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When  x = 1 ,  y  =  2(1) - 1³  =  1

So the point  (1, 1)  should be on the graph.

The bottom graph doesn't go through  (1, 1) so it can't be right.

The top graph, the one you have selected, looks right.

And there are two turning points.

CPhill: Please poke some holes in this argument !!.

There are 9C3 =84 possible triangles.

If you divide the nonagon in half by drawing a straight line from any vertex through the center of the nonagon, will have 5 vertices on either side(including the chosen vertex that divided it in two.) Any triangle formed from the 5 vertices on one side and 5 vertices on the other side will not have the center of the nonagon inside it !!

So, we have: 5C3 =10 triangles x 2 =20 triangles that will not contain the center of the nonagon.

84 - 20 =64 triangles that will contain the center of the nonagon. Or:

64 / 84 =76.2% probability. I did this for fun only !!!!!???.

Degree 2  = quadratic

Degree 3  = cubic

Degree 4  = quartic

Degree 5  = quintic

-2x^2  ( -5x^2 + 4x^3 )  =   10x^4 - 8x^5  =  -8x^5 + 10x^4

The legs  = 14 units

The area is the product of the legs  / 2.....so....the area is

[ 14 * 14 ]  / 2  =     196 / 2  =   98 units^2

2x^2 -3x + 2  = 0

a = 2, b  = -3, c =  2

x  =    ( -(-3) ±√[ (-3)^2 - 4(2) (2) ]  ) /  [2*2 ] 

x  =     ( 3 ±√ [ 9 - 16 ]  ) / 4

x =  ( 3 ± i√ 7 )  / 4

Correct choice, NSS  !!!

We want to find the values of  x  that make  y  equal zero.

We want to find what  x  values make this equation true:

0  =  x² + 2x - 8            The right side factors like this....

0  =  (x + 4)(x - 2)         Set each factor equal to zero and solve for  x .

x + 4  =  0          or          x - 2  =  0

     x  =  -4          or                x  =  2

The zeros are  -4  and  2 .

the slope between  (-2, 7)  and  (5, -3)   =   [ -3 - 7 ] / [ 5 - -2 ]   =   -10/7

And since  (3, a)  lies on the same line as those two points, then we know.....

the slope between  (3, a)  and  (-2, 7)   =   -10/7

[ 7 - a ] / [ -2 - 3 ]   =   -10/7

[ 7 - a ] / [ -5 ]   =   -10/7            Multiply both sides by  -5 .

7 - a   =   50/7                           Subtract  7  from both sides.

-a   =   50/7 - 7

-a   =   50/7 - 49/7

-a   =   1/7

The graph touches the  x-axis  one time, so there is one real root, or solution.

This appears to be a variation of the problem posed here: "Mind Your Decisions- Two Circles within a Rectangle.", on YouTube.

Thanks, That really helps!

Each leg is     14√2 / √2   = 14 units

thankk you

Their are  39.37 inches in a meter....there are 12 inches in a foot

So....the number of feet in a meter is    39.37 / 12  ≈  3.28 ft in a meter

So  5.92 m  x   [ 3.28 ]  ≈  19.42 ft

And since 3ft  = 1 yard, we can divide the first result by 3 to get the number of yards in 5.92m  =

19.42  / 3  ≈ 6.47 yards

nvm i do 

$175 x 2 =$350 combined share of 2 companies

$500 - $350 =$150 combined share of other 2 companies.

$175 /$500 =35% share of one company

35% x 2 =70% share of 2 companies

$150/2 =$75 share of one of the remaining 2 companies

$75/$500 =15% percentage share of one of the remaining companies. So that:

15% x 2 =30% percentage share of the two remaining companies. 

So that: 35%^2 + 35%^2 + 15%^2 + 15%^2 =0.29  HH Index.

anyone

i dont get it can you use it in a eqation 

Label the vertices as   {A, B,C,D,E,F,G,and H}

So, we want all the sets that consist of choosing any 3 of the 8 without regard to order...

So 

C (8,3)   =  56  triangles

9.52 Meters is equivalent to:

31.2336 Feet

10.4112 Yards

The probability of choosing a red marble from bag A:  (1/3) x (35/100)  =  7/60

The probability of choosing a red marble from bag B:  (2/3) x (55/100)  =  22/60

The probability of getting a red marble is 29/60.

Getting that red marble from bag A is  7/60 / 29/60  =  7/29.

Getting that red marble from bag B is  22/60 / 29/60  =  22/29.

This is a right triangle.....the circumcenter will be at the midpoint of the hypotenuse

The endpoints of the hypotenuse are (-1, -1)   and (5, 1)

So  the midpoint - and circumcenter -  is   [ ( 5 - 1) / 2 , (1 - 1 ) / 2 ]  =  ( 2 , 0)

3.67 x 5,280 feet x 12 inches =232,531.2 inches to your Grandparents' home.

232,531.2 / 82.6 =~2,815 revolutions of a bicycle's wheel to your Grandparents' home(That is for 1 wheel.)

thanks

From the Pythagorean theorem...

[ distance between (a, 7)  and  (2, 1) ]²   =   [a - 2]²  +  [7 - 1]²

And they tell us that the distance equals  3√5  , so

[  3√5 ]²   =   [a - 2]²  +  [7 - 1]²

45   =   [a - 2]²  +  36

9   =   [a - 2]²

±√9  =   a - 2

± 3   =   a - 2

± 3  +  2   =   a

a  =  3 + 2  =  5          or          a = -3 + 2  =  -1

and

5  +  -1   =   4