All Answers 356060 Answers

Let  🔵  = x

Let 🔴 = y

Let ⚪  = z

So....we can write this equation as 

3 [ 100x + 10y  + z]  =  100y + 10y + y

3 [100x + 10y + z ]  = 111y

100x + 10y + z  =  37y

100x + z   = 27y

Then....one possible answer  is if we let  x = 1 and z = 8, then y = 4

100(1) + 8   = 27(4)

108  = 108

So we have that

148  + 148 + 148   =  444

So.....

🔵 = 1

🔴 = 4    and

⚪ = 8

Alan's diagram shows an alternative method.

Drop a vertical from the top point (3,5) onto the horizontal through the bottom point (1, 1),

then the area of the triangle is the area of the triangle 'on the left' plus the area of the

parallelogram 'on the right ' minus the area of the triangle ' at the bottom '.

Here's another way to find this:

The product of the roots  = c / a    ....or in this case, k /a

So....using Melody's answer.......the product of the roots  = 

[ 5 + i√11] / 6   * [ 5 - i√11] / 6    =   [25 - 11* i^2] / 36 =     [25  + 11] / 36   = 36 /36   = 1

So.....

1  = k / a

1 = k / 3  

3 = k

log 28.9  =   about 1.46

The probability is given  by :

C (10, 5) * (1/2)^5 * (1/2)^5  = 63 / 256 =  about    24.6 %

For the first one, we have

a =  log ( 1 + 1/3)   →  log (4/3)    →   log (4) - log (3)   →  log(2^2) - log (3)  =  2log 2 - log (3)

Add  log(3) to both sides

a + log(3) =  2log(2)    

Divide both sides by 2

[ a + log (3) ] / 2    = log (2)

For the second we have

b = log (1 + 1/9)   →  log(10/9)  →  log (10) - log (9)  →    1 - log(3^2)   →   1 - 2log(3)

Add 2log(3)  to both sides  and subtract b from both sides

2log(3) =  1 - b      divide both sides by 2

log (3)   = [ 1 - b ] / 2

ok, the answer is  x^2  - 2x +6. You are being asked what is

(x^3 +x^2 +18)   /  (x+3)

Solve this by comparing co-efficients .....as below

Let  x^3 +x^2 +18 = (x+3)(ax^2 +bx +c)

then a=1,by comparing the co-efficients of x^3

now by comparing co-efficients of x^2,       3a +b =1   so b= -2

and comparing constants, 3c =18    so c=6

which gives

x^3 +x^2 +18 =(x+3)(x^2 -2x +6)

x³ + x² + 18

     x + 3

It's a multiple choice question and none of the choices are fractions...

A.  x² + 2x + -6

B.  x² + -4x + 15

C.  x + 6

D.  x² + 15

E.  x² + -2x + 6

You could write it as  { (x^2-2x+6) }^ (-1), then use the Binomial Theorem to give you an infinite power series,but that's about it. That would also be very messy and long-winded.

Is there a particular problem that you are trying to solve?

Hallo geno and Alan!

An equation

How many real roots does it have:

\(|\frac{1}{x}-\frac{2}{x+1}|=\frac{2}{x}\)

a)Exactly 3 real roots

b)Exactly 2 real roots

c)Exactly 1 real root

d)It doesn't have any real roots

Of course you are right.
The condition "abs" matters:
Without "absolutely" is x = - 1/3,
with the "absolutely" no root.

It applies
d) It does not have any real roots

Greeting asinus :- )

   !

{Are you sure you don't mean log1.5?   Log1.5 → log(3/2) → log3 - log2 → q - p}

log1.25 → log(5/4) → log5 - log(2^2) → log(10/2) - 2log2 → log(10) - log2 - 2log2 → 1 - 3log2 → 1 - 3p.  (Assuming log is log to base 10).

Can also write 

a = log(4/3) → log4 - log3 → log(2^2) - log3 → 2log2 - log3

and

b = log(10/9) → log10 - log9 → 1 - log(3^2) → 1 - 2log3.  (I'm assuming log is log to base 10)

From these you should be able to rearrange to get log2 and log3 in terms of a and b.

No. The slope is -3. Just look for the coefficient of x.

I suppose you mean 5+2x = 17

\(5+2x=17\\2x=12\\x=6\)

\(\text{Do you actually mean }(30 + A) + (10A + B)= 10B\;\text{?}\)

If so we will have to try each positive 1-digit integers.

First substitute A = 1

31 + 1B = B0

B have to be 9 so A = 1 didn't work.

Substitute A = 2

32 + 2B = B0

B have to be 8, so A = 2 didn't work.

Substitute A = 3

33 + 3B = B0

B have to be 7. We did it.

33 + 37 = 70.

B = 7

LOL xD

Hmm.

use graph paper for this question 

bottom 4 (5-1)

side 2 ( 5-3 ) 

side 4 ( 5-1 ) 

 0.5 x 4 x 2 x 4 = 16 m ^2

One way is to find the length of each side using Pythagoras (length^2 = (ya - yb)^2 + (xa - xb)^2)

Then use Heron's formula:  Area = sqrt(s(s-a)(s-b)(s-c)), where a, b and c are the three side lengths and s is (a+b+c)/2

.

Thx

Search Desmos graph plotter

Let a be the shorter diagonal, then b = a + 2 and we have:

a(a+ 2)/2 = 40

or:    a^2 + 2a - 80 = 0

or:  (a + 10)(a - 8) = 0

The only positive solution is a = 8 m, so b = 10 m

A(3+B)= B0

3+B= B0/A

B= (B0/A) - 3

I took your \sqrt to be just sqrt but Alan hs pointed out that you probably meant the answer that our guest gave.  :)

That is

\(\frac{3}{5}\div\sqrt{1-\left(\frac{3}{5}\right)^2}\\ =\frac{3}{5}\div\sqrt{\frac{25}{25}-\frac{9}{25}}\\ =\frac{3}{5}\div \sqrt{\frac{25-9}{25}}\\ =\frac{3}{5}\div \sqrt{\frac{16}{25}}\\ =\frac{3}{5}\div \frac{4}{5}\\ =\frac{3}{5}\times \frac{5}{4}\\=\frac{3}{4}\\\)