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GIVEN :-

398 , 436 and 542

To Find :-

The largest number

Solution :-

Let’s assume the integer is x

According to the condition given in the question

⇒ XY+7 = 398

⇒  xz+11 = 436

⇒  xk+15 = 542

⇒ xy =391

⇒  xz = 425

⇒  xk = 527

⇒  17 × 23 = 391

⇒  17 × 25 = 425

⇒ 17 × 31 = 527

So, the largest possible integer that will DIVIDE 398,436,542 & leaves reminder 7,11 and 15 respectively was 17.

Step-by-step EXPLANATION:

a is EQUAL to 11 and B is equal to 6

OPTION (d) is irrational.

now lemme tell you what are irrational and RATIONAL numbers and how to identity them.

rational numbers are those numbers which can be represented in the form of p/Q where q ≠ 0 and p and q must be integer.

whereas irrational numbers can't be represented in the form of p/q

terminating, non-terminating recurring numbers can be represented in the form of p/q so they're considered as rational numbers.

but non-terminating non-recurring can't be represented in the form of p/q so they're considered irrational.

here, option (a) is terminating. option (b) and (c) are non-terminating recurring. hence they're rational.

but only option (d) is non-terminating non-recurring. so it's the right option.

Hope my answer helps!!

1) Begin with a greeting, always open your email with a greeting, such as “Dear LILLIAN”...

2) State your purpose. (Subject)

3) Add your closing REMARKS. (conclusion)

4) Add.. (Awaiting for your reply at the EARLIEST....)

5) THANK them ( Yours Truly..)

6) End with a closing.(Mention your name)

ANSWER:

here is your answer

REFER to the ATTACHMENT

Answer:x square+4x+4=0

Step-by-step explanation: From given equation we find alpha+BETA and alpha.beta

Hence finding

alpha+beta=0

alpha.beta=-1

And then we find alpha+beta and alpha.beta from given data

alpha+beta=2ALPHA/beta+2beta/alpha =2alpha square+2beta square/alpha.beta

=2(alpha square+beta square)/-1

=2{(alpha+beta).(alpha+beta)-2alpha.beta}

=2{(0)-2(-1)} /-1

=2(2) / -1

alpha + beta= -4

alpha.beta= 2alpha/beta .2beta/alpha

After simplyfing

alpha.beta=4

Then apply formula of form an quardatic equation

X square - Sx + P=0

X square+4x+4=0 is your answer

ANSWER:

Absolutly =ENGLISH and hindi

Step-by-step EXPLANATION:

HOPE it HELPS you

Answer:

3x3.14/2

=3x1.57

=4.71

Answer:

UNIVERSAL SET = 1,2,3,4,5

let set a = 1,2,3

set b = 2,3

set c = 3,4,5

then (a-b) = 1,2

and (c-b) = 4,5

therefore

(a-b) intersection (c-b) = ()

and (a N c)= 3

therefore (a n c)-b = 0

HENCE PROVED

ANSWER:

Gottfried Wilhelm Leibniz is known as Father of CALCULUS

HOPE IT HELPS YOU❣❣✨✨✌✌

ANSWER:

jijsjjjkdjejjjjwkkjjjjnnsnsnsbshhsjwhhshshsbbsb

ANSWER:

median of 15,6,22,21,9,18,25 is18

Step-by-step EXPLANATION:

FIRST we write in ASCENDING order.then SOLVE it

ANSWER:

all are GREATER than 1/2

none is LESS than 3/4

Maybe it is CORRECT answer.

ANSWER:

Step-by-step explanation:

→ RECIPROCAL of 16/15 is 15/16

→ LET that NUMBER be x

→ so, equation formed

→ 15/16 + x = 48/77

→ x = 48/77 - 15/16

→ x = 48×16/77×16 - 15×77/16×77

→ x = 768/1232  -  1155/1232

→ x = -387/1232

→ so , -387/1232 should be ADDED to the reciprocal of 16/15 to get 48/77.

ANSWER:

SOL : Given : Let ABCD is cyclic QUADRILATERAL. To PROVE : ∠A + ∠C = 180°  and ∠B + ∠D = 180°. Construction : join OB and OD.  Proof : ∠BOD = 2 ∠BAD      ∠BAD = 1/2∠ BODSimilarly ∠BCD = 1/2 ∠DOB ∠BAD + ∠BCD = 1/2∠BOD + 1/2 ∠DOB                   =1/2(∠ BOD + ∠DOB)                   = (1/2)X360° = 180° Similarly ∠B + ∠D = 180°

ANSWER:

the no. is 112

Step-by-step EXPLANATION:

because

7*16=112, so that's why the no. wil ALSO be divisible by 112.

