CPhill

Nice answer AT....!!!

Here's another way.....

Notice that the midpoint "formula" is just ( [x₁ + x₂] / 2 , [y₁ + y₂ ] / 2  )....So, let's suppose we know (x₁, y₁)  and the midpoint - call it (m₁, m₂). Then, to find the other endpoint, (x₂, y₂),  we have (2m₁ - x₁ ,  2m₂ - y₁). The process would work in a similar manner if we were trying to find (x₁, y₁).

Basically, we're just "manipulating" the midpoint formula to find an unknown......!!!!

Hope that helps......

Note the pattern here.......

2⁰  = 1 person knows at 4:15

2¹ =  2 more people know at 4:30

2²  =  4 more people know at 4:45

2³ =  8 more people know at 5:00

  .......and note that the sum of the previous terms is always one less than the last term. Therefore 63 + 2⁶  = 63 + 64 = 127. This implies that, starting at 4:15 PM ......6 "blocks" of 15 minutes (= 90 minutes) are necessary to notify 127 students. So, by 5:45 PM, 127 students are notified. This means that one more 15 minute block will be necessary to notify all 176 students = 6:00 PM

|–7| x |5| + 18 |–6| =

7 x 5 + 18 x 6 =

35 + 108 =

143

OK, Melody...that was going to be my method, too....I just wondered if ND used something else....

Just like this:

(4/5) x (3/2)........then, just hit your Enter key or "=" on the calculator

x^2+2x-1=9    subtract 9 from both sides

x^2 + 2x - 10 = 0

This won't factor, but we do have two real solutions....we can use the onsite calculator to solve or complete the square. The onsite calculator is easier....!!!

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{10}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{11}}}}{\mathtt{\,-\,}}{\mathtt{1}}\\
{\mathtt{x}} = {\sqrt{{\mathtt{11}}}}{\mathtt{\,-\,}}{\mathtt{1}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{4.316\: \!624\: \!790\: \!355\: \!399\: \!8}}\\
{\mathtt{x}} = {\mathtt{2.316\: \!624\: \!790\: \!355\: \!399\: \!8}}\\
\end{array} \right\}$$

-1/4(x-8)+1/8(x+8)=x-5   multiply everything by 8 to clear the fractions

-2(x-8) + (x-8) = 8(x-5)   distribute across the terms in the parentheses

-2x + 16 + x - 8 = 8x - 40    combine like terms

-x + 8 = 8x - 40    subtract 8x, 8 from both sides  

-9x = -48   divide by -9 on both sides

x = 48/9 = 16/3

If f(θ) = 2 sinθ - sin θ/2, find f(π/3)

2sin(π/3) - sin[(π/3)/2] =

2(√3/2) - sin(π/6) =

√3 - 1/2 =

[2√3 - 1] / 2

First....divide both sides by 24...this gives us

4x - 16 = 12  add 16 to both sides

4x = 28   divide both sides by 4

x = 7

I'll second Melody's opinion......very nice......how did you get those screenshots on here???