Prove algebraically that the recurring decimal 0.472 can be written as
17
36

Answers

Answer 1

Given:

The recurring decimal is [tex]0.47\overline{2}[/tex].

To prove:

Algebraically that the recurring decimal [tex]0.47\overline{2}[/tex] can be written as [tex]\dfrac{17}{36}[/tex].

Proof:

Let,

[tex]x=0.47\overline{2}[/tex]

[tex]x=0.472222...[/tex]

Multiply both sides by 100.

[tex]100x=47.2222...[/tex]     ...(i)

Multiply both sides by 10.

[tex]1000x=472.2222...[/tex]        ...(ii)

Subtract (i) from (ii).

[tex]1000x-100x=472.2222...-47.2222...[/tex]

[tex]900x=425[/tex]

Divide both sides by 900.

[tex]x=\dfrac{425}{900}[/tex]

[tex]x=\dfrac{17}{36}[/tex]

So, [tex]0.47\overline{2}=\dfrac{17}{36}[/tex].

Hence proved.


Related Questions

The marked price of a watch is Rs.2700. If the percentage of discount given on marked price is twice of the percentage of VAT and the value of the watch after adding VAT is Rs.2376.Find the rate of VAT

Answers

Answer:

24%

Step-by-step explanation:

Step one:

given data

The marked price of a watch is Rs.2700

The value of the watch after adding VAT is Rs.2376

let us find the discount

= 2700-2376

=324

then the percentage discount is

=324/2700*100

=0.12*100

=12%

The VAT is twice the discount, the VAT is 12*2= 24%

please help i’ll mark brainliest

A group of friends hires a bus for a day for
$480, agreeing to share the cost equally. At
the last minute, two more people decide to go
on the trip, and as a result each person pays
$8 less.
How many people go on the trip and how much
does each person pay?

Answers

Step-by-step explanation:

i think 52 people was there cause 8×60=480 and you said that in the last minute two more people decide to go so i added two more and 52 people was the result

Answer:
67.50
Explanation:
First you add 8+8=16
Then 480+16=540
So you divide 540 ÷8=
So each of them pays 67.50$

Pls help and show workings pls
It due ASAP
please

Answers

Answer:

C. ASA

Step-by-step explanation:

2 sides & 2 angles are equal as given.

Other 2 angles are equal on basis of vertical angles

5j-5= 5
----
j5 true or false

Answers

The answer is true j5

PLEASE HELP!!!! will give brainliest!!!!

Answers

Answer: A Good luck :)

Suppose that 8 machines can complete a certain task in 9 days. if there are 18 machines, how many days would it take for them to finish the same task?

Answers

Answer:

It would require 4 days.

If there are 18 machines. Then the number of days would it take for them to finish the same task will be 4 days.

What is Algebra?

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

Time is inversely proportional to the number of the machines.

T ∝ 1/M

If the proportionality is removed, then a constant k is introduced.

Suppose that 8 machines can complete a certain task in 9 days.

Then the amount of the total work that is k will be

k = 8 x 9

k = 72

If there are 18 machines.

Then the number of days would it take for them to finish the same task will be

T = 72 / 18

T = 4 days

The number of days would it take for them to finish the same task will be 4 days.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

To factor a[tex]x^{2}[/tex]+bx+c, you have to group it as (a[tex]x^{2}[/tex]+ux)+(vx+c) so that uv=ac and u+v=b. Both addition and multiplication are commutative, so how do you determine which value is assigned to u and which to v? Or are they interchangeable?

Answers

Answer: They are interchangeable

For example, let's expand out (x+3)*(2x+1). Use of the FOIL rule should get to you 2x^2 + 7x + 3.

Now imaging that you handed 2x^2 + 7x + 3 to a friend to be factored. They do not know the factorization yet.

They would see that a = 2, b = 7, c = 3.

