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\(\mbox{you've got data points }(x_i, y_i) \mbox{ that you've done a regression on to obtain }\\ \tilde{y}(x) = m x + b \\ \mbox{The standard error of the regression estimate is given by }\\ S = \sqrt{\dfrac 1 N \displaystyle{\sum_{i=1}^N}\left(\tilde{y}(x_i)-y_i\right)^2}\)

there are really only 3 ways to get excluded values

a) you can't divide by 0

b) you can't take the square root of a negative number (over the real numbers)

c) you can't take the log of a non-positive number (over the real numbers)

there are a few other cases, like inverse trig functions but above are the main ones

in this case you have 35x^3 in the denominator.

So if x=0, 35x^3=0, and then you are dividing by 0 which is forbidden.

So the excluded point here is x=0

Rotate 90 counter clockwise about the origin 

\(\begin{array}{rcl} \dbinom{x_p}{y_p}\cdot \begin{pmatrix} \cos{(90)} & \sin{(90)}\\ - \sin{(90)} & \cos{(90)} \\ \end{pmatrix}\\\\ = \dbinom{x_p}{y_p}\cdot \begin{pmatrix} 0&1\\ -1& 0\\ \end{pmatrix}\\\\ =\dbinom{-y_p}{x_p} \end{array} \)

Determine where f(x) intersects the x-axis ( f(x) =0) .

f(x)=x^2+5x+6

\(\begin{array}{rcl} &x^2+5x+6 &=& 0\\ \text{Factorisation }& (x+2)(x+3) &=& 0\\ &x_1 &=& -2\\ &x_2 &=& -3 \end{array}\)

Determine where f(x) intersects the x-axis ( f(x) = 0 ).

f(x)=x^2+9x+18

\(\begin{array}{rcl} &x^2+9x+18 &=& 0\\ \text{Factorisation }& (x+3)(x+6) &=& 0\\ &x_1 &=& -3\\ &x_2 &=& -6 \end{array}\)

can you put brackets in this equation to make it correct: 24/6-2^2-1^2=9

\((~(~24/6-2 ~)^2-1~)^2=9\)

Remember that we can write 8 as 8/1   ....so we have

(1/4) x (8 / 1)   =   8 / 4   =  2

\(((5/2*(2*x-1600)+3)/(sqrt((x^2)-(1600*x)+890000)))=0\\\\ \frac{5/2*(2*x-1600)+3}{\sqrt{x^2-(1600*x)+890000}}=0\\ \mbox{I think that is your question}\\ \mbox{you need to note that the bottom cannot be zero}\\ 5/2*(2*x-1600)+3=0\\ \frac{5}{2}*(2*x-1600)+3=0\\ \frac{5}{2}*(2*x-1600)=-3\\ \frac{5}{\not{2}}*\not{2}(x-800)=-3\\ 5(x-800)=-3\\ x-800=-3/5\\ x-800=-0.6\\ x=800-0.6\\ x=799.4 \)

This is the same as our guests answer :)

now you need to check that this does not make the denominator 0

799.4^2-1600*799.4+890000 = about 250,000  so that is ok :)

x= 799.4

What ARE you doing Sir CPhill !!!

Talk about turning a mole hill into a mountain.

\(a-\frac{4}{5}=12\\ \mbox{add 4/5 to both sides}\\ a=12\frac{4}{5} \)

946 / 1340  ≈ .706  ≈ 70.6%

a - 4/5 = 12      note 12 = 60/5  ... so we have

a - 4/5 = 60/5    add 4/5 to both sides

a = 64/5

Thanks for answering Liza but I think that the question is

\(a-\frac{4}{5}=12\)

Haha! Yes! I did it right.. thanks. I'm taking my math ged test and trying to learn a whole lotta math.. real fast. 

b= -10

5x5=  just the a-4 and 12x5= 60

a-4+4=a

60+4=64

a=64

4sqrt (12)  =

4sqrt(4 * 3)  =

4sqrt(4)*sqrt(3)  =

4 (2) * sqrt (3)  =

8sqrt (3)

Yes it is

but I am really pleased that you have told us of your confusion.  That is how you will learn.

-3 - 6x =9 what is the value of x?

The negative sign (almost) always belongs to the number or term behind it.

so here we have    -3    and  -6 x     and  +9  

Umm..

I will try doing it more slowly.

-3 - 6x =9

First you want the lots of x by itself  so you need to get rid of the 'tacked on' -3 off the left side.

-3+3=0   so you need to add 3 to the left.

BUT if you add 3 to the left then you must add three to the right as well

so you get

-3-6x+3=9+3

-3+3-6x=12

0 - 6x =12

-6x = 12

Now you want the x all by itself so you need to get rid of the -6 from the left hand side.

What does -6x really mean?   it means -6 * x   there is an invisible multiply sign hiding there.   

so

-6*x = 12

x*-6 = 12

Now what id the opposite of multiplying?      Well dividide is !

So if you divide the left side by -6 you will get rid of the -6   BUT

if you divide the lift by minus 6 then you must also divide the right by -6

AND a divide sign is the same as a fraction line

so we have

\(-6x=12\\ -6*x=12\\ x*-6=12\\ \frac{-6x}{-6}=\frac{12}{-6}\\ x=-2\)

(-3)(-5)(2)(-10)

(15)(-20) =

-300

but 6 is not negative...

-3 - 6x =9    add 3 to both sides

-6x  = 12    divide both sides by -6

x = -2

1.5 * F = 180  

Now solve for F (First day)

Can you do that by yourself ?

By the way:

I gave your question preferential treatment because you said "please" - I appreciate good manners.

step by step?

((5/2*(2*x-1600)+3)/(sqrt((x^2)-(1600*x)+890000)))=0

Solve for x over the real numbers:
(3+5/2 (2 x-1600))/sqrt(x^2-1600 x+890000) = 0

Split into two equations:
(x^2-1600 x+890000)^(-1/2) = 0 or 3+5/2 (2 x-1600) = 0

Raise both sides to the power of -2:
x^2-1600 x+890000 = 0 or 3+5/2 (2 x-1600) = 0

Subtract 890000 from both sides:
x^2-1600 x = -890000 or 3+5/2 (2 x-1600) = 0

Add 640000 to both sides:
x^2-1600 x+640000 = -250000 or 3+5/2 (2 x-1600) = 0

Write the left hand side as a square:
(x-800)^2 = -250000 or 3+5/2 (2 x-1600) = 0

(x-800)^2 = -250000 has no solution since for all x on the real line, (x-800)^2 >=0 and -250000<0:
3+5/2 (2 x-1600) = 0

Expand out terms of the left hand side:
5 x-3997 = 0

Add 3997 to both sides:
5 x = 3997

Divide both sides by 5:
Answer: | 
| x = 3997/5

Sorry for being late in answering your question:

1- The monthly payment at 9.50% compounded annually would be =365.88 pounds

2-The monthly payment at 9.50% compounded monthly would be   =367.32 pounds

Remember, once you are asked to make monthly payments, the interest rate is no longer "simple", but compounded.

\(29 = 12n + 5 \\ 24 = 12n \\ 2 = n\)

\(A_{circle} = \pi \left( \dfrac D 2 \right)^2 = \pi (14)^2 = 196 \pi cm^2\\ \mbox{If the circle is inscribed in the box then the box will have side length }D \mbox{ with area }D^2 \\ A_{square} = D^2 = (28)^2 = 784cm^2\)