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I agree with BiulderBoi.  

\(\left(1 - \frac12 \right) \cdot \left(1 - \frac13 \right) \cdot \left(1 - \frac14\right) \dotsm \left(1 - \frac {1}{2009} \right) \\=\left(\frac{1}{2}\right) \cdot \left(\frac{2}{3} \right) \cdot \left(\frac{3}{4}\right) \dotsm \left(\frac{2008}{2009} \right) \\=\frac{1}{2009}\)

The rest cancels out.

I feel like there's a way that we can factor out \(1\)from it then multiply the fractions but I have absolutely no idea where to go from there.

Multiply the numerators: \(12x^{3 \over 2} \times 5 \times 2 \times x^{1 \over 2}\times 6x^{32} = 720x^{34}\)

Multiply the denominators: \(3x^{24} \times 2x^{5 \over 2} \times 3x^{7 \over 2} = 18x^{30}\)

So, \({720x^{34} \over 18x^{30}} = \color{brown}\boxed{40x^4}\), just as proyaop found 

14 fl oz per ____? 

g(x) will reflect f(x) across the x axis, intersecting with f(x) at the 2 roots.

h(x) will reflect f(x) across the y axis, intersecting with f(x) at the y interception of f(x).

to see why g(x) and h(x) are reflections of f(x) across the x and y axis respectively, try seeing what happens when you change the input for the 2 functions.

4 years  x  12 months ==48 months

Use this formula to find the FV of 48 payments:

P=300;   R=0.05/12;  N=4*12;    FV=P*((1 + R)^N - 1)/ R

FV ==$15,904.47 - FV of 48 payments of $300 each

Note: I have taken 5% APR as "Compounded Monthly"

Exponents properties!!!

4/x^22.5 * 5/x^2 * 2x^28.5

40x^28.5/x^24.5

40x^4

Because \(x \in (-\infty, 2)\cup(8,\infty)\), we know when x = 2, y = 0 and when x = 8, y = 0. 

So, the quadratic is \((x-2)(x-8) = \color{brown}\boxed{x^2 - 10x + 16}\)

Open up the parenthesis:

2x + 6x - 9 + 8 - 4x - 2x

2x - 1

Divide everything by 4

x^2 + y^2 - 4y - 5 = 0

(x^2) + (y - 2)^2 - 9 = 0

x^2 + (y - 2)^2 = 9

where the diagram?

You can distribute the power to the numerator and denominator: 

(5/7)^3 = (5^3/7^3)

125/343 or 0.36443

e = amount of cholestrol in an egg

c = amount of cholestrol in a cupcake

p = amount of cholestrol in a slice of pizza

e + c + p = 300

Since cupcakes is plural, I will assume cupcakes = 2 "cupcake"

2c + p = 82

2e + c = 568

Adding both of those two equations together, we get

2e + 3c + p = 650

Subtracting the first equation from our new equation, I obtain

e + 2c = 350.

Using elimination, I get

3e = 786

e = 262 

c = 44

We can plug the values of -7 and 2 into the equation and we get -7a + 2b = 3. The slope of a standard form equation is -a/b, and the sloper of x + 3y = -5 is -1/3, so a/b = 1/3, 3a = b. -7a + 2(3a) = 3. -a = 3, a = -3. b = -9.

Thus the value of B - A = -6.

First combine like terms:

x^2 + 9x + 18 = 0 -> (x + 6)(x + 3) = 0.

Either x + 6 or x + 3 = 0 (not both), so x = -6 and x = -3. 

If -6 and -3 are the values of u and v, plugging in we have u/v + v/u, -6/-3 + -3/-6 = 2 + 1/2 = 2.5

Take the average of the x1 and x2 coordinates, and the average of the y1 and y2 coordinates:

Midpoint of PQ = (-1, -6)

First we combine like terms: (I will not be using quadratic formula or a calculator)

x^2 + 6x + 6 = 0 

First we can use sum of cubes a^3 + b^3 = (a + b)(a^2 - ab + b^2). Then we can see by using Vieté's Formula, it will be easy to solve.

The sum of the roots = -6 = a + b

The product of the roots = 6 = ab

a^2 + b^2 = (a + b)^2 - 2ab

a^3 + b^3 = (a + b)[(a + b)^2 - 2ab - ab]

Plugging in the values, we have:

(-6)[(-6)^2 - 2(6) - (6)]

-6(36 - 18)

-6(18)

a^3 + b^3 = -108

Well... the parenthesis are pretty useless, if we remove them it turns from +(-66) to -66. The first and last terms of the expression are 75 and -75. The common difference is 3. So the middle term will be 0. Then we can deduce that every term cancels out, and then the answer is ZERO!!!

The formula for compound interest is A = P(1 + r/100)^nt where A is the answer, P is the principle amount which is 300$, r is the compounded rate, n is the amount of times compounded per year, and t is the number of years.

Plugging in our values we have A = 300(1 + 0.05)^4. The answer is 364.65$