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Thank you, CPhill! I will memorize that!

(2x+7)(x-5) = -43 + jx     simplify

2x^2 - 3x - 35  = -43 +   jx

2x^2 -   3x - jx + 8 =  0

2x^2 - (3 + j)x + 8 = 0

If we have only one real root.....the dicriminant must = 0.....so

(3 + j)^2 - 4(2)(8)  = 0

(j + 3)^2 - 64  =  0       factor as a difference of squares

[ (j + 3) - 8 ]   [ (j + 3) + 8 ]  = 0

[ j - 5 ]  [ j + 11]  =  0

Setting both factors to 0  and solving for j  produces 

j = 5    or     j  = -11

So...    -11, 5

Again I ask.

Do you use these resources yourself?  How helpful do you find them ?

Thanks I have added that one to reference material too :)

Thanks, mathtoo......

A function must pass the vertical line test.....that is.....any vertical line drawn on a graph can only cut the graph once

By this criteria...graphs A and D   are functions.....the rest are not

Thank you, CPHill!

x^2 + 6mx + m  =  0

If this has one real root the discriminant  is  0

So...

(6m)^2 - 4m  =  0

36m^2 - 4m = 0

9m^2 - m  =  0            factor

m (9m - 1)  = 0

Setting each factor to 0 and solving for m produces

m =  0       or     m =  1/9

The equation of the line joining  (0, 0) and (1, 2)  is

y = 2x

So  when y = 1.8   x =  .9

The equation of the line joining (1, 2) and (2, 1) is

y = -(x - 1) + 2

y = -x + 3

So.....when y = 1.8

1.8 = - x + 3

-1.2 = -x

1.2 = x

The equation of the line joining (2, 1) and (3, 3)  is

y = 2(x -3) + 3

y = 2x - 6 + 3

y = 2x - 3

When y = 1.8

1.8 = 2x - 3

4.8 = 2x

2.4 = x

I assume you want the sum of the x coordinates when y = 1.8???

If so...we have

.9 + 1.2 + 2.4   =

4.5

\(\text{as }a \text{ and }b \text{ are solutions to }x^2 + ax + b = 0\\ \text{we can write}\\ x^2 + ax + b = (x-a)(x-b) = x^2 -(a+b)x + ab\\ a = -(a+b) \text{ and } b= a b\\ b = -2a\\ b = a(-2a) = -2a^2\\ -2a = -2a^2 \Rightarrow a = 1\\ b = -2a = -2\\ (a,b) = (1,-2) \)

I just read about pretty hard functions, hope I can solve it!!

\(g(x)=f(f(x))=\frac{1}{2x-5}=\frac{1}{2(\frac{1}{2x-5})-5}=\frac{2x-5}{27-10x}\)

Thus, the largest \(x\) not in the domain of \(g(x)\) is .\(\boxed{\frac{27}{10}}.\)

\(2.8-6=\boxed{-3.2}\).

We first go by the exterior angle measure: \(\frac{360}{n}\).

Now, \(n\) has to be a factor of \(360\) , so we count how many factors this number has.

Since \(360=2^3*3^2*5\)\(\) , we add one to each power, resulting in    \(4*3*2=24\) factors.

Finally, a polygon cannot have one or two sides; thus the answer is \(24-2=\boxed{22}\) regular polygons.

Thanks you, CPhill!

This number of miles is given by :

25100 *  (45 /360)  =  3137.5 milies  ≈   3200 miles  (rounded to the nearest 100 miles)

HIt latex and use \frac{2}{3} or what ever numbers you want. \frac{2}{3} becomes \( \frac{2}{3}\).

That is the Product of Sequences symbol, sometimes known as “Big Pi;” it means to multiply.

It’s analogous to the Summation symbol for addition.   

Why did you wait until the eleventh hour to reply? This post is about to lock, and Rom will not be able to answer your question without messaging one of the Moderators to unlock it. That’s a big pain in the ass for all parties.  You are probably not worth the trouble.  If you care enough to ask the question, you should care about the solution enough to ask follow up questions within a reasonable time.

GA

Here is a more extensive "Math Keyboard" :http://usefulwebtool.com/en/math-keyboard.php

 ∑ - This is the capital Greek letter "sigma" for "summation".
∏ - This is the capital Greek letter "Pi" for "Product of"

Rom, I'm not sure what that bold pi looking thing is. Could you explain that?

Substitute \(2x+3=y\) into the first equation!

\(x+19=2x+3-3, x+19=2x, x=19\)

Then 2(19)+3=41, so \((x, y)=(19, 41)\)

You are very welcome!

:P

Thanks guest

I have now worked out exactly what it can do but it does look interesting.

I am sure if could be used by people on this forum.

Do you use it yourself?

I have added this reference to our 'reference material' sticky topic.  (under calculators)

It's the 4th option.

Observing the oblique straight line for x < -2, we see its slope is 1.

Extend the straight line, and it meets y-axis at (0,5).

Therefore when x < -2, f(x) = x + 5.

On the other hand, when x >= -2, it is a horizontal straight line with y-intercept 4. 

Therefore when x >= -2, f(x) = -4.

This is why the 4th option is the answer.