Draw a diagram.
First, draw a rectangle representing the un-cut piece of cardboard.
Label the sides. L and W would be good names (representing the length and width, respectively).
Now draw four dotted lines, representing where the piece of cardboard...

What does Newton's second law say?
It takes a certain amount of net force to accelerate any mass, because according to the first law, objects with mass have an inertia that prefers to stay at rest if at rest and keep traveling at a constant velocity (in a straight line) if in motion...

Hi Joey,
I've subscribed to your question.
I've written my answer as a series of hints, so you can try to use as few of them as possible. Stop reading if a hint gives you a big enough kick-start to finish the problem on your own. If you have an attempt...

I think your second x might have supposed to have been a y. Am I right?
What have you tried so far?
The addition method involves adding one equation to another. If the second x were a y, and you added the two equations together, what would you get on the...

Whenever you multiply a matrix on the left with dimension m * n (m rows and n columns) by a matrix on the right with dimension p*q (p rows and q columns), the rule is:
If you write each matrix's dimensions below it, observe the following.. by thinking about what carrying out the matrix...

First, notice that the series you wrote is
∑ (-3)(n) for n ∈ [0,5]
There is a general formula for the sum of a basic geometric series that you should know or learn.
Here's a hint: How can you simplify the product of (1-x) and a summation, for...

So you need to apply your equation:
T(t) = 35 + 41e-0.058 t
to find T.
They want you to figure out the temperature of the pudding, and they have told you they decided to call it
T.
The notation T(t) means T is a function of t. In...

The NPV of the project cost is 250000.
What is the NPV of a future return?
You have to discount the future returns because of the fact that a dollar today is going to be worth $1.05 next year, 1*(1.05)^2 after two years, and so on. So conversely getting a dollar...

Vivian got off to a great start, but didn't explain any methods for finding the x-intercept.
One way is to manipulate the equation from y = m x + b
to a new form y = m ( x + b/m) by factoring m out of both terms.
For the students who know that
a)...

Well, there isn't enough information to "solve" this equation in the way we usually mean when we say "solve the equation".
Why? What do we usually mean when we say "solve the equation?"
There is only one equation and it contains two variables, "x"...

I don't see a way to solve this question directly and exactly.
There are still several ways to find a solution, though.
Some of the ways are:
a) Graphing two expressions to see where they intersect
b) using Taylor series to expand...

The idea of solving a system by substitution is to eliminate the unknowns by converting some of the equations into a form which can be substituted into the other equation. To do this, you have to:
1) Decide which variable to eliminate and which to solve for (At the end of the...

I'd love to help, unfortunately the first statement is not an equation.
If you meant 3x + 4y = 2x + 3y , the equation represents a line.
I can tell that by seeing that both x and y are multiplied to the first power, in other words there are no terms where either x or y are...

Yes, I have seen this before when viewing the Rocky Mountains of the some of the remote areas of eastern Banff National Park in the west from the area about thirty miles south-east of Red Deer, Alberta, Canada On certain days, you can see the mountains, somewhere between one hundred and two...

Yes, Jim is entirely correct.
I would only augment his answer by pointing out that in general you need to manipulate the parametric equations to eliminate the parametric variable.
It made the most sense to eliminate t by solving the first equation for t,
in this particular...

I think Julia has given a great answer.
I would add that when doing calculations (whether by hand or with a calculator), if you have time, it is often a good idea to do a quick mental check whether your answer seems reasonable by comparing it to what you would expect if you just guessed using...

We are asked to find the value of the expression:
3xy + 2x in the case where x = 2 and y = 3.
This is a case of what I might call "numeric substition for variables". It's a very important skill because it usually comes up at least once in many types...