proyaop

Combine like terms: -4t^2 + 8t - 15

Use vertex form: -4(t^2 - 2t + 1) - 11

-4(t - 1)^2 - 11      => (h, k) = (1, -11)

Maximum possible value is -11

The range is what makes the domain the domain, and as you can see x/(1 - x) cannot be undefined, or 1 - x cannot be = to 0. Thus the range is:
(-inf, 1) U (1, inf)

You can use the quadratic formula:

\(x = {16 \pm \sqrt{256 - 12}\over2}\)

\(x = {16\pm2\sqrt{61}\over2}\)

\(x = 8\pm\sqrt{61}\)

Number line has length \(2\sqrt{61}\)

A = 2/3

B = some big number above the thousands

C = 8/25

D = some negative number

E = 3*1.414

DCAEB

13 is prime, so we know we can write it as (13x _ _)(x _ _)

17 is also prime so we can guess put it into either one as (13x - 17)(x + 1) or (13x + 1)(x - 17) or (13x - 1)(x + 17) or (13x + 17)(x - 1).

FOILing it out:

(13x - 17)(x + 1) = 13x^2 - 4x - 17

(13x + 1)(x - 17) = 13x^2 - 220x - 17

(13x - 1)(x + 17) = 13x^2 + 220x - 17

(13x + 17)(x - 1) = 13x^2 + 4x - 17

Values of n: -220, -4, 4, 220

You can use vertex form a(x - h)^2 + k, so that the vertex of the parabola is at (h, k) = (12, -4).

a(x - 12)^2 - 4 = y

Plug in 18

a(18 - 12)^2 - 4 = 0

36a = 4

a = 1/9

(x - 12)^2 - 36 = 9y

If y = 0

x - 12 = +-6

The other x - intercept is (6, 0)

Note how AB is vertical on the line x = 3, and CD is also vertical on the line x = -3. What does this mean? It means that ABCD is a trapzoid, with a height of 3 - (-3) = 6. The base AB has length 4, and the base CD has length 3. The area of a trapzoid is (b1 + b2) * h * 1/2. (4 + 3)*6*1/2 = 21

Combine like terms: x^2 + 10x - 20

Manipulate: r^2 + s^2 = (r + s)^2 - 2rs

Vietas formula: r + s = -10, rs = -20

Substitution: (-10)^2 - 2(-20) = 100 + 40 = 140

Assuming that p is not equal to 0 and q is not equal to 0, simplify p*q*3*3*4*2p*q*2*p*q*q^3

Do the variables: p^3 * q^6

The constants: 3*3*4*2*2 = 144

\(144p^3q^3\)

Combine like terms: x^2 + 10x - 20 = 0

r^2 + s^2 = (r + s)^2 - 2rs

Vietas formula: r + s = -10, rs = -20

Plug it in: (-10)^2 - 2(-20) = 100 + 40 = 140