The friend needs to find two numbers u,v such that they multiply to a*c = 2*3 = 6 and add to b = 7

Through trial and error (I recommend making a table of values), your friend would get

u*v = 1*6 = 6u+v = 1+6 = 7

But as you mentioned, your friend could easily swap the order of addition and multiplication to say

u*v = 6*1 = 6u+v = 6+1 = 7

----------------------

If we go with the first option, then the factor by grouping looks like this

2x^2 + 7x + 3

2x^2 + 1x + 6x + 3 ... break up 7x into 1x+6x

(2x^2+1x) + (6x+3) .... group up the terms into pairs

x(2x+1) + 3(2x+1) .... factor each grouping

(x+3)(2x+1) ..... factor out the overall GCF

---------------------

Or we could have the factor by grouping looks like this

2x^2 + 7x + 3

2x^2 + 6x + 1x + 3 ... break up 7x as 6x+1x

(2x^2+6x) + (1x+3)

2x(x+3) + 1(x+3)

(2x+1)(x+3)

(x+3)(2x+1)

We end up with the same factorization.

Convert -2x+6y=-24 to slop intercept form​

Answers

Answer:

y= 1/3x - 4

Step-by-step explanation:

hope this helps

What is the equation of the ellipse with major vertices at (-6, 0) and (6, 0) and minor vertices at (0, 3) and (0, -3)?

Answers

Answer:

b

Step-by-step explanation:

Please help me find the value of x the answer must be exact

Answers

Answer:

[tex]x=11[/tex]

Step-by-step explanation:

This is a 45°-45°-90° triangle. The two legs are the same length, and the hypotenuse is that length times the square root of two:

[tex]leg=x\\hypotenuse=x\sqrt{2}[/tex]

Therefore, the value of x is 11.

You can double-check using the sine ratio:

[tex]sineX=\frac{opposite}{hypotenuse}[/tex]

Insert the values:

[tex]sin45=\frac{x}{11\sqrt{2} }[/tex]

Insert the equation into a calculator:

[tex]x=11[/tex]

:Done

*It's important to know that, when working with trigonometry ratios, the hypotenuse is never considered the adjacent or opposite side, and the 90° angle is never used in the ratios.

please help me my brain is to small for dis I need da right answer

Answers

Answer:

it is in its simpliest form there are no equivalent expressions because all factors are odd numbers

Step-by-step explanation:

pls give me brainliest

If the area of a square table is 392 sq.ft. what is the length of each side?

Answers

Answer:

multiply 392 by 4 that should be your answer

Step-by-step explanation:

I can do your homework for you

Answers

Answer:

thanks for the free points

Step-by-step explanation:

Answer:

can u answer these ones

Step-by-step explanation:

What is the area of the figure below?

Answers

Answer:

3 x 3 = 9 + 3 x 3 = 9 which would be 18, then add 7 and 3 which would be 10 then multiply it by 5 which would be 50 then divided by 2 and you would get 25 add 25 two times which would be 50 once you do, you add the 18 which would be 68 in square.

Step-by-step explanation:

15 pointsss

The wholesale price of a dress at Macy's is $250 before they markup the product by 3/4. Sally, a customer, purchases the dress using a coupon giving her 1/5 off of the dress. How much does she pay after markup and discount is applied?

A. $200
B. $87.50
C. $250
D. $350

Answers

The answer to this question is option B

Tyesha has x feet of wood for a project. She has lengths of wood that are 7 1/2 feet, 5.25 feet, and 6 3/4 feet long. What is the total length of wood she has for this project?

Answers

i’m guessing to just add up all of those numbers and fractions or whatever they are and get the answer and if that don’t work then i don’t know

Please help me with these....or one and explain how to put into calculator please.....

Answers

Answer:

1. x= -20

2. x= 6.33

Step-by-step explanation:

Question 1:

10=7

x=x+6

(Cross multiply)

10(x+6)=7x

10x+60=7x

10x-7x=-60

3x=-60

x=-60/3= -20

Question 2:

6=4

8=x-1

(Cross multiply)

6(x-1)=4×8

6x-6=32

6x=32+6

6x=38

x= 6.33

hope it helps! please mark me brainliest

thank you! have a good day ahead

UMS Grade 7 Math CUA- Unit 4 / 6 of 10
A garment is on sale for 35% off the regular price. If the regular price is $48.80, then what is the sale price?
O A $16.27
O B. $17.08
OC. $31.72
O D. $32.53
PLEASE HURRY IM DOING THE TESTTT NOWWWW

Answers

B because 48.80*0.35=17.08

I need help please

4d + 8

Answers

Answer:

4  ( + 2 )

Step-by-step explanation:

Answer:

i am going to assume 4d+8=0 so 4d=-8 and  d=-2

Step-by-step explanation:

1.
We want to solve the following system of equations using the substitution method.
Equation 1
y = 4x + 17
Equation 2
y = 2x + 7

First solve for x.

