CPhill

y=2(x-3)(^2) -3

For the form y = a(x-b)^2 ± c

This is an upward turning parabola that has a minimum at (b, -c), i.e. (3, -3)

The domain is all real numbers, while the range is [-3, ∞ )

The Pythagorean Theorem says that the sum of the squares of both legs of a right triangle equals the square of the hypoteneuse......

So

x² + y² = z²      where x, y are the legs and z is the hypoteneuse.......x and y aren't necessarily the same.....and z has to be less than the sum of x and y (by the Triangle Inequality)

(-8,0) and (0,5)

Let's get the slope, first

Subtract the y's    so we have  5 - 0  = 5

Subtractt the x's in the same order    0- (-8)  = 8

Put the first result over the other  .. 5/8 ...  this is the slope = m

Using one of the points - I'll select (-8, 0) -   we can use the point-slope form

y - y1 = m(x - x1)      and using (-8,0) for (x1, y1)

y - 0  =  (5/8)(x - (-8))

y = (5/8)(x + 8)

y = (5/8)x + 5

And there's the equation !!!

Slope-intercept form is     y = mx + b      so we have

y = (-1/7)x + 4/5

(845.5x^15)-(80x^14)-1001=0    ......   multiply through by 2

1691x^15 - 160x^14 - 2002 = 0

88- 3x = 8x + 22       add 3x to both sides

88 = 11x + 22           subtract 22 from both sides

66 = 11x                   divide by 11 on both sides

6 = x

y =  c -  x ² - 2 x; (-1, 3)

So we have

3 = c - (-1)² - 2(-1)

3 = c - 1 + 2

3 = c + 1        subtract 1 from both sides

2 = c

There are infinite possibilities, but here's one:

√(4.7321²) ≈ √22.39277041

I'm making the following assumptions

1) There are 3 spaces for the letters but we can have repeats

2) There are "N" blank spaces

So, the total number of spaces is N + 3

And we want to fill 3 of the spaces with a letter (allowing repeats)......so we have 3³ = 27 ways of choosing the letters.

And the number of arrangements of these blank spaces and letters is just C(n+3, 3),

So the total possibllities are  27*C(n+3, 3)

Let's see how we got that answer.....

"Is" means "equal"

"Of" means "multiply"

"What".....we'll let this be "N"

So we have.....

846 = .76 x N         divide both sides .75

1113.157 ≈ N ≈ 1113.2