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10a + b = 43.

The answer is 12.

i got it wrong :(

Sorry, it's not correct.

There are actually 6 stars and 5 bars, as there are 6 of these integers. You should be able to sovle the problem now, Builderboi just made a tiny error. 

thank you so much!

If 3 squares are red, the 5 squares have to be R _ R _ R. 

Can you take it from here?

Let's say we have the expression \(x^2 + 8x + 15\). 

We need 2 numbers that add to 8 and multiply to 15 (5 and 3).

Now, rewrite the expression: \(x^2 + 3x + 5x + 15\) (the order of the 3 and 5 doesn't matter)

Now, factor \(x^2 + 3x \) and \(5x + 15\): \(x(x+3)\) and \(5(x+3)\)

The equation is basically the sum of \(x(x+3) \) and \(5(x+3)\), so it is \((x+5)(x+3)\). (Notice how the constants in both terms are the numbers we chose initially (3 and 5). This can be used as a time saver once you get used to it.)

B - A = 25/3.

sweet thx

210 is incorrect according to the system.

x=3

y=4

what about right triangle ABC?

Does it not say =6 at the end?. On my screen it says u+v+w+x+y+z=6

Wait a minute.  Too late to edit my above.  Does the problem mean she has to buy only as many as she sells?  In that case.  

Price   Number Sold   Income      Cost       Profit

  50           500            25,000     20,000    5,000 

  51           490            24,990     19,600    5,390 

  52           480            24,960     19,200    5,760 

  53           470            24,910     18,800    6,110 

This isn't shaping up like I thought it would. 

We've got to find where it breaks over.   

  60           400            24,000     16,000    8,000  

  69           310            21,390     12,400    8,990 

  70           300            21,000     12,000    9,000  

  71           290            20,590     11,600    8,990 

It looks like the profit maxes out at 300 bouquets at $70 each. 

_.

We can remove 1/x as 1/x would approach 0 when x is approaching infinity.

For any number x, 1^x = 1. So the limit does exist :)

f(x) = (x - r)(x - s)(x - t)(x - u)

f(-2) = (-2 - r)(-2 - s)(-2 - t)(-2-u) = (2 + r)(2 + s)(2 + t)(2 + u).

Solve for f(-2) and you will receive your answer!

What is it specifically asking us to find?

Use the law of cosines, and find the area using Heron's formula.

I'll use Sophie Germain's Identity for this problem and don't think it would be posssible to use the Simon's favorite factoring trick. The Simon's favorite factoring trick is only applicable in:

- Two variable problems

- Degree of no more than 2. 

z^4 + 4(1^4) = (z^2 + 2z + 2)(z^2 - 2z + 2)

You can find the complex roots by using the quadratic formula from there.

For this problem, you can even use Roots of Unity: https://artofproblemsolving.com/wiki/index.php/Roots_of_unity.