Answers

Answer:

2x + 7= 4x + 17

x=−5

Mr. Martin and his son, Luke, decide to walk a 12
kilometer trail. Mr. Martin takes a 1-hour head start and
walks at a pace of 3 km/hr. Explain how fast Luke should
walk to reach the end of the trail in 3 hours, the same time
as Mr. Martin.

Answers

Answer:

4km/h

Step-by-step explanation:

we have the dad walking 3 km per hour but he had a headstart menaing he has 4 hours to do it, 3 times 4 is 12. now we have the son doing 12 kilometers in 3 hours so we divide 12 by 3 meaning he has to be going at a pace of 4 km per hour.

Answer:

It will take Mr. Martin 4 hours to walk the trail, and Luke should walk faster than Mr. Martin. Using the equation 12 = (3)(x), Luke should walk 4 km/hr to finish the trail in 3 hours.

Step-by-step explanation:

This is the sample on Edge.

Hope this helped!! :)

Brainliest?!?!

Stay safe and have a wonderful day/afternoon/night!!!

1. What is the slope of a line that is perpendicular to the x-axis ​

Answers

Answer:

The slope of a line that is perpendicular to the x-axis ​is undefined.

Step-by-step explanation:

We know that the x-axis is a horizontal line.

We also know a line that is perpendicular to the x-axis ​is basically a vertical line.As the slope of a perpendicular line is undefined because no matter what the value of y is, the x-value remains the same.

Therefore, the slope of a line that is perpendicular to the x-axis ​is undefined.

For example, the slope between (1, 2) and (1, 4) is:

Using the slope formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

                 = [4 - 2] / [1 - 1]

                  = 2 / 0

                  = ∞

please help and show work if you can​

Answers

Answer:

7.  x = 5

8. x = 2, y = 6

9. x = 21, y = 39

Step-by-step explanation:

For a parallelogram, the lengths across intersection are equal.

7. For a parallelogram, the lengths across intersection are equal.

So that,

3x = 4x - 5

4x - 3x = 5

 x = 5

8. For a parallelogram, the lengths across intersection are equal.

So that,

2x = 4

x = [tex]\frac{4}{2}[/tex]

x = 2

and

y - 1 = 2y -7

7 - 1 = 2y - y

y = 6

x = 2, y = 6

9. For a parallelogram, opposite angles have equal value.

Thus,

3x = (4x - 21)

3x = 4x - 21

x = 21

and

3y = (y + 78)

3y = y + 78

3y - y = 78

2y = 78

y = [tex]\frac{78}{2}[/tex]

  = 39

y = 39

x = 21, y = 39

someone pls help me 10 points

Answers

y = 2x is the equation

What is the distance between the points? Round to the nearest tenth if necessary

Answers

Answer:

5

Step-by-step explanation:

Pythagorean Theorem States: [tex]x^{2} +b^{2} = c^{2}[/tex]

[tex]3^{2} + 4^{2} = c^{2}[/tex]

9+16=25

[tex]\sqrt{25}[/tex]=5

Paul cut a rectangular piece of paper. He then cut off a semi-circular piece from each end, as shown below. What is the area of the remaining paper? Use 3.14 for

Answers

Step-by-step explanation:

Area of remaining paper

= Area of rectangle - 2 * Area of semicircle

= Area of rectange - Area of circle

= (4in * 8in) - (π * 2in * 2in)

= 32in² - 4πin²

= 19.44in². (A)

Jose has 3/5 kilograms of peppermints and 2/3 kilograms of of candy canes how much candy dose he have

Answers

The answers is 2.793 kilograms

The sales tax for an item was $36.90 and it cost $410 before tax. Find the sales tax rate. Write your answer as a percentage.

Answers

Answer:

36.90/410 = 0.09

0.09 X 100 = 9%

Find x given Circle P.
PLEASE HELP !!!

Answers

Answer:

360 - 60 = 300

x = 300

Step-by-step explanation:

Answer is x=300 thank me later

Please help, thank you! What is the difference between the probabilities of 4/4 and 100%?
(no choices)

Answers

Answer:

There is no difference

Step-by-step explanation:

because they are both equal to a 100% chance of that makes sense

hope that helps:)

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