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a)  If it is odd...it will be symmetric with the origin

See that this is so, here :  https://www.desmos.com/calculator/jxqiwmmria

b) If it is odd  we will hve the points  (-x, -y)  and (x , y) on the grpah

So   by a table

x         y

-3      -33

3        33

-2       -12

2         12

-1       -3

1         3

c)   If it is odd      

f(-x) = - f(x)

f(-x) = (-x)^3 + 2(-x)  =   -x^3 - 2x     =  - [ x^2 + 2x ] = - f(x)

The slope of the line drawn from the top left vertex of the square to the bottom right vertex of the triangle = -1/2

The equation of this line is    y  = (-1/2)x + 10    (1)

The point at the top vertex of the triangle is  (15, 10)

The slope of the segmnent  joining (10,0)  and (15,10)  =   10/5 = 2

So....the equation of the line joining these two points  is    y = 2(x - 10)  ⇒   y = 2x - 20   (2)

The  x coordinate of the intersection of these lines can be found by setting (1) = (2)

(-1/2)x + 10   =  2x - 20

30 =  [5/2] x

x = 12       and y =    2(12) - 20 = 4

So....the height of the triangular  shaded area = 4     and its base = 10

So...its area =   (1/2)(4) (10)  =   20 units^2

Wait quick question, shouldn't it be \(5a^2-8a<0\) because it's \(b^2-4ac<0\) which comes out to \((3a)^2-4(a^2+2a)\) which is \(9a^2-4a^2-8a=5a^2-8a\) instead of \(5a^2-4a\) ?

2.Let $f(x) = 3x + 2$ and $g(x) = x^2 - 5x - 1.$ Find $f(g(x)).$

f(g(x)  = f(g)    means that we are just subbing    g into   f.....so we have

3 ( x^2 - 5x - 1) + 2         simplify

3x^2 -15x -3 + 2  =

3x^2 -15x  - 1

in 3x+2     put in  x^2-5x-1   for 'x'  and see what you find.....

We will have no real solutions if the discriminant is < 0

So

(3a)^2 - 4(a^2 + 2a)(1) <  0

9a^2 - 4a^2 - 8a < 0

5a^2 -8a < 0       factor

a ( 5a -8) < 0

This will =  0       whenever a = 0    or   a = 8/5

If a > 8 / 5....it will be positive

And if a < 0  it will be positve

So.....the values of a that produce no real solutions are   when a is on the interval (0, 8/5)

Not very good with these, but it might be 1296

f(x) = 2/sqrt(x)      domain is all x that do not result in a denominator = 0

(-inf,0) U (0, + inf) 

f(x - g(x) + h(x)   =   2x^2+3x-9     - 5x-11    +-3x^2+1        gather like terms and simplify

                             - x^2 - 2x -19

No.....the summation calculators can only go so far....so I put in 99999 to 'imitate' infinity....then the calc spits out all of the calculations....

   the result was .9999900000000131      so I think it is safe to THINK/assume   ' 1 ' would be the answer.....

f(3) = 5    g(3) = 16

f(3) + g(3) = 21

The exterior angles add to 360

the interior and exterior angles add to 180     so exterior angle is 60

360 / 60 = 6 sides

try subbing it in formula b^2-4ac < 0 ( this represents when a quadratic formula has no real solution)

then rearrange it 

I know that these geometry questions can be infuriating and I hope someone gives you a helpful hint.     But NOT a solution.

(Although sometimes that is very difficult for answerers to do - I mean it can be difficult to give hints without giving solutions)

Still fully working on this. The area of ABC = \(\sqrt{79251200}\). Try to do something with the angle bisector theorem. Also, if you extend CI to AB at Z, AZ = 2/5 AB

What have you tried?

I'd try using the quadratic formula. The bit under the square must be great or equal to zero or else the answer/s will not be real.

Think of south as negative and north as positve, and since it's distance, you're answer is going to be the absolute value. It goes to -10, then add 8. It's -2, which means 2 miles south. 

Oh ok so that last equation means an infinite number 

thanks 

Here is a big hint.

8 laps  x   1/4 mi/lap = 2 miles 

2 miles = 3219 meters

18 minutes = 1080 s

3219 m / 1080 s = ~~ 2.98 m/s

18 minutes = 18 * 60 =  1080 sec

Distance =   (1/4) * 8 =  2 miles

Convert miles to meters

1 mile  = 1609.344 m

So

2 *1609.344 m /  1080 sec     ≈  2.98 m / s

Thank you so much, sorry I did mean n, thank you!!!