Are all terminating and repeating decimals rational numbers? Explain.

Answers

Answer 1

Answer:

All terminating and repeating decimals are not rational numbers. For example, pi is a non-terminating & irrational number.

Step-by-step explanation:

Are All Terminating And Repeating Decimals Rational Numbers? Explain.
Answer 2

The given statement "Are all terminating and repeating decimals rational numbers? Expla" is true.

Yes, all terminating and repeating decimals are rational numbers. A

rational number is defined as any number that can be expressed as a ratio of two integers, with the denominator not equal to zero.

Terminating decimals are those decimals that end after a finite number of digits.

For example, 0.75 is a terminating decimal because it ends after two digits. To show that such decimals are rational,

We can rewrite the decimal as a fraction.

0.75 can be expressed as 75/100 or simplified to 3/4.

Since both the numerator and denominator are integers, 0.75 is a rational number.

Now

Repeating decimals are those decimals that have a repeating pattern of digits after the decimal point.

For example, 0.3333... is a repeating decimal because the digit 3 repeats infinitely.

To show that repeating decimals are rational, we can use a similar approach to terminating decimals.

Take 0.3333... as an example.

We can represent this decimal as an infinite series:

0.3333... = 3/10¹ + 3/10² + 3/10³+ ...

This can be simplified using the formula for the sum of an infinite geometric series:

0.3333... = 3/10¹ + 3/10² + 3/10³+ ...

               = (3/10)/( 1 - 1/10)               (by sum of infinite geometric serires)

               = 3/9

Since 3/9 can be simplified to 1/3, we can conclude that 0.3333... is a rational number.

Thus, all terminating and repeating decimals are rational numbers because they can be expressed as a ratio of two integers.

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Related Questions

Select all that apply. Proteins _____. are part of antibodies consist of amino acids contain carbon, hydrogen, oxygen, and nitrogen. are derived from fruits and vegetables

Answers

Answer:

parts of antibodiesconsist of amino acids containing carbon, hydrogen, oxygen, and nitrogen

Step-by-step explanation:

Antibodies are immune system-related proteins called immunoglobulins.

Proteins are made up of amino acids, which are small organic molecules made up of carbon, hydrogen, nitrogen, and oxygen.

Hope that helps.

Larissa rolls to number cubes each with the numbers one through six. Larissa adds the numbers that appear on the role. Which 2 sums have an equal chance of occurring?
3 and 11
4 and 7
5 and 8
Or
6 and 9

Answers

Answer:

5 and 8 i think

Step-by-step explanation:

sorry if you get it wrong

The period of a pendulum is the time the pendulum takes to swing back and forth. The function relates the length L= 0.81t in feet of a pendulum to the time t in seconds that it takes to swing back and forth. A convention center has a pendulum that is 90 feet long. Find the period.

Answers

Answer: 111.11 seconds

Step-by-step explanation:

Given: The period of a pendulum is the time the pendulum takes to swing back and forth

The function relates the length [tex]L= 0.81t[/tex] in feet of a pendulum to the time t in seconds that it takes to swing back and forth.

If L= 90 feet then put this in the above function, we get

[tex]90=0.81t\\\\\Rightarrow\ t=\dfrac{90}{0.81}\\\\\Rightarrow\ t=111.1111111\approx111.11\text{ seconds}[/tex]

Hence,  the period = 111.11 seconds

does anyone know the answer ​

Answers

Answer:

x = 22

Step-by-step explanation:

90 = (5x - 20)

+20         +20

110 = 5x

/5      /5

22 = x

Hope this helps!

what is the answer to -3z > -4.5 ?

Answers

Answer:

z<1.5

Step-by-step explanation:

(4). Simplifying polynomials, help pls:) brainliest involved

Answers

Answer:

Explanation:

To simplify a polynomial, we have to do two things: 1) combine like terms, and 2) rearrange the terms so that they're written in descending order of exponent.

First, we combine like terms, which requires us to identify the terms that can be added or subtracted from each other. Like terms always have the same variable (with the same exponent) attached to them. For example, you can add 1 "x-squared" to 2 "x-squareds" and get 3 "x-squareds", but 1 "x-squared" plus an "x" can't be combined because they're not like terms.

Let's identify some like terms below.

f(x)=−4x+3x2−7+9x−12x2−5x4

Here you can see that -4x and 9x are like terms. When we combine (add) -4x and 9x, we get 5x. So let's write 5x instead:

f(x)=5x+3x2−7−12x2−5x4

Let's do the same thing with the x-squared terms:

f(x)=5x+3x2−7−12x2−5x4

f(x)=5x−9x2−7−5x4

Now there are no like terms left. Our last step is to organize the terms so that x is written in descending power:

f(x)=−5x4−9x2+5x−7

Step-by-step explanation:

Graph y = -2x - 1. Plot the y-intercept on the graph.

