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Answers by John R.

The potential energy of the pinecone before it drops is mgh (given the ground is used as the zero potential energy reference). After if falls the energy is all kinetic energy or (1/2)mv^2 Equating these gives v^2 = 2gh. Note that you can now determine the energy loss due to air friction by the difference...

What is f(x)? (answer)

f(x) is a notation for a "function of x." Usually it is written as f(x)= "something", which is an expression with x as what we call the independent variable. Many times f(x) and y are the same thing. In solving a quadratic equation you are looking for the roots of the expression in the form of a^2...

The x coordinates are measured to the right of origin (or y axis) and y values are measured up from the origin (or the x axis).

First recall the formulas -(a - b) = (b - a) and x^2 + a^2 = (x + a)(x - a). If you rearrange the equation with these formulas in mind you get: 1/(x-3) + 2/(x-3) = 4/[(x + 3)(x - 3)] Now you can add the terms on the left hand side and multiply through by [(x + 3)(x - 3)]. That should give you...

Recall that the square root of a number is a number when squared equals the first number. mathematically if b = sqrt(a) then b^2 = a. So what you are looking for is the square root of 19. It turns out that this is an irrational number (a number continues in its decimal places forever) and usually...

It's always a good idea to check your answer by substituting your solution for x back into the original equation to see if it works. This will give you confidence that you have the right answer or let you know if you need to try again. All professionals will do this. In most practical...

It is a little out of the ordinary for me to see an equation with two equal signs but if we look at the first part (-7x - 2y = 11x - 2y) we can see by adding 2y to both sides that x must equal zero. By substituting x = 0 into a second equation, let's use 11x - 2y = 11 we can get the value for y.

A fraction is simply a division. Think of 7/42 as seven divided by 42. But before you do anything factor the denominator into 6(7). This way the 7's will cancel leaving you with 1/6. From here just do the long division i.e. 1 divided by 6. your answer will be less than 1 so you will have a decimal...

(a = b)^4 is the same as (a + b)(a + b)(a + b)(a + b) carrying out the first product (a^2 + 2ab + b^2)(a + b)(a + b) and keep going (a^3 + 2(a^2)b + ab^2 + ba^2 + 2ab^2 + b^3)(a + b) or (a^3 + 3ba^2 + 3ab^2 + b^3)(a + b) Just carry out the last multiplication being careful with the...

Hi Leanna, I'm going to take a quess at what you are after here. It looks like you are trying to find a number that will allow you to right this expression as a square of another expression in the form of Ax + B. In other words, we want 5x^2 + 11 + Blank = (Ax + B)^2 Let's...

Is f(x) = 4x + .5 ? If so: Just multiply it by itself i.e. (f(x))(f(x)) = (4x + .5)(4x + .5). From here just carry out the multiplication.

9x-4=(4x-4)-5x+4 (answer)

Start by dropping the parenthesis then you will notice the 4s on the right side will cancel. Then add like terms. Get the x terms to one side and the constants to the other (by adding or subtracting the appropriate terms from both sides). Then divide by the coefficient of the x term.

4t+14=6t/5+7 (answer)

Probably the easiest way to approch this one is to first subtract 7 from both sides, multiply through (both sides) by 5, collect like terms, and solve for t.