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this is not correct.

x * x   IS   x^2   

x squared not x* x

(x *x) / x  = x 

well if it is a conflict of interest between two ideas then try to ask someone about it 

why not ?

Let ( x, y)  be  the coordinates of Q

Using the  mid-point formula  we have

x coordinate of P + x coordinate of Q 

_________________________________   =   x coordinate of  M

                     2

[ 11 + x ]        =       5           multiply both sides by 2

_______

      2

11 +  x  = 10     subtract  11 from both sides

x  =  -1

And  

 y coordinate of P  +  y coordinate of Q     =  y coordinate of M

_________________________________

                      2

[ -10  +  y  ]   =   -  2                multiply both sides by  2

___________

        2

-10 +   y  =  -4          add 10 to both sides

y   = 6

So.... Q =  ( x, y  )  =  ( -1 , 6 )

ya totally its ok to do stuff that you think is important 

We need to know each contractor's rate per hour to answer this....

Where is "The Rate per hour for each Contractor, i.e., the cost in $ per hour"????

E=h x f, where h=Planck's constant, f=frequency

E=[6.63E-34] x [6.8E15] =4.5084 E-18 - Joules - the energy of the photon.

simplify | log(5)/(2 log(5) - log(3)) = log(5)/log(25/3) =~0.7591. Enclose the denominator(on the bottom) in brackets.

I found this definition

"A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x. We can give a general defintion of a polynomial, and define its degree."

This is the definition that I thought was right...

By this definition A and D are NOT polynomials 

100%-68%=32%

SO THE PERCENTAGE I GOT WRONG IS 32!

Present population =PP
Future population =FP
2022 - 2010 =12 years = t
FP =PP x [ 1 + 1.4%]^t
FP =5,655 x [1 + 1.4/100]^12
FP =5,655 x [1.014]^12
FP =5,655 x 1.181559.......
FP =~6,682 - estimated population of the town in 2022

The axis of symmetry can be found at \(x=\frac{-b}{2a}\), and we know that \(x=-3\), so \(\frac{-b}{2a}=-3\). We can now use algebraic manipulation to solve in terms of \(\frac{b}{a}\).

\(\frac{-b}{2a}=-3\\ \frac{b}{2a}=3\\ \frac{b}{a}=6\)

There is a common factor of y in the numerator and denominator of \(\frac{x}{\textcolor{red}{y}}*\frac{\textcolor{red}{y}}{z}\). Thus, it can be canceled out.like Alan showed. \(\frac{x}{y}*\frac{y}{z}=\frac{x}{z} \). 

We know from the given information that \({x \over y}={2 \over 3} \text{ and } {y \over z}={7 \over 5}\). Substitute these values in for \(\frac{x}{y}\text{ and } \frac{y}{z}\). I guess I will rewrite Alan's work:

\(\textcolor{red}{\frac{x}{y}}*\textcolor{blue}{\frac{y}{z}}=\textcolor{green}{\frac{x}{z}}\\ \textcolor{red}{\frac{2}{3}}*\textcolor{blue}{\frac{7}{5}}=\textcolor{green}{\frac{14}{15}}\)

At this point, Alan just took the reciprocal of both sides to get the equation in terms of \(\frac{z}{x}\):

\(\frac{x}{z}=\frac{14}{15}\\ \boxed{\frac{z}{x}=\frac{15}{14}}\)

"I fail to see how the result connects to "x" and "z"...please explain if that's okay?"

The original question asked for the ratio of z to x, and we have found that answer to be 15 to 14. Does that clear it up for you?

Hi Alan,

thanx for the response, but I do not understand..

Why is the result of step 1, equal to \(x \over z\) ?

I fail to see how the result connects to "x" and "z"...please explain if that's okay?

thank you kindly..

Like so:

\(\frac{x}{y}\times\frac{y}{z}=\frac{2}{3}\times\frac{7}{5}\\\frac{x}{z}=\frac{14}{15}\\\frac{z}{x}=\frac{15}{14}\)     

I'd like to see the answer for #2.

I'm consistently getting 3.30828 as the expected number of steps but I could be doing it wrong.

A polynomial function is a term used when there is more than one part to an equation. polynomial, in this case, they all are except A. Becasue D is a binomial and B/C are both trinomials 

Multiply second equation by '3' then add the two equations together to get

10x = 11a       and with x= 3

30 = 11 a       or a = 30/11

Cylinder volume = pi r^2 h

now double r   and triple h

volume = pi (2r)^2 3h = pi 4r^2 3h= 12 pi r^2 h     or 12 times the original volume     12 x 10 = 120 ft^3 (new volume)

Thanks for verification,guest. My professor like to give the student some wired question.He is differently something else and very infamous in my University. He even taught the co-chair of Department of Math & Computer Sicence of my University,so you can imagine his age. I am pretty sure that sample problem in the link is the best and the only sample I can found.Thanks again for your suggestion. 

10 + 12 = 22    SUbtract 22

123422 - 22 = 123400

amc + amc = 1234      amc = 617      6+1+7 = 14