Melody

It is best to ask just one question at a time.

Learn from the answer or ask questions about it.

THEN

move to the next question if you still need help with it.

\(\begin{align*} y &= 2x^2 + kx + 6 \\ y &= -x + 4? \end{align*}\\~\\ y=2x^2+kx+6\\ -x+4=2x^2+kx+6\\ 0=2x^2+kx+x+6-4\\ 0=2x^2+(k+1)x+2\\ \mbox{If there is to be only one solution, the discriminant must equal 0}\\ \triangle=(k+1)^2-16=0\\ (k+1)^2=16\\ k+1=\pm4\\ \mbox{The only negative solution for k is }\\ k=-5 \)

Here is the graph.  

Thanks to the three of you.  :)

I rather like Mathyeah's answer.  :)

Or        13*1

Maths jokes on a maths site are always a good thing   

Hi Max,

Did you trigger the automated off topic by putting [fun] in square brackets ?

Good thinking Alan :)

Here is another way - I used the calculator.  LOL

(2001^2 - 1992^2) / (2003^2 - 1997^2) = 1.497375

I have never seen a root written like that before but I would say that you are both correct :)

I am not sure how it should be represented but I'd just say   1.05v

the revenue would become     1.05vu = \(1.05*\begin{pmatrix} 1800,\;\; 1200 \end{pmatrix}* \begin{pmatrix} 94300\\ 5200 \end{pmatrix}\)

Find the angle between vectors u and v if u= i + 4j and v= -i+2j. a. 40.60 degrees b. 41.56 degrees c. 39.36 degrees d. 42.01 degrees e. 38.67 degrees

u is in the first quadrant.    Angle with pos x axis is  atan(4/1)

v is in the second quadrant  Angle with pos x axis = 180-atan(2)

angle between them = 180-atan(2)-atan(4)

180-atan(2)-atan(4) = 40.601294645004                     40.60 degrees

However I do not understand why there is an i and a j.  

C = (2/3 -1/4) Find C - 2E

C = 8/12 - 3/12 = 5/12

C-2E = 5/12 - 2E