Answers

Answer:

so u put the first point at -1 go down 2 to the right 1

The graph of equation y = - 2x - 1 and the y-intercept (0, - 1) is shown in image.

We have to given that,

To plot the equation y = - 2x - 1 and the y-intercept on the graph.

Since, The equation of line in slope intercept form is,

y = mx + c

Where, m is slope and c in y - intercept.

Here, Equation is,

y = - 2x - 1

After comparing,

y - intercept = - 1

So, y - intercept of equation (0, - 1)

Learn more about the equation of line visit:

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Which expression is modeled by this arrangement of tiles?

16 negative tiles are split into 2 groups of 8 negative tiles.

Answers

Answer:

16 negative tiles are split into 2 groups of 8 negative tiles.

Negative 16 divided by 3

Negative 16 divided by 2

Negative 8 divided by 8

Negative 8 divided by 2

Step-by-step explanation:

42+__________=68 vhrvwfruybtglh

Answers

Answer:

42 + 26 = 68

Step-by-step explanation:

I hope this helped :)

Plz help me quickly I’ll give brain list !!!!!!!plz

Answers

Answer:

8  3/4 is your answer  

Step-by-step explanation:

If you want to multiply in a simplier form convert into decimals

2.5*3.5= 8.75 = improper fraction form its  8*4+3=35/4= 8 3/4

pls give brainliest i need two more and i level up and hope this helps

Answer:

The answer is 8.75

Step-by-step explanation:

First make 2 1/2 and 3 1/2 to improper fraction.

5/2 * 7/2= 35/4

After you multiplied you make you answer into a mixed number fraction by

dividing the  numerator and denominator. 35/4=8.75

Answer:8.75

Hope this helps!!

PLZ HELP DUE SOON

Mia has $50 on a gift card to her favorite coffee shop. Each time she visits the coffee shop she spends $3.75 on her favorite drink. Write an equation to represent the relationship between x, the number of times she visits the coffee shop, and y, the total amount on her gift card.

Answers

Answer:

50 = x · 3.75

Step-by-step explanation:

2. The water level of a river was measured each day during a two-week period. The
graph models the linear relationship between the water level of the river in feet
and the number of days the water level was measured.
Water Level of River
The initi
28
Ο Ο Ο
The max
24
20
The wate
16
Water Level (ft)
12
o
The water
CLEAR ALL
4
0
2
4
12
6 8 10
Number of Days
Which statement best describes the y-intercept of the graph?
< PREVIOUS
O 3
Os Oo Or
0.8
HH
Type here to search
O

Answers

Step-by-step explanation:

day during a two-week period. The

graph models the linear relationship between the water level of the river in feet

and the number of days the water level was measured.

Water Level of River

The initi

28

Ο Ο Ο

The max

24

20

The wate

16

Water Level (ft)

12

o

The water

CLEAR ALL

4

0

2

4

12

6 8 10

Number of Days

Which statement best describes the y-intercept of the graph?

< PREVIOUS

O 3

Os Oo Or

0.8

HH

Answer:

It is C. The initial water level is 16 ft

Step-by-step explanation:

The Y-intercept goes across 16 lol

Two functions are shown below
f(x)=2x+1 g(x)=−72x−5
What is the approximate value of x when f(x) = g(x)?
A.1.3
B.0.5
C.1.8
D.3.1

Answers

f(x)= g(x) so 2x+1 = -72x-5
2x+72x = -1-5
74x = -6
x= -3/37 = 0.08 so option B

8(12+a) I'm Having trouble with this

Answers

Answer:

8a+96

Step-by-step explanation:

8(12+a)

= 96+8a

Answer:

8a+96 or a+12

Step-by-step explanation:

Distribute

In a certain country the fines for speeding in a school zone are $160 plus an additional $4 for every mile per hour over the speed limit. A. Write a function to represent the speeding fines

Answers

Answer:

T= 160 + 4x

Step-by-step explanation:

Giving the following information:

The $160 fine is a fixed cost. It will remain constant.

The $4 additional fine acts as a variable cost. It varies with the number of miles per hour.

To calculate the total cost (T), we need to use the following formula:

T= 160 + 4x

x= miles per hour exceeding the speed limit.

I need help with this problem

Answers

Answer:

X=13

Step-by-step explanation:

So if ΔABC ≅ ΔDEC, then that means that ∠B is ≅ ∠E. Therefore you would write the equation 3x=6x-39 and solve for X to get 13.

Use the distribution property to expand 7(8x - 2y) - 5

Answers

56x -14y - 5 is correct !

