

= 5 hours

!helppppppppp meeeeeeee emmmmmm!

Answers

Answer & Step-by-step explanation:

Take the last  expression:

[tex](3*3)*(4*4)[/tex]

This can be simplified using exponents. [tex]x*x=x^2[/tex] :

[tex]3^2*4^2[/tex]

So, take the two numbers within the parentheses from the first expression and write separately, including the exponent with each. Do this with the next problem:

[tex](5*6)^3=5^3*6^3[/tex]

:Done

if x^2+y^2=14 annd xy=5 find the value of (1/2x+1/2y)^2

Answers

Answer:

             7

Step-by-step explanation:

 [tex]\left(\frac12x+\frac12y\right)^2=\\\\=\left[\frac12(x+y)\right]^2=\\\\=\left(\frac12\right)^2\left(x+y\right)^2=\\\\=\frac14\left(x+y\right)^2=\\\\=\frac14(x^2+2xy+y^2)=\\\\=\frac14(x^2+y^2+2xy)=\\\\=\frac14(14+2\cdot5)=\\\\=\frac14\cdot28=\\\\=7[/tex]                          

how do you solve this problem ? 4(-3x+1)-3x=71

Answers

Answer:

x = -67/15 = -4-46667

Step-by-step explanation:

4(-3x+1) - 3x = 71

4*-3x + 4*1 - 3x = 71

-12x + 4 - 3x = 71

-15x = 71-4

-15x = 67

x = 67/-15

x = -4.46667

check:

4(-3*-4.46667 + 1) - 3*-4.4666= 71

4(13.4+1) + 13.4 = 71

4*14.4 + 13.4 = 71

57.6 + 13.4 = 71

(x-1)(x+4) write in standard form

Answers

Answer:

x^2+3x-4

Step-by-step explanation:

(x-1)(x+4)

x^2+4x-x-4

x^2+3x-4

Hope this helps ;) ❤❤❤

Answer:

y = x² + 3x -4

Step-by-step explanation:

we can use the FOIL formula

(x-1) (x+4)

x² + 4x - x -4

x² + 3x -4

therefore, the standard form would be y = x² + 3x -4

1. Tell whether the number 47 is prime
or
composite. Then write all the factors of the number.
2.Tell whether the number 81 is prime
or
composite. Then write all the factors of the number

Answers

Answer:47 is a prime and 81 is a composite

Step-by-step explanation:47={1,47}

81={1,3,9,18,27,81}

1. The number 47 is prime. The only factors are 1 and itself. We can check by dividing 47 over the list of primes smaller than 47. To be more efficient, we can stop once we reach sqrt(47) = 6.85. So we only need to check the primes {2, 3, 5} to show they are not factors of 47 to show that 47 is prime.

=====================================

2. The number 81 is composite. It is not prime because it has factors other than 1 and itself.

There are 5 factors and they are

1, 3, 9, 27, 81

Note how each factor listed is a power of 3 (1 = 3^0, 3 = 3^1, 9 = 3^2, 27 = 3^3, 81 = 3^4)

The prime factorization of 81 is

81 = 3*3*3*3 = 3^4

What is the solution to -33 + m = 10?
A. m = -43
B. m = -23
C. m = 23
D. m = 43

Answers

Answer:

D. m = 43

Step-by-step explanation:

Answer: D. m=43

Step-by-step explanation:

-33 +m = 10move 33 and make it postive m = 10 + 33m = 43

ANSWER QUESTIONS QUICKLY PLZZZZZZ ​

Answers

Answer:

See below.

Step-by-step explanation:

Since the two triangles are similar, this means that their corresponding sides are proportional. In other words:

[tex]\frac{PQ}{XY}=\frac{QR}{YZ}=\frac{RP}{ZX}[/tex]

Part A:

We already know PQ, RP, XY, and YZ.

To find XZ, we can use the first and third proportions:

[tex]\frac{PQ}{XY} =\frac{RP}{ZX} \\=\frac{7.2}{18}=\frac{6.5}{ZX}[/tex]

Cross multiply:

[tex]117=7.2(ZX)\\ZX \text{ or } XZ = 16.25[/tex]

Part B:

The same thing as Part A, but with the first and second proportions:

[tex]\frac{PQ}{XY}=\frac{QR}{YZ}\\\frac{7.2}{18}=\frac{QR}{7}\\50.4=18(QR)\\QR=2.8[/tex]

A ​108-inch is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.

