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(1, 4) is correct for the first one

Look at the second graph closely

The function is positive where it is above the x axis

Note that this occurs at  (-4, 0)  and (6, 8 ]

(6,8] is correct

[-6,-4) is not

Any terminating or repeating decmal can aways be written as a rational number

The square root of any non-square will always be irrational

So....tertre is correct

f(x) =  [ 1 + 2x] / x

g(x) = 2 + x

Look at the top graph....when x = 1...plug this value into the functions and find that  ...f(1) = 3   and g(1) = 3

So....this x value is correct....the graphs intersect at (1, 3)

Likewise.....on the graph, when x = -1, plug -1 into both functions and find that....  f(-1) = 1    and g(-1) = 1

So.....this x value is also correct....the graphs also  intersect at (-1,1)

So...the x values are

x = 1

x = -1

To see why the other graph is incorrect....x = 2 , y = 0 appears to be an intersection point 

But f(2)  = 5/2 = y

And g(2) = 4 =y

So...this can't be correct because the y values are different...and both should be = 0

Does this make sense ???

x/y            (x+6)/y  = x/y + 1      and     x/(y+36) = x/y -1      solve these two equations for x and y

                 x+6   = x + y             

                  6 = y                        and    x/(6+36)=x/6  - 1     results in  x=7

original fraction thus equals   x/y = 7/6         

      add 6 to numerator , it increases by 1     add 36 to denominator   7/42 = 1/6    ...it has decreased by 1 

Irrational means it repeats infinitely, but not in repeating blocks, so I believe choice (B) is the answer.

Jenny....It looks like they just want you to select the x values of their intersections

These would be

-1

1

well wouldnt we put them to equal? and that would lead to x=3 and x=1 , so the answer would 3 and 1 ?

(vf - vi)/time = Average acceleration       Vf = velocity final   Vi = velocity initial

(30-0)/40sec  = 3/4 m/s^2

b estimate would be the point on the graph which is closest to parallel to the line drawn from 0,0   to 40, 30

       my estimate is 10 or 11 seconds

You were correct!!!!

THANKS MATH GOD

OK....I guess they are asking for the x values where the graphs intersect

These are

x = 1     and x = -1

Sorry I missed that  !!!

In Heureka's diagram, angle ACB intercepts  diameter  AB

So....the arc that it intercepts = 180°

But...since angle ACB is an inscribed angle interceptng this arc, it has 1/2 of its measure = 90°

So...remember....any inscribed angle intercepting a diameter = 90°

The question actually isnt regrading the graphs its asking

What is the solution to f(x)=g(x) ?

Select each correct answer.

−1

1

2

3

it either -1,1,2,or 3 for the answer

Hello Heureka,

In your solution, one of the (k) factors seems to have randomly evaporated:   

\(\dfrac{3}{2}\cdot \sum \limits_{k=1}^{\infty} \dfrac{1}{\underbrace {k}_{evaporated?}(k+1)} \quad | \quad \boxed{\dfrac{1}{k+1} = \dfrac{1}{k} - \dfrac{1}{k+1} } \\\\ \dfrac{3}{2}\cdot \sum \limits_{k=1}^{\infty} \left(\dfrac{1}{k} - \dfrac{1}{k+1} \right) \\\\\)

I thought you would like to fix this _^fuckup. 

GA

Both B and D are rational

B is just       83587643  /  100,000,000

D is just  1/3

Yep... ...I'd just check the intersection points

On the top graph  the points appear to be ( 1 , -1)  and  (-1, - 3)

So  putting   x = 1 into both functions results  in y = -1

So this is correct

And putting -1 into each function results in y = -3

So....this is also correct

So....we don't even need to check the bottom graph...the top graph has to be the correct one !!!

\(\text{momentum of a given system (excluding friction) is constant, so just pick any time and compute it}\\ \text{we'll pick a time prior to the collision}\\ p = (5~kg)(25~m/s)\hat{i} + (1~kg)(0~m/s) = 125\hat{i}~\dfrac{kg \cdot m}{s}\)

Heureka, where was it stipulated that ABC is a right angle?  I'm going crazy trying to find that.   

im not to sure

if so , wouldnt it then be -1 and 1 for the 2 answers?

clarence is finishing his basement. he needs sheet sof drywall that are 4' by 8' but his doorway is only 85" by 36" wide because of the corners in the stairwell, the sheets of drywall must be carried vertically. Will the drywall fit through the doorway?

The drywall is 8' high, which is 96" so the drywall held upright will not go through the 85" high doorway.

Maybe we could tilt the drywall just a little and use the greater distance from one corner of the doorway to the opposite corner.

Consider the line from one corner to the opposite corner as the hypotenuse of a right triangle with legs 85" and 36".

Using the Pythagorean Theorem:  hypotenuse² = leg² + leg² = 85² + 36² = 8521

The lenght from corner to opposite corner = the square root of 8521 = 92.3

The 96" drywall will not go through the doorway by tilting it either.

You didn't actually provide any of the questions.

Good joke though.