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2 years ago

Prove algebraically that 0.5 recurring = 5/9

Mathematics

1 answer:

weeeeeb [17]2 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

We require 2 equations with the recurring part after the decimal point.

Let x = 0.555..... → (1)

Multiply both sides by 10, then

10x = 5.555..... → (2)

Subtract (1) from (2) thus eliminating the recurring decimal

(10x - x) = (5.5555 - 0.5555 ), that is

9x = 5 ( divide both sides by 9 )

x = $\frac{5}{9}$

You might be interested in

Which value of x would make ? 1 6 8 10

Liono4ka [1.6K]

Answer:

$x=8\ in$

Step-by-step explanation:

we know that

If NO is parallel to KJ

then

Triangles LNO and LKJ are similar by AA Similarity Postulate

Remember that

If two figures are similar, then the ratio of its corresponding sides is equal

$\frac{LO}{LJ}=\frac{LN}{LK}$

substitute the values

$\frac{x-4}{x-4+x}=\frac{x-3}{x-3+x+2}$

$\frac{x-4}{2x-4}=\frac{x-3}{2x-1}\\ \\(x-4)(2x-1)=(x-3)(2x-4)\\ \\2x^{2}-x-8x+4=2x^{2}-4x-6x+12\\ \\-9x+4=-10x+12\\ \\10x-9x=12-4\\ \\x=8\ in$

3 0

2 years ago

1+1=2 2=2=8 3=3=18 4+4=?

Aloiza [94]

32
Because
1 times 1=1 ,1plus1=2
2 times 2=4,4plus4=8
3 times 3=9,9plus9=18
4times4=16,16plus16=32

4 0

3 years ago

A regular octagonal pyramid. Each side of the base is 6 cm long. it has a height of 10cm. Find the surface area of the pyramid

attashe74 [19]

9514 1404 393

Answer:

470.16 cm²

Step-by-step explanation:

The apothem of the base is used for two purposes: to find the area of the base, and to find the slant height of each face.

The apothem of the base for side length s is ...

s/2 = a·tan(π/8)

a = s/(2·tan(π/8)) ≈ 7.24 cm

The slant height of a triangular face is found using the Pythagorean theorem. The apothem of the base and the height are legs of the right triangle whose hypotenuse is the slant height. For slant height x, we have ...

x² = 10² + a² = 100 +52.46

x ≈ √152.46 ≈ 12.35

The area of the 8 triangular faces will be ...

A = 1/2Px . . . . where P is the perimeter of the pyramid

The area of the base will be ...

A = 1/2Pa

So, the total surface area is ...

A = 1/2P(a + x) = (1/2)(8)(6 cm)(7.24 +12.35 cm) ≈ 470.16 cm²

8 0

3 years ago

Read 2 more answers

zepelin [54]

The question is incomplete. Below you will find the missing figure.

Two friends, Andrew and Liz, are playing a game using this spinner. If the

spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?

A. Yes. Each friend has a 1/4 probability of winning.

B. Yes. Each friend has a 1/6 probability of winning.

C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.

D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.

The correct option is Option A: Yes. Each friend has 1/4 probability of winning.

Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.

P = no. of favorable outcome/ total no. of outcome

Here given in the question,

If the spinner touches region 2 or 3, Andrew wins

If the spinner touches region 4, Liz wins.

This is fair play because both have the same size of region for winning.

If we cut the circle into 8 pieces,

as region 1 is the sum of 2 sub-parts of the circle,

possibility of spinner touching region 1= 2/8= 1/4

possibility of spinner touching the small region = 1/8

So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4

Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4

possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4

Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.

Learn more about the probability

here: brainly.com/question/24756209

#SPJ10

6 0

2 years ago

A taxicab charges $3.00 per person

Delicious77 [7]

Answer:

I believe the answer would be 20 miles max for one passenger.

Step-by-step explanation:

This is because if you create an equation out of this, knowing that only one passenger will be riding, you will get:

$3.00+$1.25x=$28 ($3 added too $1.25 times the number of miles (x) which equals the total amount you have ($28)).

x being the number of miles (so we need to calculate for x)

$3 + $1.25x = $28

-subtract 3 on both sides-

$1.25x=$28-$3

$1.25x=$25

-divide by 1.25 on both sides-

x=$25/$1.25

x=20 miles

Not sure if all calculations are correct, but I hope this helps :)!

6 0

2 years ago