7(8x - 2y) - 5 = 56x - 14y - 5   [multiply the expression in the parentheses by 7 and then subtract 5]

Rhianna has $100 in a savings account that earns 5% interest per year.The interest is not compounded.How much interest will she earn in 1year?Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answers

Answer:

$5

Step-by-step explanation:

Using the formula given i=prt we can do the following: 100 x 0.05 x 1= $5

Therefore the total interest after one year would be $5

Expand the following:
a)2(x + 3)

Answers

Answer:

2x+6

Step-by-step explanation:

2(x+3)

=(2)(x+3)

=(2)(x)+(2)(3)

=2x+6

The values in the
the range is called the

Answers

Answer:

values in range

Step-by-step explanation:

Another word for finding the opposite of an integer is BLANK An integer

Answers

Answer:

The answer is at the bottom!!

Step-by-step explanation:

Another word for finding the opposite of an integer is negative number of an integer.

Decrease, spend, and decline are examples of words that mean negative. An integer is any positive whole number or its opposite. Here, opposite means sign. So a positive integer has a negative opposite and vice versa.

Hope this helps!!

Plz help me answer this!!!!

Answers

Answer:

Dude, it could literally be any number. It doesn't even provide us with a starting number to actually solve the problem with XD

Step-by-step explanation:

which table represents a linear function ?

Answers

Answer:

The first one in the left hand corner. And r u from Georgia it look like yu doing iready?

Step-by-step explanation:

Please help me answer this!!!

Answers

Answer:

NO NO NO NO NO

Step-by-step explanation:

If cos(x) = Negative one-fourth and tan(x) < 0, what is sin(2x) ? Negative StartFraction StartRoot 15 EndRoot Over 4 EndFraction Negative StartFraction StartRoot 15 EndRoot Over 8 EndFraction StartFraction StartRoot 15 EndRoot Over 8 EndFraction StartFraction StartRoot 15 EndRoot Over 4 EndFraction

Answers

The value of sin(2x) is [tex]\sin(2x) = - \frac{\sqrt{15}}{8}[/tex]

How to determine the value of sin(2x)

The cosine ratio is given as:

[tex]\cos(x) = -\frac 14[/tex]

Calculate sine(x) using the following identity equation

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

So we have:

[tex]\sin^2(x) + (1/4)^2 = 1[/tex]

[tex]\sin^2(x) + 1/16= 1[/tex]

Subtract 1/16 from both sides

[tex]\sin^2(x) = 15/16[/tex]

Take the square root of both sides

[tex]\sin(x) = \pm \sqrt{15/16[/tex]

Given that

tan(x) < 0

It means that:

sin(x) < 0

So, we have:

[tex]\sin(x) = -\sqrt{15/16[/tex]

Simplify

[tex]\sin(x) = \sqrt{15}/4[/tex]

sin(2x) is then calculated as:

[tex]\sin(2x) = 2\sin(x)\cos(x)[/tex]

So, we have:

[tex]\sin(2x) = -2 * \frac{\sqrt{15}}{4} * \frac 14[/tex]

This gives

[tex]\sin(2x) = - \frac{\sqrt{15}}{8}[/tex]

Read more about trigonometry at:

https://brainly.com/question/8120556

Answer:

B

Step-by-step explanation:

on Edge

A new arcade opened up in town. A play package is available to purchase. It includes 15 tokens for games,plus 5 dollars off. Let x represent the cost per token

Answers

Answer:

The total cost of the games (play package)

= 15x - 5

Step-by-step explanation:

Number of tokens in the games = 15

The cost per token = x

Discount off the total cost = $5

Therefore, the cost of the play package = 15x - 5

where x is in dollars

However, ‘x’ can also assume any value.

Check:

If x = $15

The total cost of the game can be said to be 15(10) - 5 = $220

Please help me with this

Answers

Step-by-step explanation:

The question implies the two angles are equal because of the positioning of the named vertices. m∠A = m∠E so to say.

You can substitute the values and solve the inequality to find x, then solve for m∠A.

m∠A = m∠E; Given (Inferred)

6x - 8 = 4x + 1; Substitution

6x = 4x + 9; Addition Property of Equality

2x = 9; Subtraction Property of Equality

x = 4.5; Division Property of Equality

m∠A = 6x - 8; Given

m∠A = 6(4.5) - 8; Substitution

m∠A = 19; Solve

Hope this helps!!

48/5 - 6/25 as a fraction

Answers

Answer:

9 9/25

Step-by-step explanation:

234/25 = 9 9/25

Answer:

the answer is 9 9/25

Step-by-step explanation:

i need help like asap ! please someone help

Answers

Answer:

should be B

Step-by-step explanation:

Hope it helps

the answer is b i’m fairly sure

Simplify 2 + 3[4 + (7 – 3) – 23]
*0
*2
*10
*8

Answers

Isn’t it supposed to be -19
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