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Note that \(f(x) = y\). f(x) can also be written as y. 

I answered this question already...

My example was \(f(x) = 2^x\). It is exponential because \(y\) never equals 0, and \(x\)\(\)  and \(y\) can be infinitely large. 

Hope this helps,

- PM

Explanation: If the graph intersects the x-axis, then y must equal 0. We have the equation , \(f(x) = y\)which becomes \(f(x) = 0\). The function will be equal to 0 when the opposite of\(x\) is added to it (when added, cancels out each other to make 0). When x = -3, we can add 3 to make f(x) = 0, and when x = 5, we can subtract 5 to make f(x) = 0. We have our equation for f(x): \(\boxed{f(x) = (x+3)(x-5)}\).

Hope this helps,

- PM

Here is a graph: 

https://www.desmos.com/calculator/0fkbsm68yi

- PM

OK.....what length of pipe is a cubic foot?

pi x r^2 x l = 1

3.14 x 2^2 x l = 1      l = .079577 ft of pipe is a cubic foot

1 foot per second is then    1/.079577 ft^3 of water per second = 12.566 ft^3/sec

12.566 ft^3/sec x 3600 sec/hr x 24 hr = 1,085,734 ft^3/day ~~~ 1,090,000 ft^3 /day

 \(f(x) = 2^x\). The y-coordinate never reaches 0, and the x and y-coordinates can be infinitely large. 

Hope this helps,

PM

The formula to find the axis of symmetry for any parabola is x= -b/(2a) for the quadratic equation of ax^2+bx+c.

(a) Therefore, the formula for the axis of symmetry for this parabola is x= 14/(-2) = -7. The final answer is x=-7.

(b) By top, I am assuming you mean the vertex. Since we know the axis of symmetry, x=-7, we know that the x-coordinate of the vertex of the parabola is -7. Substituting x=-7 into the quadratic equation, we get:

-49+98-53=-4

So, the coordinates for the vertex of the parabola is (-7,-4)

(c) The graph would look like:

Oh, I'm really sorry, I meant ticks. I typed it wrong.

Congratulations CoolStuffYT  

3L/8min    2L/5min     find(lowest) common denominator  (40)

15L/40min      16L/40min         At 40 minutes they will have combined 15+16 = 31 laps

(added 'lowest')

Does Sejes run 100 bar race in 9.58 seconds.....or 9.58 ticks?

ANother perspective;

the situation in the question is described by the following equation:

18/(x-9) = 18/x +4/60      where x = her usual speed in mph   (x-9) = new (slower speed) &  4 minutes = 4/60 hr

solve for x

18 = (18x-162)/x  +4/60x - 4/60(9)

18x = 18x-162  + 4/60 x^2 - 36/60 x

0 = .06667 x^2 -.6x - 162       Use Quadratic Formula to find x = 54 mph

Her new (slower) speed = 54-9 = 45 mph     so the trip will take her   18 m / 45m/hr = .6hr= 24 minutes

First, find the slope    = rise/run = (y1-y2)/(x1-x2) = (5-17)/ (4-8) = (-12)/-4 = 3    

   This is 'a'

  So the line , so far looks like

      y = 3 x + b      Now, let's put one of those x, y points in there to find 'b'

      5 = 3(4) + b

       5-12 = b    b = -7

So the equation for this line is   y = 3x -7      and    a-b = 3-(-7) = 3 + 7 = 10

Thanks for that answer, Neworleans   !!!!!

If we conect WY.....we have an isosceles right triangle.... WY = 4sqrt (2)  = √32

And angle  WYX   = 45.....so angle WYZ = 135 - 45 = 90

So...triangle WYZ is a right triangle with WZ the hypotenuse and  WY a leg

So....by the Pythagorean Theorem     

a =  √ [ WZ^2 - WY^2 ] = √ [ 9^2 - (√32)^2 ] = √ [ 81 - 32 ]  = √49 =  7

good

We have 46+22+319+73=460 people unemployed. In total, we have 1017+649+2715+919+460=5760 people. Thus, \(\frac{460}{5760}*100\approx8\) or (B).

Total in sample  = [ 1017 + 46 + 649 + 22 + 2715 + 319 + 919 + 73 ] =  5760   (1)

Total unemployed   =  [ 46 + 22 + 319 + 73 ]  =  460     (2)

% Unemployed   =   (2)   /(1)   =   460 / 5760   =  7.9%    (round to 8% ) ⇒  "B" 

Let her normal time be  T

Let her normal rate be R

So

RT = D

RT = 18    ⇒   R  =   18/T     (1)

We need to convert 4 minutes to hours  =  4/60   = 1/15 hr

So....when she is slowed we have

(R - 9) ( T + 1/15)  = 18     (2)

Sub   (1)   into (2)   and we have

(18/T - 9) (T + 1/15) = 18      simplify

18 - 9T + (18)/ (15T) - 9/15 = 18     subtract 18 from both sides

 - 9T  + (6)/(5T) - 3/5 =  0       multiply through by -5T

45T^2 - 6 + 3T = 0

45T^2 + 3T - 6  = 0       divide through by 3

15T^2 + T-  2  =   0

(5T + 2) ( 3T - 1)  = 0

The first factor set to 0 and solved  for T produces a negative anser

The second factor set to 0 and solved for T produces   T  =1/3

This is in hrs

So   (1/3) hr   =  20 min   = her normal time to get to work

So....now...at the slowed rate   it takes her 4  minutes longer = 24min

And  24 minutes = 24/60 hrs  = 2/5 hrs

Check

R =  18 / (1/3) = 54mph

And   54mph * 1/3 hr = 18 miles

And at the slower rate

(54 - 9) ( 1/3 + 1/15)

(45) ( 18/ 45)   =  18 miles

Thank you.

A note to ALL forum users.

NEVER delete your question.  It is the height of rudeness!

If you have good reason to edit it that might be ok but ALWAYS indicate very clearly what you have changed.

Thank you.

Sel runs  3/8 lap in one minute

Mar runs 2/5 lap in one minute

So.... Mar runs  (2/5 - 3/8) =  [ 16 - 15] / 40    =  1/40   of a lap farther than Sel does in one minute

So....in 40 minutes....they will be even again

In this time     Sel runs (3/8)*40 = 15 laps

And Mar runs (2/5)*40 =  16 laps

So...combined.....they run 15 + 16   = 31 laps

Sorry, its 3.

You left out the number of times that Sel ran around the track.....

We found this equation as

f(x) = .003(2.04)^x

When x = 15, we have

.003 (2.04)^15   = 132.3 ⇒   C