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4 years ago

14

If you multiply the four-digit number abcd by 4, the order of digits will be reversed. That is, abcd x 4=dcba. The digits a, b,

c and d are all different. Find abcd. That means what numbers are abcd equal to?

2 answers:

kogti [31]4 years ago

6 0

Answer:

The number is 2178, multiplied by 4 gives 8712.

Step-by-step explanation:

Let us say the number is written as abcd $(1000a+100b+10c+d)$ .....(1)

When you multiply it by 4, it gives dcba $(1000d+100c+10b+a)$

Now, $4\times(abcd)=dcba$

We get;

$4000a+400b+40c+4d =1000d+100c+10b+a$

=> $3999a+390b=996d+60c$

=> $1333a+130b= 20c+332d$ ......(2)

Now, we can relate few properties:

The first digit is a quarter of the last one as d=4a .

or $a=d/4$

or $a=0.25d$

The second digit is one less than the first.

$b=(a-1)$

Now, from equation 2, we get

$1333a+130b= 20c+332d$

Replacing b and d, we get

$1333a+130a-130=20c+1328a$

=> $135a=20c+130$

=> $27a=4c+26$

or, $a =(4/27)c+(26/27)$

There is only one single digit integer solution.

c = 7; a = 2

Now,

$b =2-1$ =1 and d =4(2) =8

Hence, 2178 is the number.

And we can see that $4\times2178= 8712$

Arisa [49]4 years ago

5 0

The given is that A B C D <span>x 4 = D C B A
</span><span>
Possible values of A are 1 or 2. It can't be 1 since the </span><span> </span><span>final result A is in unit place and 1 is not possible when we multiply any number by 4
</span><span>
2 B C D x </span><span>4 = </span><span>D C B 2</span>
It is clear above, that D = 8
2 B C 8 x <span>4 = </span><span>8 C B 2</span>
Possible values of B should be 1 or 2
We try B=1

2 1 C 8 x <span>4 = </span><span>8 C 1 2

</span>To find for C, you can use the equation:

(2000+100+10C+8) x 4 = 8000+100C+10+240C = 432-12 = 420
Therefore,

C = 7
So, the number is 2178.

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CaHeK987 [17]

The true statement about Sam’s conjecture is that the conjecture is not correct

<h3>How to determine if Sam’s conjecture is correct or not?</h3>

Sam’s conjecture is given as:

For x ≤ - 2

It is true that x^5 + 7 > x^3.

The inequality x ≤ - 2 means that the highest value of x is -2

Assume the value of x is -2, then we have:

(-2)^5 + 7 > (-2)^3

Evaluate the exponents

-32 + 7 > -8

Evaluate the sum

-25 > -8

The above inequality is false because -8 is greater than -25 i.e. -8 > -25 or -25 < -8

Hence, the true statement about Sam’s conjecture is that the conjecture is not correct

Read more about conjectures at

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2 years ago

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Step-by-step explanation:

These problems make use of three rules of exponents:

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$\left(\dfrac{4mn}{m^{-2}n^6}\right)^{-2}=\left(4m^{1-(-2)}n^{1-6}}\right)^{-2}=\left(4m^3n^{-5}}\right)^{-2}\\\\=4^{-2}m^{-6}n^{10}=\dfrac{n^{10}}{16m^6}$

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<u></u>

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