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There were some sweets in Bags A, B and C. Tom moved 1/3 of the sweets in Bag A to Bag B. Later, he moved 2/5 of the sweets in Bag B to Bag C. In the end, each bag contained 36 sweets. Find the ratio of the number of sweets in Bags A, B, and C at first.

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3 * 36 = 108

A = 36 + 1/2(36) = 54

B =>           (B + 18) - 2/5(B + 18) = 36     B = 42

C = 108 - (54 + 42) = 12

54:42:12   =   9 : 7 : 2

Hi, Guest! 

BD cannot be 12 !!!          (BD = 9 would work )

Check the numbers, and correct the question, please.

The only way to do this is brute force.

The smallest n that works is 200: 200 = 2^2 + 14^2 = 10^2 + 10^2 = 14^2 + 2^2

https://web2.0calc.com/questions/help_54234#r3

vf = at

44 =  (5) t

44/5 = t = 8.8 hr

\(\ddot x=5\\ \dot x = 5t\\ when\\ \dot x = 44\\ 5t=44\\ t=8.8 \;hours \)

I have not bothered with constants because when t=0, x=0 and v=0

The graphs of 2y + x + 3 = 0 and 3y + ax + 2 = y + 2x are perpendicular. Solve for a.

Hello Guest!

\(y=-\dfrac{x}{2}-1.5\ |\ \color{blue}m_1=-\frac{1}{2}\\ 2y + (a-2)x + 2 = 0\\ y+\dfrac{(a-2)x}{2}+1=0 \)

\(m_2=-\dfrac{1}{m_1}=2\\ \dfrac{a-2}{2}=2\)

\(a=-2\)

  !

How many positive five-digit numbers are divisible by each of 7, 8, 9, 10, and 11?

It must be divisable by  7, 2^3, 3^2, 2, 5 and 11

That is 7,2^3, 3^2, 5 ,11     (the 2 is included in the 2^3)

7*8*9*5*11 = 27720

27720*1=27720

27720*2 = 55440

27720*3=  83160

that is it.

n has 3 divisors, these muct be 1, itself and one other, which means that n is a perfect square (of a prime number)

so

n=a^2 where a is prime

n^3=(a^2)^3 = a^6

This will have 6+1=7 factors (divisors)

Find a/b when 2*log(a - b) = log(a) + log(b).

Hello Guest!

\(2\cdot log(a - b) = log(a) + log(b). \\ (a-b)^2=ab\\ a^2-2ab+b^2=ab\ |\ -ab\\ a^2-3ab+b^2=0\ |\ +\frac{a}{b} \\ a^2-3ab+b^2+\frac{a}{b}=\frac{a}{b} \)

\(\dfrac{a}{b}=\dfrac{a^2b-3a+b^3+a}{b}\\ \color{blue}\dfrac{a}{b}=\dfrac{a^2b-2a+b^3}{b}\\\)

  !

how much is the cosine of pi multiplied by 56 cubed and add 8 to the fourth power?

\((cos\pi)*56^3+8^4\\ =-1*175616+4096\\ =-175616+175616\\ =-171520 \)

A line has a slope of $-\frac{3}{5}$ and its y-intercept is (0,18). What is its x-intercept?

Hello Guest!

\(f(x)=-\dfrac{3}{5}x+18=0\ |\ -18\\ -\dfrac{3}{5}x=-18\ |\ \cdot -\frac{5}{3}\\ x= \dfrac{18\cdot 5}{3}\)

\(x= 30\)

its x-intercept is 30.

  !

You posted them within minutes of each other!

Besides,

If you want to repost you give the address of the original and ask people to answer on the original thread.

n ==9

(1, 3, 9)>>Total = 3 divisors

9^3==729

(1, 3, 9, 27, 81, 243, 729)>>Total = 7 divisors

There are just 3 such numbers:

27720 , 55440 , 83160 , Total =  3

You can't use infinity the same way you'd use a number. 

Just a wild guess, 990? 

how-
for (i) it is \((7/8)x=11424 \)

My thinking:

1)  

  (a)   (i) 9996 (\(11424*\frac{7}{8}\))

         (ii) It is then a consequential error, if you have (i) wrong,

              then you would also have (ii) wrong.

              21420 (\(11424+9996\))

  (b)   (i) rounded to 50.61% (\(\frac{42320}{100}\)) is 423.2 and (\(\frac{21420}{423\frac{1}{5}}\))

  From here I have to go.

Straight

Angles NPM and NZM are congruent!

∠NPM + ∠NZM = 142 degrees