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Solve the following system:
{2 + 4 x + 8 y = -8 + 7 x + 7 y | (equation 1)
-6 + 11 x + 15 y = 180 | (equation 2)

Express the system in standard form:
{-(3 x) + y = -10 | (equation 1)
11 x + 15 y = 186 | (equation 2)

Swap equation 1 with equation 2:
{11 x + 15 y = 186 | (equation 1)
-(3 x) + y = -10 | (equation 2)

Add 3/11 × (equation 1) to equation 2:
{11 x + 15 y = 186 | (equation 1)
0 x+(56 y)/11 = 448/11 | (equation 2)

Multiply equation 2 by 11/56:
{11 x + 15 y = 186 | (equation 1)
0 x+y = 8 | (equation 2)

Subtract 15 × (equation 2) from equation 1:
{11 x+0 y = 66 | (equation 1)
0 x+y = 8 | (equation 2)

Divide equation 1 by 11:
{x+0 y = 6 | (equation 1)
0 x+y = 8 | (equation 2)

x = 6                             and                           y = 8

square root of 5 times by square root of 45

\(\sqrt5*\sqrt{45}\\ =\sqrt5*\sqrt9*\sqrt5\\ =\sqrt{25}*\sqrt9\\ =5*3\\= 15\)

OR just 16+5=21

21/7 = 3 bottles

10 inches per hour

Thanks for the puzzle Hectictar.  That was a good one :)

Why is (2/10)/(-1/5)=-1 and not 0? 2/10=0.2 and -1/5=-0.2, right? I really can't wrap my head around this one..

I will try to answer you but I may not home in on exactly what your problem is so I would very much like you to respond to what I say :)

1)   First   /  is a fraction line which is the same as divide.

for instance

\(2/3=\frac{2}{3 }=2\div 3\)

2)   next, a positive number divided by a negative number is always negative.

\(\frac{2}{-3 }=2\div -3 = -\frac{2}{3}\)

3) Any number (including fractions and decimals) divided by itself is 1

 For example:

       5 divided by 5 means how many 5s go into 5 and the answer is obviously 1

4)  When you divide some number by another then you are cutting the first one into peices.

So if you have a non zero number and you divide it by another number then the answer can NEVER be 0.  That would be impossible!     So the answer definitely cannot be 0.

5) I think you have division and subtraction muddled up.  The 2 are totally different things.

         2 divided by 2 = 1        whereas         2-2=0

NOW

\((2/10)/(-1/5)\\=\frac{2}{10}\div \frac{-1}{5}\\=0.2\div -0.2\\=-(0.2\div0.2)\\=-1\)

Think about all the points I have made. This is a conceptual problem you are having and hopefully what I have written will help you sort it out :)

I do not know what you are asking ://

"Use the identity a²-b²=(a-b)(a+b) to solve the problem:  (3x-2)²=(5x+1)²"

Rewrite as:  (5x+1)² - (3x-2)² = 0

Let a = 5x+1 and b = 3x-2

(5x+1)² - (3x-2)² → (5x+1 - (3x-2))(5x+1 + 3x-2) → (2x + 3)(8x - 1)

so (2x + 3)(8x - 1) = 0

Hence 2x + 3 = 0   giving  x = -3/2

or  8x - 1 = 0  giving  x = 1/8

.

How can i find the end behavior with these two functions?

\(f(x)=\frac{-6x}{3x-5}\\ f(x)=x^2-4x-5\)

\(\frac{-6x}{3x-5}=x^2-4x-5 \)

\(-6x=(x^2-4x-5)\times (3x-5)\\ -6x=3x^3-5x^2-12x^2+20x-15x+25\\ \color{blue}3x^3-17x^2+11x+25=0\)

\(x_1 \approx-.88231\\ x_2\approx 2.1443\\ x_3 \approx 4.4041\\ WOLFRAM\ |\ ALPHA\)

  !

I think you have misunderstood the question guest ://

j is not a complex number.

x^2-3x+2j=0

Solutions for x

\(x=\frac{3\pm\sqrt{9-8j}}{2}\)

The roots will be complex when  the discriminant is negative.

That is

\(9-8j<0\\ 9<8j\\ 9/8 9/8\\ j>1.125\)

So the solutions (for x) of  x^2-3x+2j=0    will be complex if   j>1.125

There is no direct calculation that will give you the annual return for this type of investment. What you have to do is to guess a rate that will equate the PV of all the 10 payment plus the PV of the $300,000 to the purchase price of $100,000. For that purpose, you have to use this formula, or a bunch of them added together like this:
PV = FV / [1 + R]^1 + FV / [1 + R]^2 + FV / [1 + R]^3........FV / [1 + R]^10.
Through repeated iterations of R, you will eventually hone in on the actual rate of return. This is called "Cash Flow Analysis", and the rate you are looking for is called IRR, or "Internal Rate of Return". My computer has this programmed into it and can arrive at an answer almost instantaneously, once you enter all the above income payments plus the $300,000 into it. And it comes up with an annual return of 17.70% over the 10-year period of this investment.

