AWQSed

Okay, I actually haven't solved the problem but I quickly noticed some things.

First, we can ignore all horizontal lines (we can't move sideways so thinking about moving left or right isn't exactly correct).

Second, due to ignoring the horizontal lines, we can limit our problem to a rhombus shape (forgive me I don't know how to create diagrams).

Now instead of thinking it as a rhombus shape imagine it as a square (or a 4x4 grid as shown)

Take one corner as the entrance and the opposite corner as the exit and now it's become an easier path problem.

Hope this makes sense.

Thanks

No geno3141 is correct, the problem states to compute the expression when n = 2020, not when the expression equals 2020.

To find the number of terms in an arithmetic sequence we can use formula

\[n = \frac{a_n - a_1}{d}\].

In this case, n is the number of terms in the sequence so \(a_n\) is the last term of the sequence.

\(d\) is the common difference between each term.

Using this formula we plug in the terms we already know \(d = 7, a_n =2008, a_1 = 13 \).

\[n = \frac{2008-13}{7} +1= \frac{1995}{7} +1 = 285 +1 = \boxed{286}\]

hint:

look into Vieta's theorem.

I have answered the question.

We have the equation: \(5x^2+kx=4\) we also know that one root is 2. This means that if we plug in 2 for x the equation should be satisfied.

If we do that we get: \(5(4)+2k=4\) this is simplified to \(k=-8\).

We now plug in the value of k and get: \(5x^2-8x=4\) or \(5x^2-8x-4=0\).

Factoring the quadratic (use the fact that we know that 2 is a root to make it easier) gives us \((x-2)(5x+2)\)

The other root is: \(\boxed{-5/2}\)

Hope you can understand this. :P

Let's take two arbitrary numbers: \(n,m\) therefore we have \(n+m = 6\) and \(nm = 3\).

So we have to find the sum of the reciprocals or: \(\frac{1}n+\frac{1}m \)

Adding them we get: \(\frac{m+n}{nm}\) using the sum and product of the two numbers we can say \(\frac{m+n}{nm} = \frac{6}3 = \boxed{2}\)

20 divided by 1/4 \(= \frac{20}{\frac{1}{4}} = 20 *4 = 80\)

9/10 divide by (-4/5)  \(= \frac{\frac{9}{10}}{\frac{1}{4}} = \frac{9*4}{10*1} = \frac{36}{10} = \frac{18}{5}\) or 3.6