CPhill

Yep...the diagonal of any parallelogram always divides the parallelogram into two equal triangles....we can prove this with Side-Side-Side congruency......

The diagonal will be common to both triangles, and by definition, the other two respective sides are equal [and parallel]. Thus, the two triangles are congruent.

Using the fact that   a^m * aⁿ = a^m+n, we have

y^2(4y^4+2y-3)  =

4y^6 + 2y^3 - 3y^2

It appears that this is always true, even if we have an obtuse triangle.....see the pic......

The reason for this is that ΔAEF will always have (1/2) the height of ΔABC, and it's base will always be (3/4)  of  ΔABC.

So Area of ΔABC = (1/2)bh = (1/2)(8)(16)  = 64 cm^2

And Area of ΔAEF = (1/2)([3/4]*8)([1/2]*16)  =  (1/2)(6)(8)  = 24 cm^2

y/8 - 3/4 = 7/12     add 3/4 to each side

y/8  = 7/12 + 3/4     get a common denominator on the right

y/8 = 7/12 + 9/12

y/8 =  16/12

y/8 = 4/3      multiply both sides by 8

y = 32/3

LOL!!!....Melody always says that she likes to "complicate" things.....actually, both approaches are good .... the "Rational Zeros" approach is always helpful if it's not immediately obvious how to factor a polynomial [if it's actually capable of being factored, that is ]

Here's another approach:

(x^3-3x^2)-(2x-6)=0     factor  by grouping

x^2(x - 3) - 2(x -3)  = 0

(x^2 - 2) (x - 3) = 0        set each factor to 0  ....     and  we find that x = ±√2, 3

Here's a graph.......

Dragonlance, you usually give good answers.......we mods aren't always correct, either....I seem to remember a few days ago that you spotted one of my errors on a Physics question....!!!!

The second elevation is irrelevent

The third elevation is 94 feet higher than where he began = -418 + 94 = -324  feet

If he descends another 132  feet, we have   -324 - 132 =  -456 feet

Looks like you're OK with your answer  !!!!

We have

[1 + x]/2 = 3                 and                               [ 5 + y] / 2  = -5

                   Multiply both sides of each equation by 2   

1 + x  = 6                                                           5 + y = -10

subtract 1 from each side                                   subtract 5 from both sides

x = 5                                                               y = -15

So....the other point is  (5, -15)

If f(x) = x^2 + 5    and g(x)  = √(1 - x)....then you already have (f/g)(x)