Answers

Answer: Short piece is 27 inches

Long piece is 81 inches

====================================================

Explanation:

x = length of short piece

3x = length of the longer piece (3 times longer)

x+3x = 4x = total length

total length = 108

So 4x = 108 is the equation which solves to x = 27 after dividing both sides by 4.

The short piece is x = 27 inches and the long piece is 3*x = 3*27 = 81 inches. Adding the two pieces gives 27+81 = 108 which helps confirm the answer.

420 miles in 6.5 hours unit rate​

Answers

Step-by-step explanation:

Given,

distance =420 miles

time 6.5 hrs

now,

420miles took 6.5 hrs.

1mile took 6.5/420hrs

=0.015476hrs

Therefore, 0.015476hrs to cover 1 mile distance.

Hope it helps...

Answer:

64.6153846 miles/hour

0.0154761905 hours/mile

Step-by-step explanation:

If we want to find the miles driven in one hour, we must divide the total miles by the total hours.

miles / hours

We know that 420 miles were driven in 6.5 hours

420 miles/ 6.5 hours

Divide 420 by 6.5

420/6.5=64.6153846

64.6153846 miles/hour

In one hour, 64.6153846 miles are driven.

If we want to find the time to drive one mile, divide the time (hours) by the miles.

hours / miles

We know that 420 miles were driven in 6.5 hours.

6.5 hours/420 miles

Divide 6.5 by 420

6.5/420=0.0154761905

0.0154761905 hours/ mile

It will take 0.0154761905 of an hour to drive one mile.

The fuel efficiency of one type of car is recorded in a scatterplot where the amount of gas used, x (in gallons), is paired with the distance traveled, y (in miles), for various trips. The equation for the line of best fit for the data is y = 28x. How can the y-intercept and slope of this line be interpreted

Answers

Answer:

The answer can be interpreted by the distance moved by each gallon :))

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Just took it. Edg 2020. Hope this helps :)

The day before an exam, Jacob spent 2 1/5
hours studying in the morning and 3 3/4 hours
studying in the afternoon. How many hours
did Jacob spend studying that day?

Answers

Answer:

  5 19/20 or 5.95

Step-by-step explanation:

You can add these numbers as decimal numbers or as mixed numbers.

Decimal

  2.2 +3.75 = 5.95 . . . hours spent studying

Mixed Numbers

  (2 1/5) +(3 3/4) = (2 4/20) +(3 15/20) = (2 +3) +(4/20 +15/20)

  = 5 19/20 . . . hours spent studying

Consider the functions below. Which of the following statements describes the graph of function g? f(x)=x g(x)=1/5x A.The graph of g is one-fifth of a unit to the left of the graph of f. B. The graph of g is one-fifth of a unit to the right of the graph of f. C. The graph of g is five times steeper than the graph of f. D. The graph of g is one-fifth as steep as the graph of f.

Answers

Answer:

one fifth

Step-by-step explanation:

42

Answer:

The graph of g is one-fifth as steep as the graph of f.

Step-by-step explanation:

find the area of a rhombus with a 120 degree angle and sides 10 cm

Answers

Answer:

              A = 50√3 cm²

Step-by-step explanation:

[tex]A=s^2\cdot \sin\alpha\\\\s=10\\\alpha=120^o\\\\A=10^2\cdot\sin(120^o)=100\sin(180^o-60^o)=100\sin(60^o)=100\cdot\frac{\sqrt3}2=50\sqrt3[/tex]

I need help with 6 and 7

Answers

Answer:

Step-by-step explanation:

6):

Take the small right triangle with the sides 25 and 7.

☆ The Pythagorian theorem ☆

Let x be the third side.

● 25^2 = x^2 + 7^2

Substract 7^2 from both sides

● 25^2 -7^2 = x^2 +7^2 -7^2

● x^2 = 25^2 -7^2

● x^2 = 576

● x = 24 inches

The third that we find is the half of the side of the square.

Multiply it by 2 and get the side of the square.

● 24 × 2 = 48 inches

The perimeter of the square is the side times 4.

