BuilderBoi

\({4\over 3}^3 = {4\over 3}\times {4\over 3}\times {4\over 3} = {64\over 9} = \color{brown}\boxed{7 {1\over9}}\)

\(21\times {1\over3} = \color{brown}\boxed{7}\)

You made a mistake Pavlov, in adding \(-4 -10+10 +4 = 0\).

Thus, \(10a+10b+10c+10d = 0\)

So, \(\color{brown}\boxed{a + b + c+d=0}\)

\(18\) is incorrect. Here is how you solve it:

\({\text {sum}\over n} = 10\)

\(\text {sum} = 10n\)

\({{10n+50}\over {n+2}} = 12\)

\({10n+50} = 12n+24\)

\(50 = 2n+24\)

\(26 = 2n\)

\(n=13\)

Thus, there are \(\color{brown}\boxed{13}\) terms in the original sequence that make for a mean of \(10\), and when the numbers \(20\) and \(30\) are added, the sum becomes \(180\), making the mean \(12\).

\((6a^3+11a^2-4a-9)\over(3a-2) \)

I thought about this problem as factoring. 

At the end, it will be \((3a-2)(xa^2+ya+z) + r\)

In this equation, \(x\), \(y\), and \(z\) are coeficents, and \(r\) is the remainder.

We know that x must equal 2, because \(2a^2(3a-2)=6a^3-4a^2\)

We know that y equals 5, because (note we already have a -4 so it will add to 11): \(5a(3a-2) = 15a^2-10a\)

We know that z must equal 2, because(Note: we already have a -10, so it will add to -4): \(2(3a-2) = 6a-4\).

When we add everything, we have: \(6a^3+11a^2-4a-4\). This means that the remainder is \(\color{brown}\boxed{-5}\), and the quotient is \(\color{brown}\boxed{2a^2-5a+2}\)

I brute forced the problem. \({{6a^3}\over {3a } } = 2a^2\)... and so on, until I found the quotient, which is the trinomial: \(\color{brown}\boxed{2a^2+5a+2}\).

When you multiply this by \(3a-2\), you get: \({6a^3+11a^2-4a-4}\). The remainder to this problem is \(\color{brown}\boxed{-5}\)

(I'll explain it more in-depth in 45 min once I get home.)

The x-value of the vertex can be also be found by doing \(-b\over2a\), in a quadratic equation with the format \(a^2 + bx + c = 0\).

This also yields \(\color{brown}\boxed5\)

The least exterior angle has to be the greatest interior angle. We know that \(\color{brown}\boxed{\angle{P}}\) is the greatest, because it is greater than the sum of the remaining \(2\) angles. 

There are \(4\) times as many daffodils as roses, which means that there are \(45 \times 4 = 180\) daffodils.

The second peice of information tells us there are \(15\) tulips than roses, meaning there is \(45+15=60\) tulips. 

We already know there are \(45\) roses.

We can not solve anymore, because we do not know how many flowers are in a bouquet.

The red line represents the equation \(y=2x+5\).

The bue point represents the point\((6,2)\)

The green line represents the line that is perpendicular to the red line, while crossing the blue point. 

The reflection must be a point on the green line that has an x-intercept at \(-6\) (\(6\) units to the left of the intersection, since the blue point is \(6\) units to the right)

This means that the reflection is at \(\color{brown}\boxed {(-6,8)}\)