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Look it up in your Textbook, or google it!!.

To find a positive co-terminal angle...add 2pi to 9pi/ 2

So we have   2pi + 9pi/2  =  4pi/2 + 9pi/2  =  13pi/2

To find a negative co-terminal angle....subtract 6pi from 9/pi/2

So we have

9pi/2 - 6pi  =     9pi/2  - 12pi/2  = -3pi/2

You are correct HL.....infinite answers are possible...!!!!

Your answers seem correct, but maybe the question wants a negative angle? (ex. -3π/2 )

Also, this is one of those questions where there are infinite possible answers, so maybe other people just wrote down something different.

Thank you very much!

Here you go RP

Find the slope of MA  = [ 3 -1] / [ 1 - - 1 ]  =  2/2  = 1

Find the slope  RK   =  [3  - - 2] / [ 4 - -1]  = 5/5 = 1

So....since the slops are equal, MA and RK are parallel

Find the distance between  A and R =

sqrt   [ (- 1 - -1)^2 + ( 1 - -2)^2 ]  = sqrt [ 0^2 + 3^2]  sqrt (9)  =  3

Find the distance between M and K

sqrt [ (4 - 1)^2 + (3 - 3)^2 ]  =  sqrt [ 3^2 + 0^2] = sqrt (9) = 3

So AR = MK

So....two opposite sides are parallel   and two  opposite non-parallel sides are equal....so isosceles trapezoid !!!

We need to have  [ since the result inside the radical can't be negative ]

-10x^2 - 11x + 6  ≥  0     (1)     multiply both sides by  -1,  reverse the inequality sign

10x^2 + 11x - 6 ≤ 0      set to 0 and factor

10x^2 + 11x - 6  =  0

(5x -2) ( 2x + 3) = 0

Set each factor to 0 and solve for x

x =  2/5        or    x = -3/2

The intervals that make (1)  true come from either

( -inf, -3/2)    or    [ -3/2, 2/5]     or  (2/5, inf)

Test a point in the middle interval   - I'll pick 0 -  and test it in (1)

If  0, makes it true, then this is the correct interval....so...

-10(0)^2  - 11(0)+ 6  ≥  0        is true

So...you are correct Ant !!!.....the answer is    [ -3/2, 2/5 ]

AE and AD divide sides AB and AB proprtionally

Therefore....DE is parallel to BC

And angle  FAC = angle MAE

And since AF is a transversal cutting parallel lines DE and BC, then angle AME = angle AFC

So.....byAA concruency, triangle AME is simiar to triangle AFC

But since AE = 1/2 AC....then AM = (1/2) AF

And since G is a centroid, then AG = (2/3)AF

Then GM = AG  - AM  =  (2/3)AF - (1/2)AF = (1/6)AF

Therefore   GM : GA  =    (1/6)AF / (2/3)AF =   (1/6) / (4/6) =  1 : 4   

How do i do that though

If you are given a point  x,y    then displacement from the origin is   sqrt(x^2 + y^2)

   Can you be more specific?

Remember that length*width=area, so 1 1/2*x=1 4/5. Try to solve for x!

Exactly! Thanks, CPhill! 

Thank you, guys! I understand now!

First, multiply the first two

(x - 1) ( x + 2)  =    x^2 - 1x + 2x - 2  = x^2 + x - 2

Now,  multiply   

( x^2 + x - 2) (x + 3)

Multiply the  three terms in the parenthses by each of the terms in the second set of parentheses

So we have

x^2 * x  +  x* x  -2*x  =   x^3 + x^2 - 2x       (1)

x^2 * 3 + x*3   -2*3  =  3x^2 + 3x - 6    (2)

Combine (1) and (2)   and we have

x^3 + x^2 + 3x^2 + 3x - 2x - 6  =

x^3 + 4x^2 +1x - 6

Im glad that i could help you :D

Fantastic!! Thank you so much for your help. Hello to the German community!! 

Hi, I hope  I did not missunterstood the question/diagram

my way would be : (Below Age 50) Total number of person = 93 

Probality a customer below the age of 50 would be willing to pay an extra 35 dollars : 38/93 = 0.4086 (*100) = 40.86% 

Hope thats right 

Greets from the german community ;)

Show that two sides are parallel ...they have the SAME slope.

Show that the OTHER two sides are the SAME LENGTH.    Proof !

Here's the way to prove it, RP

AC and BC are the legs 

Show that AC = BC

Then....show that AC is perpendicular to AB

If you need help....let me know

We have the form

y = ax^3 + bx^2 + cx + d

Because f(0) = 0....then d = 0...and we can solve this system

a(-1)^3 + b(-1)^2 + c(-1) = 15

a(1)^3 + b(1)^2 + c(1) = 5

a(2)^3 + b(2)^2 + c(2) = 12          which translates to

-a + b  - c  =  15

a  + b  + c  =   5

8a + 4b + 2c =  12  

Adding the first  two equations produces  2b = 20 ⇒  b = 10

Using the last two  equations, we have

a + 10 + c = 5    ⇒  a + c =  - 5

8a + 40 + 2c = 12 ⇒  8a + 2c = -28 ⇒  4a + c = -14

Multiply the last equation by -1 and add to the frist equation

-4a - c = 14

a + c = 10

________

 -3a = 24   ⇒ a = -3

And a + c = -5 ⇒  c = -2   

So....the polynomial is

-3x^3 + 10x^2 - 2x    factor this and set to 0

x ( -3x^2 + 10x - 2) = 0

We  know that one root is  x = 0   [ this is one x intercept ]

So we need to solve this

-3x^2 + 10x - 2  = 0       multiply through by  -1

3x^2  - 10x + 2 = 0

Using the quadratic formula the other two x intercepts are

5 ±√19

______

     3

Are the legs the SAME LENGTH?

Are their slopes PERPINDICULAR?     m1 = slope and the other is  -1/m1

   THAT proves it....

No prob....I  just answered the last one  a little while ago

So let's dissect this problem, with the info we are given.

The degree of the polynomial is three, which means that there is at most ax^3, a being a coefficient, typically just one.

The problem tells you a set of coordinates, in a different manner. Instead of (x,y)... they give it to you in a statement.

The simplest way to think about this is the template f(x) = y.

OR

Stating if the function plugs in x then it equals y,

OR (how you will hear it most commonly in class)

"f of x" (fancy way of saying f(x) but comes in handy) equals y coordinate.

"If f(-1) = 15" means the ordered pair (-1,15)

"f(1) = 5" means (1,5)

"f(2) = 12" means (2,12)

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The question is asking to find x intercepts which means you'll be factoring your polynomia when you find out what it even... is.

To do this, think of how a graph x^3 is graphed, just for visually plotting all your points.

I'm sure someone else can continue this because, I am short on time.

Hope this helps in some regard c:

P.M. me if you need more assistance, I'm always on my computer and can always use a math break. Except that's oxymoron to what I just mentioned. You get the point. >.>

By a property of medial triangles, each side of the medial triangle will be parallel to one side of its enclosing triangle....and the length of each of the sides of the medial triangle will be (1/2) the length of its respective parallel side....so....this must mean that the perimeter of triangle DEF will be twice that  of the perimeter of  triangle XYZ

And ....by like reasoning.....triangle ABC will have twice the perimeter of triangle DEF

So....the perimeter of ABC   =    5^(2)^2  =  20 units

Thank you for your help! Sorry for late response!