ANSWER:

I have a few THINGS to do but I'm GOING to

ANSWER:

because they LIKE it,.......... fghgddggddtyuj

Answer:

KYU BATAYE ....... main nhi BATA Raha ....

2,16,901,1796,1976,10961

Let the number of students=x, and share of each=y.

So, the FIRST equation:-

xy=1450……(1)

y=1450/x……(a)

Now, 4 students did not come, so each student had to increase their share by ₹ 8.

So, the second equation:-

(x-4)(y+8)=1450

xy+8x-4y-32=1450

xy+8x-4y=1482……(2)

Now, putting the VALUE of eqn (a) in eqn (2):-

x×1450/x+8x-4×1450/x=1482

1450+8x-5800/x=1482

8x²-5800-32x/x=0

8x²-5800-32x=0

-8(-x²+4x+725)=0

-8(-x²+29x-25x+725)=0

-8(-x×(x-29)-25(x-29))=0

-8(-(x-29)(x+25))=0

8(x-29)(x+25)=0

(x-29)(x+25)=0

So, the TWO solutions are:- 29 and -25

But here, we will consider the POSITIVE solution only.

So, x=29……(b)

Now, putting eqn (b) value in eqn (1):-

29×y=1450

y=1450/29

y=50

So, original share per student=₹ 50

Verification:-

•For first equation:

xy=1450……(1)

29×50=1450

1450=1450

So, LHS = RHS, hence verified.

•For second equation:

(x-4)(y+8)=1450

(29-4)(50+8)=1450

25×58=1450

1450=1450

So, LHS = RHS, hence verified.

FIRST ANGLE of a triangle=60

Let the SECOND angle be=3/2x

Let the third angle be=4/2x

sum=180degree(sum of ANGLES of a triangle)

A.T.Q.

60+3/2x+4/2x=180

3/2x+4/2x=180-60

7x/2=120

x=120×2/7

x=140/7

x=20

No these NEGATIVE VALUE is the ADDITIVE INVERSE

Answer:

21 years old

Step-by-step EXPLANATION:

LET the youngest ONE be=x

So accordingly,

x

x+4

x+8

x+12

x+16

The eldest child here is x+16

According to the question,

x+x+4+x+8+x+12+x+16 = 65

5x+40=65

5x=25

x= 25/5 = 5

If x = 5 then the eldest child = x+16= 5+16 = 21

Extra: ALL THE CHILDREN; 5, 9, 13, 17, 21

HOPE THIS HELPS ^_^

ANSWER:

two consecutive positive integer is 9 and 10

Step-by-step explanation:

let the two consecutive positive integers = X , x+1

A.T.Q

x² + (x+1)² = 181

x² + x² + 1 + 2x = 181

2x² + 2x + 1 - 181 = 0

2x² + 2x -180 = 0

2x² + 20x - 18x - 180 = 0

2x(x+10).-18(x+10) = 0

(2x-18)(x+10) = 0

x = 9 or -10

but number is positive integer

so , x = 9

then two consecutive positive integers is 9 and 10

Clear your Q mate PLZ it is not POSSIBLE to read and UNDERSTAND your Q

Answer:

PERIMETER is 8x

Step-by-step EXPLANATION:

LET the width of RECTANGLE = x

then length is = 3x

perimeter of rectangle = 2(l+b)

= 2(3x + x)

= 2 × 4x

= 8x

Answer- here is your answer hope you like it if you have any doubt plz ask me

ANSWER:

RAY have ONE END POINTS

I am taking alpha as x and beta as y for convenience :3

Now onto the question,

COSY cos(2x-y) = cos²x -sin²(x-y)

Taking RHS FIRST,

cos²x-sin²(x-y)

we KNOW, by identity,

cos²a - sin²b = cos(a-b)cos(a+b)

Now, putting this identity in USE in RHS we GET,

cos²x - sin²(x-y)

=>cos(x-(x-y)) cos(x+x+y)

=>cos(x-x+y) cos(2x+y)

=>cos y cos(2x+y) = LHS

Cheers!