● P = 48 × 4

● P = 192 inches

■■■■■■■■■■■■■■■■■■■■■■■■■■

7):

Both triangles are righr and they have a khown angle.

Start with the small one and calculte the third angle.

The sum of a triangle angles is 180°

Let B be the third angle.

● B = 180-(90+51) = 39°

That's equal to the second angle of the second's triangle.

So it's an AA similarity.

So:

● x/24 = 7/15

● x = (7/15)×24

● x = 11.2

I Need Help With This One :/

Answers

Answer:

(-5) ^ 11

Step-by-step explanation:

(-5) ^5 / (-5) ^ -6

We know that a^ b / a^ c = a^ ( b-c)

(-5)^ (5 - -6)

(-5) ^ (5+6)

(-5) ^ 11

Answer:

-5

Step-by-step explanation:

Mathaway

Simplify 4 to the 2nd power times 4 to the eighth power 

A. 4 to the 16th power
B. 4 to the 10 power
C. 16 to the 16 power
D. 16 to the 10 power

Please help ASAP!!!!!!!!

Answers

Answer:

4 to the power of 10.

Step-by-step explanation:

A rule is that x to the power of y + x to the power z of must equal x to the power of z+y.

Answer:

Option B

Step-by-step explanation:

4²×4^8

4^(2+8)

4^10

4 to the 10th power

3. Miss. Mead pays Miss. Adams $160.00 per week. She works 40 hours per week. Miss. Adams
was idle for 4 hours and 30 minutes during one week. How much did Miss. Mead pay for idle
time?
SHOW
a. $16.00 b. $18.00 c. $22.00 d. $24.00

Answers

Answer:

B. $18.00

Step-by-step explanation

160/4 divide 160 by 4 to see how much Miss Adams makes and hour

She makes $4 an hour

multiply this ($4) by her idle time (4.5) hours to get $18

If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse?

Answers

Answer:

8.94~9.0

Step-by-step explanation:

If A squared plus B squared equals C squared. Then you can used this formula and find that 4 squared plus 8 squared equals 80. then square root 80 to find 8.94 or rounded to 9. This would equal C or the hypotenuse. Hope this helps!

The required length of the hypotenuse of the triangle is 16√5.

Given that,
If the lengths of the legs of a right triangle are 4 and 8, what is the length of the hypotenuse is to be determined.

What are Pythagorean triplets?  

In a right-angled triangle, its side, such as hypotenuse, perpendicular, and the base is Pythagorean triplets.

Here,
Applying the Pythagorean theorem,
Hypotenuse²  = perpendicula² + base²
Hypotenuse²  = 8² + 4²
Hypotenuse²  = 64 + 16
Hypotenuse²  = 80
Hypotenuse  = √80
Hypotenuse  =  16√5

Thus, the required length of the hypotenuse of the triangle is 16√5.

Learn  more about Pythagorean triplets here:

https://brainly.com/question/10174253

#SPJ2

I NEED HELP ON THE PROBLEM!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!!

Answers

Answer:

A.) As x increases, the rate of change of g exceeds the rate of change of f

Step-by-step explanation:

Let's take the options given and look at them to actually know which is true.

Option A

We notice that as x increase in value the rate of change of g starts exceeding the rate of change of f.

Then it's exceeds it from the value x = 5

Option B

At x= 4.39

F= 2616.689

G= 2606.657

They are different values

Option C

That's opposite of option A

But option A is true which signify option C to be false

Option D

Not true also.

We can see from x= 0 to 4 the rate of change of F exceeds that of G

Miguel's basketball team is down seven points from their opponents. If they make a two-point field goal, how many more points do they need to tie the game? Justify your answer by writing a number sentence to represent this situation.

Answers

Answer: Answer is the steps

Step-by-step explanation:

If they are down by seven points then it means that they are losing by 7 points.And fortunately they made  two-point field goal so they will now be down by 5 points. Which means that they need 5 more points to tie the game.

For example,

-7 represents the points that they are down by and they made 2  points so

-7 + 2 = -5   which means that they are now down by 5 points to make a tie game.

