KnockOut

Hello! Yet again, this question also has been asked before.

https://web2.0calc.com/questions/a-use-the-fundamental-theorem-of-algebra-to-determine

Thank you!

Hi, this question has been asked before. 

https://web2.0calc.com/questions/factor-the-polynomial-function-over-the-complex-number

Thanks!

For any integer \(n\), \(\dbinom{n}{n}\), or \(nCn\), is equal to 1.

Now in thirty minutes, Kailee would run

\(30 * \frac{2}{5} = \boxed{12}\) laps.

Now for part (b), I'm going to assume that 2.2 and 4.4 are the number of laps, and 11 and 5.5 are the number of minutes (Since that seems the most logical.)

Our slope is \(\frac{2}{5}\).

Therefore, Kailee ran \(\boxed{\frac{2}{5}}\) laps per minute.

Okay. I'm glad you were able to provide me with points instead.

For part (a), our slope is going to incorporate the equatuation \(\frac{y_2-y_1}{x_2-x_1}\). Solving with this equation, we get \(\frac{4.4 - 2.2}{11 - 5.5}\), which simplifies to \(\frac{2.2}{5.5}\), or \(\frac{2}{5}\).

So the answer for part (a) is \(\boxed{\frac{2}{5}}\).

Hi, I would like to help, but snag.gy servers are down for another 2-3 hours. If you need answers to these quick, you might consider providing with me or anyone else two points on the graph so that we can find the slope for you. 

Off-Topic. Thanks!

You can do that on any calculator. Just keep dividing both numerator and denominator until it reaches a point where they cannot be simplified further on.

However, to answer your question,

\(\frac{84}{16} = \frac{42}{8} = \frac{21}{4}\).

So our answer would be \(\boxed{\frac{21}{4}}\). If you wanted it in a mixed number, it would be \(\boxed{5\frac{1}{4}}\).

\({ \sqrt{5x^2+11}} = x + 5\)... you have this equation.

Sqaure both sides to give you \(5x^2 + 11 = (x+5)^2\)

Solving this, we get \(5x^2 + 11 = x^2 + 10x + 25\).

This is equal to \(4x^2 - 10x - 14 = 0\)

Factorizing this equation, we get \((2x-7)(2x+2) = 0\). (You can test that out to see if it matches the previous equation of \(4x^2 - 10x - 14 = 0\).) 

Since \((2x-7)(2x+2)\) has to equal zero, at least one of the brackets need to equal zero for the equation to equal zero. Therefore, we can end up with two solutions.

\(x\) is either \(\boxed{\frac{7}{2}}\), or \(x\) is \(\boxed{-1}\).