1 gram = 1/1,000 kg

5 grams = 5/1,000 = 0.005 kg.

A truck travels 278 miles each day.

How far does the truck travel in 1 day  ?  278 miles

How far does the truck travel in 2 days?  278 miles  +  278 miles

How far does the truck travel in 3 days?  278 miles  +  278 miles  +  278 miles   =   3 * 278 miles

How far does the truck travel in 4 days?  4 * 278 miles

So....how far does the truck travel in 25 days?

Just multiply them together:

278 x 25 =6,950 miles.

Alright thanks

I replaced your "j" with "i", which is a more commonly used "complex number"

Solve for x:
2 i - 3 x + x^2 = 0

Subtract 2 i from both sides:
x^2 - 3 x = -2 i

Add 9/4 to both sides:
x^2 - 3 x + 9/4 = 9/4 - 2 i

Write the left hand side as a square:
(x - 3/2)^2 = 9/4 - 2 i

Take the square root of both sides:
x - 3/2 = sqrt(9/4 - 2 i) or x - 3/2 = -sqrt(9/4 - 2 i)

Add 3/2 to both sides:
x = sqrt(9/4 - 2 i) + 3/2 or x - 3/2 = -sqrt(9/4 - 2 i)

Add 3/2 to both sides:
x = 3/2 + 1/2 sqrt(9 - 8 i)      or      x = 3/2 - sqrt(9/4 - 2 i)

$7 - $5 =$2 Cost of 1 bottle of olive oil.

$16 - $2 =$14 You are left with this much after you buy the first bottle for $2.

$14 / $7 = 2 More bottles of olive oil that you can buy with your $16. So:

1 + 2 = 3 bottles of olive oil you can buy with $16 and a $5 discount.

Here is option one:

f(x)  =  (x - 1)(x - 3)(x - 5)  =  (x - 1)(x² - 8x + 15)  =  x³ - 9x² + 23x - 15

f(x)  =  x³ - 9x² + 23x - 15

We can multiply the previous polynomial by any number and the resulting polynomial will have the same zeros....I picked  -2. Here is option two:

f(x)  =  -2(x - 1)(x - 3)(x - 5)  =  -2(x³ - 9x² + 23x - 15)  =  -2x³ + 18x² - 46x + 30

f(x)  =  -2x³ + 18x² - 46x + 30

Solve for x:
(3 x - 2)^2 = (5 x + 1)^2

Take the square root of both sides:
3 x - 2 = 5 x + 1 or 3 x - 2 = -5 x - 1

Subtract 5 x - 2 from both sides:
-2 x = 3 or 3 x - 2 = -5 x - 1

Divide both sides by -2:
x = -3/2 or 3 x - 2 = -5 x - 1

Add 5 x + 2 to both sides:
x = -3/2 or 8 x = 1

Divide both sides by 8:
x = -3/2         or          x = 1/8

Yep, you got it!! 

Simplify the following:
b/3 + (2 b)/3 - (5 (b + 1))/6

Put each term in b/3 + (2 b)/3 - (5 (b + 1))/6 over the common denominator 6: b/3 + (2 b)/3 - (5 (b + 1))/6 = (2 b)/6 + (4 b)/6 - (5 (b + 1))/6:
(2 b)/6 + (4 b)/6 - (5 (b + 1))/6

(2 b)/6 + (4 b)/6 - (5 (b + 1))/6 = (2 b + 4 b - 5 (b + 1))/6:
(2 b + 4 b - 5 (b + 1))/6

2 b + 4 b = 6 b:
(6 b - 5 (b + 1))/6

-5 (b + 1) = -5 b - 5:
(6 b + -5 b - 5)/6

Grouping like terms, 6 b - 5 b - 5 = (6 b - 5 b) - 5:
((6 b - 5 b) - 5)/6

6 b - 5 b = b:
(b - 5)/6

Number the sacks from 1 to 10.

Take 1 coin from sack No.1, 2 coins from sack No.2, 3 coins from sack No.3.............to 10 coins from sack No.10. Add them all up: 1+2+3+4..........+10 =55. Anything over 55 such as 55.7 ounces, that simply means that sack No.7 is the fake one, since 7 coins are overweight by: 7 x 0.1 ounces =0.7 of an ounce.