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1  -x^2 + 4x = 13

     -x^2+4x-13 = 0        simplify things by multiplying by -1 (not NECCESSARY)  and use Quadratic Formula

  x^2-4x+13 = 0  

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)      a = 1    b = -4   c = 13

                                results in   x = 2+-3i

You can try the second one...

7x^2-2x+4 = 0      Quadratic formula    a = 7   b = -2  c = 4

X intercept occurs when y = 0     sub in y=0 to find x intercept

5x -2(0) = 10       x intercept = 2     (2,0)

Y intercept occurs when x= 0     sub in x = 0 to find y-intercept

5(0) - 2y = 10       y intercept = - 5     (0, -5)

Second graph : https://www.desmos.com/calculator/hn25azutsv

Domain : All real numbers

Range : (-inf, 4.848 ]

Rel max at (-1,0)      Global max at  (1.366, 4.848)

Rel min at (-.366, -.48)

End behavior : DOWN on both sides

Inc intervals :  (-inf, -1)   and (-.366, 1.366)

Dec Intervals :  (-1, -.366) and (1.366, inf )

Here is the first graph :  https://www.desmos.com/calculator/tujglplzxg

Domain : All real numbers

Range : All real numbers

Rel max : (-4, 7)

Rel Min : (-4/3, -2.481)

End behavior   :    as f(x) approaches Inf  ....UP

                             as x approaches - inf ....DOWN

Inc intervals   (-inf, -4)   and (-4/3, if)

Dec intervals :  ( -4, -4/3)

Let the first number = x

And the second number  = x + 3

And we know that

2(x + 3) + 4  = 3x     simplify

2x + 6 + 4  =  3x

2x + 10 =  3x

10 =  x   =  the smaller number

first number=x

second number=y

y-3=x

2y=3x-4

Solve. 

2y-6=2x

2y=3x-4

-6=-x+4

-2=x

x=2

NOW FIND Y, IF Y IS SMALLER

I think the problem that you are having is determining which graph is the correct one

Consider the funtion     (7/3)x - 3

This is straight line

Note that when x = 0   then y = -3

So   the line contains the point (0, - 3)

Note that the second graph has to be correct because the straight line contains the point (0, -3)

Notice that the graphs intersect at  x = 0    and x = 3  .....the are the solutions

Does that make sense ???

I like this problem.....!!!

Were you assigned this or did you make it up   ????

Yes, we already know that.

Let's find the slope to   7x + 6y = 17

The slope in the form Ax + By = C  is    -A / B

So....the slope is  -7 / 6

And a perpendicular line to this will have negative reciprocal slope =    6/7  = m

And  if this perpendicular line has a y intercept of 12....the point (0, 12) is on the line = (x1, y1)

So...the equation is

y = m ( x - x1) + y1         fill in what we know

y = (6/7) ( x - 0 ) + 12

y = (6/7)x + 12

Here's a graph : https://www.desmos.com/calculator/oyd29rauvm

Thanks Chris :)

It is the sum of this sequence:

1/(1.2.3) + 3/(2.3.4) + 5/(3.4.5) + 7/(4.5.6) +...............+ (2n - 1) / n(n+1(n+2) = 3 / 4

Yes, you are right! Thank you!

Wolfram|Alpha says to do it using the comparison test.

Here is a video on the comparison test.

Note: I have not wached the video but Khan Academy produces many great video clips.

Great job !!!!

oh so 1 and 9

Look at the table

At  what x values  is f(x) = g(x)  ???

You should find two of them...

Post your  answer and I'll check it   

OK....no prob, EP...

Sorry...CPhill....   I read this as two separate Q's....added a note to my answer....

However.....

g(x)  =   x + 2

But in the second graph

g(x) =  x - 2

So....this graph isn't the correct one

x = 0      and x = 2

These are the solutions

For the second graph....the points of intersection are where  f(x) = g(x)   (whatever f(x) and g(x) are)

  theis occurs at x = -2  and x = +2

sorry forgot to include this but What is the solution to f(x)=g(x) ?

The first graph is correct

The  intersection points are 

x = -1      and

x = 1

3(4x+4)+15x=120       Use distrib property to expand left side

12x + 12 + 15x = 120      Collect the 'x' terms

27x + 12 = 120              subtract 12 from both sides

27x = 108                     divide both sides by 27

x = 4