ANSWER:

BECAUSE OUR TEACHER TEACH US THAT

xd

(a)0.6bar

p/q=0.66_ _ _ _ _ (1ST EQUATION)

Multiply by 10 on both the sides

10p/q=6.66_ _ _ _ _ (2ND equation)

SUBTRACT equation 1from equation 2

(a - b)³

as we KNOW

(a - b)³ = (a - b) (a - b) (a - b)

= and here by the multiplying TWO (a - b) we get

= a² + b² - 2ab × (a - b)

= a³ - a²b + ab² - b³ - 2a²b + 2ab²

= a³ - b³ - 3a²b + 3ab² ( VERIFIED )

ANSWER:

table answer will be after 11,14,17

Step-by-step EXPLANATION:

I don't KNOW the other answer

ANSWER:

I HOPE it will HELP you.....

SOLUTION:-

Let the one number be 'x'

So, its reciprocal will be 1/x

Now, according to the question.

x + 1/x = 61/30

(x² + 1)/x = 61/30 after cross multiplying, we get

30x² + 30 = 61x

30x² - 61x + 30 = 0

30x² - 36x - 25X + 30 = 0

6X(5x - 6) - 5(5x - 6) = 0

(6x - 5) (5x - 6) = 0

6x = 5

x = 5/6

And,

5x = 6

x = 6/5

So, the numbers are 5/6 and 6/5

Answer.

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Question from Sophia, a parent:

Hello

Please help my son with the solutions to the following:

a) Determine the remainder when 2^2009 + 1 is divided by 17;

b) Prove that 30^99 + 61^100 is divisible by 31;

c) It is known that numbers p and 8p^2+1 are primes. Find p.

Again, your assistance is greatly appreciated.

Thanks

Sophia

Sophia,

a) Determine the remainder when 22009 + 1 is divided by 17;

Look at the remainder when the first 20 or so powers of 2 are divided by 17. You don't need to actually find all the powers:

2,4,8,16,15 [from 16*2=32],13[from 15*2 = 30],9,...

In a while you will see a pattern.

Now use this to answer the question.

b) Prove that 3099 + 61100 is divisible by 31;

Do this in MUCH the same way. Remember that if 3099 has remainder A and 61100 has remainder B, then their sum has the same remainder as A+B does.

c) It is known that numbers p and 8p2+1 are primes. Find p.

Experiment. You will find one answer fairly quickly. But you're not done yet...in math we prove things

What do you notice about all your other values of 8p2+1? (If you are making sensible use of divisibility tests to see if the numbers you get are prime, you may notice something interesting.)

Now prove that this will always happen whenever p is prime. (Hint: this part is why this problem belongs with the other two.)

Good Hunting!

RD

Sophia wrote back

Hello,

Thank you for your suggestions. My son and I have spent time reading through your suggestions and have found that the sequence to the fist part is:, 4, 16, 15, 13, 9, 1. Now we are stuck at this level. What's next?

"the sequence to the fist part is:, 4, 16, 15, 13, 9, 1" ... and this repeats forever with a period of 8.

THUS 21, 29, 217,...,22009 all have the same remainder upon dividing by 17.

The same principle lets you answer the second part easily, and will help with the third part.

-Good Hunting!

RD

How did you come up with the 21, 29, 217,...,22009 ?

Note that the remainder from A multiplied by the remainder from B is equal to the remainder from AB.

28 gave a remainder of 1 when divided by 17, so 29 has a remainder of 2, 210 has a remainder of 4, and so on - the pattern repeats every 8 steps forever.

So if P and Q have the same remainder when divided by 8, 2P and 2Q have the same remainder when divided by 17.

How do we calculate the answer from this?

1 and 2009 have the same remainder when divided by 8, so 21 = 2 and 22009 have the same remainder (=2) when divided by 17.

How will this part of the question assist with the following two parts?

The second problem can be solved using exactly the same ideas (and the obvious fact that "divisible by 31" means "remainder = 0 when divided by 31". The sequence of remainders from 301, 302, 303... divided by 31 is at least eventually periodic [in fact it has period 2 - can you think of an easy way to see this? It may help to think of 30 as "-1" in this context?] So what is the remainder when you divide 3099 by 31? (And so on...)

The third problems needs a couple more ideas. If a _prime_ number is not 3, what can you say about its remainder when divided by 3? [Experiment!] So what can you say about the remainder (upon dividing by

3) from p2? 8p2? 8p2 + 1? And what else does this tell you about 8p2 + 1?

Good Hunting!

RD

However in part A there is a +1 in the equation, what happens to this?

The basic idea here is that remainders can be added, subtracted, or multiplied (and divided when the DIVISOR is prime.) Thus the remainder from dividing 2^2009+1 by 17 is 1 greater than the remainder from dividing 2^2009 by 17 - unless that gives 17, in which case the remainder is 0.