Answer:-7+2+5=0

Step-by-step explanation:

Two numbers are in ratio 3 by 2 and their difference is 5 find numbers

Answers

Answer:

          The first number is 15, the second number is 10

Step-by-step explanation:

a:b = 3:2    ⇒   a = 3x  and  b = 2x

a - b = 5

3x - 2x = 5

x = 5

a = 3•5 = 15

b = 2•5 = 10

Re:A package of 8-count AA batteries costs $6.32. A package of 20-count AA batteries costs $16.00. Which statement about the unit prices is true?
A. The 8-count batteries have a lower rate unit price of $0.79 per battery

B. The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.

C. The 20-count pack of AA batteries has a lower unit price of $0.80 per battery.

D. The 8-count pack of AA batteries has a lower unit price of $0.80 per battery.

Answers

Answer:

b

Step-by-step explanation:

Answer:

B. The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.

Step-by-step explanation:

I just have an educated guess out of the info that you gave me.

Other Questions
a jogger runs a mile in 8.92 minutes. 1 mi=1609m; calculate her speed in km/hr An object has a mass of 50.0 g and a volume of 10.5 cm cubed. What is the object's density? A. 60.5 g/cm cubed B. 0.21 g/cm cubed C. 4.76 g/cm cubed D. 525 g/cm cubed What point is the author trying to make in these sentences? white fang . Which is a likely location for primary succession? grassy hillside newly mowed field forest floor large boulder How is one product determined to specialize in between the two What tactics did CREEP use to undermine President Nixons political opponent in the 1972 election? It raised money from other political candidates. It threatened opponents so they would stop running. It distributed negative campaign flyers about opponents. It broke into the opponents offices to steal documents. The federal government has the legal authority to prevent a company from adding products through acquisitions if the acquisition threatens to lessen competition.A. TrueB. False Which tribes were from the southwestern part of North America? Select all that apply. Mogollon Shoshone Hohokam Anasazi Adena Find the equation of a circle with PQ as diameter, where P(2,-6) and Q(-6,-4) The magnitude of the magnetic field at point P for a certain electromagnetic wave is 2.12 T. What is the magnitude of the electric field for that wave at P? (c = 3.0 108 m/s) Which of the following pieces of information is given in a half-reaction?O A. The number of electrons transferred in the reactionB. The compounds that the atoms in the reaction came fromC. The state symbol of each compound in the reactionD. The spectator ions that are involved in the reaction You're on a fishing trip with friends and you look over and see a boat filled with people. You look away for a minute then look back at the same boat and yet you don't see a single person on it. Why? PLS ANSWER I WILL GIVE BRAINLIST AND A THANK YOU!!! :) "Twenty dogs are initially presented with numerous CS-tone/US-footshock pairings. These dogs are then placed in a shuttle box, and movement from one side of the shuttle to the other terminates periodic presentations of the CS tone. No shocks are delivered in the shuttle box, but the dogs learn to move to the other side of the box to escape the tone. This is an example of _________________________" Refer to the following scenario to answer the following questions. Five fishermen live in a village and have no other employment or income-earning possibilities besides fishing. They each own a boat that is suitable for fishing but does not have any resale value. Fish are worth $5 per pound, and the marginal cost of operating the boat is $500 per month. They all fish a river next to the village. According to the following schedule, they have determined that when there are more of them out on the river fishing, they each catch fewer fish per month.Boats Fish Caught per Boat (pounds) 1 200 2 190 3 175 4 155 5 130 How many fishermen will choose to operate their boats? What wavelength measuresA. Depth B. Distance C. Energy D. Speed E. TimeF. Volume A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters? Zhi and her friends moved on to the card tables at the casino. Zhi wanted to figure out the probability of drawing a king of clubs or an ace of clubs Stock Investment Transactions On September 12, 2,000 shares of Aspen Company were acquired at a price of $50 per share plus a $200 brokerage commission. On October 15, a $0.50-per-share dividend was received on the Aspen stock. On November 10, 1,200 shares of the Aspen stock were sold for $42 per share less a $150 brokerage commission. In your computations, round per share amounts to two decimal places. When required, round final answers to the nearest dollar. For a compound transaction, if an amount box does not require an entry, leave it blank. Journalize the entries to record the original purchase, the dividend, and the sale under the cost method. Professor Sanders wants to study how constant distractions during an exam affect student performance. She randomly assigns her students to different classrooms where the experimental group will receive a predetermined number of distractions while taking an exam. In this study, the independent variable is the ________ and the dependent variable is the ________.