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3 years ago

What is the fraction for 0.27 repeating?

1 answer:

5 0

It has a fixed method in regards o finding the fraction for 0.27 repeating. Let us now write down the method for you to understand clearly

Let us assume that

x = 0.27272727.....
Now let us multiply both sides by 100 to get a second equation
100x = 27.272727......
Let us now subtract the first equation from the second. We get
100x = 27.272727......
x = 0.27272727....
We get
99x = 27
x = 27/99
= 3/11
From the above deduction, we can conclude that the fraction for 0.27 repeating is 3/11.

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Solve this GCSE question

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Answer:

C 60π cm³

Step-by-step explanation:

1/3 x π x6² x 5

=60π

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Mark all true statements. Group of answer choices

laiz [17]

Answer:

True

False

Step-by-step explanation:

a) The first statement is the basis for Euclid's algorithm to compute the gcd of two nonnegative integers a,b. You can prove this as follows.

Let G=gcd(a,b). Since r=a-bq and G divides a and G divides b, then G divides r. Now, G divides a and G divides r, hence G divides gcd(b,r).

On the other hand, since a=bq+r, and gcd(b,r) divides b and r, then gcd(b,r) divides a. Therefore gcd(b,r) divides a and b, which implies that gcd(b,r) divides G.

x divides y and y divides x implies that |x|=|y|. The GCD's are nonnegative, therefore G=gcd(b,r).

b) It is false. In general, to test for primality of N, you have to check that all primes smaller than N do not divide N. In this case, we have to check for 2,3,5,7,11,13,17,19,23,...

101 is prime, but this may be false in general. For example, consider N=13*11=143. N is not prime, and n is not divisible by 2,3,5, or 7.

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3 years ago

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2 years ago

The diagonal of a square is 8 cm.

VladimirAG [237]

the length of the side of this square is $4\sqrt{2} \:or \:5.65$ cm

Answer:

Solutions Given:

let diagonal of square be AC: 8 cm

let each side be a.

As diagonal bisect square.

let it forms right angled triangle ABC .

Where diagonal AC is hypotenuse and a is their opposite side and base.

By using Pythagoras law

hypotenuse ²=opposite side²+base side²

8²=a²+a²

64=2a²

a²= $\frac{64}{2}$

a²=32

doing square root on both side

$\sqrt{a²}=\sqrt{32}$

a=± $\sqrt{2*2*2*2*2}$

a=±2*2 $\sqrt{2}$

Since side of square is always positive so

a=4 $\sqrt{2}$ or 5.65 cm

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3 years ago

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Solve the following 3 × 3 system. Enter the coordinates of the solution below.

love history [14]

The system is:

i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) –4x – 4y – 2z = 10

the last equation can be simplified, by dividing by -2,

thus we have:

i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5

The procedure to solve the system is as follows:

first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:

i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5

2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.

Equalize:

3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9

similarly, using i and ii, eliminate x:

i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7

multiply the second equation by 2:

i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14

thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:

3y+2z+4=-6y-4z-14
9y+6z=-18

So we get 2 equations with variables y and z:

a) 5y+3z=-9
b) 9y+6z=-18

now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.

Let's use elimination method, multiply the equation a by -2:

a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:

-10y+9y-6z+6z=18-18
-y=0
y=0,

thus :
9y+6z=-18
0+6z=-18
z=-3

Finally to find x, use any of the equations i, ii or iii:

2x – 3y – 2z = 4

2x – 3*0 – 2(-3) = 4

2x+6=4

2x=-2

x=-1

Solution: (x, y, z) = (-1, 0, -3 )

Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:

check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.

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3 years ago

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