-RD

Hello,

I and my son have EXHAUSTED ourselves in attempting to answer the Divisibility questions, even after your guidens.=0A=0ACan you please provide the answers in order for us to work backwards? My son has guessed part A's answer to be 2, Is this correct?

Your assistance to supply the answers is greatly appreciated.

Kind Regards,

Sophia

2, 29, 217,...,22009 all have remainders of 2 when divided by 17, so 22009+1 has a remainder of 2+1 = 3.

302 = 900 which has a remainder of 1 when divided by 31. So every odd power of 30 has a remainder of 30 when divided by 31, every even power has a remainder of 1.

Powers of 60 (= 1x31+30) have the same pattern of remainders

So 3099 + 61100 has the same remainder as 30+1, which is 0.

"It is known that p and 8p2+1 are primes. Find p."

Experiment shows that (3,73) works. More experiment shows that every other number of the form 8p2+1 is divisible by 3. We try to prove this:

Every prime number q except 3 has a remainder of 1 or 2 when divided by 3. q2 has the same remainder (on dividing by 3) as 12 = 1 or 22 =4 : that is, 1 in each case. 8q2+1 thus has the same remainder as 1x8+1, which is 9. But this is divisible by 3 and cannot be prime. So p=3 is the unique solution.

-RD

About Math Central

Answer:

Step-by-step explanation:

Here, 2/9 > - 4/9 > - 5/9

The denominators of all the fractions are same. But as we know that, NEGATIVE of any smaller number is greater than the negative number greater than that smaller number.

Therefore, the largest number is 2/9 and the LEAST number is - 5/9.

Now, the difference between the larger and the smaller number is : -

[as we know, (-) × (-) = (+)]

Here, both the denominators are same. So, you can directly add the numerators by keeping the denominator same and WRITE it only one time.

Now,

So, the difference between the GREATEST and the least number is

Let x = 1.32( bar on 2)

x = 1.3222............ ------(1)

MULTIPLY EQ 1 by 10

10x =10 × 1.3222

10x = 13.2222…… ------(2)

Multiply eq 2 by 10

10 × 10x = 10 × 13.2222…...

100x = 132.2222…… ------(3)

Subtract eq 2 from 3

100x - 10x =132.2222 - 13.2222

90x = 119

x= 119/90

Let y = 0.35 (bar on 35)

y = 0.353535........ -------(1)

Multiply eq 1 by 100

100y = 35. 353535..... -----(2)

Subtract eq (1) from (2)

100y - y = 35. 353535 - 0.353535

99 y = 35

y = 35 / 99 ----------(3)

GIVEN: 1. 32 (bar on 2) + 0.35 (bar on 35)

x + y

Put the value of x and y from above

= 119 / 90 + 35 / 99

= (119× 11 + 35 × 10) / 990

= (1309 + 350)/990

= 1659/990

= 553/330

Hence, the value is 553/330.

HOPE THIS ANSWER WILL HELP YOU...

sin²30 cos²45+ 4tan²30+1/2sin²90-2cos²90+1/24

=>(1/2)²(1/√2)² + 4(1/√3)² +1/2(1)² -2×0 +1/24

=>1/4×1/2 +4/3+1/2-0+1/24

=>1/8+4/3+1/2+1/24

=>48/24

=>2

Cheers!

Answer:

HEY MATE THE ANSWER IS

62

AS WHEN U WILL ADD 23 AND 39 U WILL GET 62

HOPE THIS HELPS U

MARK MY ANSWER AS BRAINLIEST AND I WILL FOLLOW U PLEASE

XD

Answer:

26117 DIVIDED by 13 is 2009

ANSWER:

(2r - 14)(R + 6)

Step-by-step explanation:

84 - 2r - 2r^2

= 2r^2 -2r - 84

= 2r^2 + 12r - 14r - 84

= 2r(r + 6) - 14(r + 6)

= (2r - 14)(r + 6) ANS

Hope I helped

Answer:

75- 23+41+11

This will HELP U!!

HEY mate here is UR ANSWER ...

..,..............

mark in brain list ..

ANSWER:

the VALUE of COS is

Step-by-step EXPLANATION:

-0.866025404

ANSWER:

NEW vertices of the triangle is

Step-by-step EXPLANATION:

(4,2)->(6,-3)

(-3,5)->(-1,0)

(-2,4)->(0,-1)

Step-by-step EXPLANATION:

I THINK ANSWER is 105

According to me its 105