Daniel posted a good answer.... to complement his answer, I'd also point out that there is a way to factor this even without factoring out the three first. The key is to realize that you don't have to restrain yourself to whole numbers, but you can use
square roots. Thus, the...
Since Lauren has already provided an excellent answer, although without an illustration, here's one:
^-- that is a quadrilateral
:) :) :)
If we let X be the amount of money that Dean had at the start, we can write a single equation like this:
/------------------- Initial amount
/ /------------------ Cab
/ / /---------------- Dinner
Your question is a bit ambiguous.... In the answers below, George has used calculus to iteratively estimate and then drive closer to the answer (this is the fundamental procedure of Newton's method which Robert also demonstrated in the comment-answer).
Roman has provided...
When trying to prove trig identities, it is often helpful to convert TAN functions into SIN/COS functions:
Proof Step 1: Start with the original equation to prove:
tan2x - sin2x = (tan2x)(sin2x)
Proof Step 2: Replace tan with sin/cos
(sin2x/cos2x) - sin2x = (sin2x/cos2x)(sin2x)
I believe that you have copied your problem incorrectly. There are no 4 consecutive EVEN integers that multiply out to 1680.
You can see this for yourself - lets pick the first 4 even integers: 2, 4, 6, 8. The product of these even integers is 384 - too small. The...
This is a problem which defines two different conditions that must be satisfied at the same time, from which we can write two equations.
Condition #1: The perimeter must be 22ft
Equation #1: L + L + W + W = 22
There are two main forms that you can write a line in:
Point-Slope: y-y1 = m(x-x1)
We use point-slope when we know the slope m and a point
Slope-Intercept: y = mx + b
We use slope-intercept when we know the slope m and the y-intercept
Division by complex numbers is handled very much like division by radicals... when there is a radical in the denominator, we "rationalize" it by multiplying both the numerator and the denominator by the radical. This has the effect of "getting rid of"
The general equation governing changes in fixed-quantity gasses is
--------- = -------
This is what is known as the "combined gas law" because it covers...
The first step when converting a word problem to equations is to assign variables to the unknown quantities. In this case, we don't know how many of EACH type of coin she has, although we do know that she has 35 coins total.
So let's assign some variables - we'll call "d"...
Test: θ θ θ Θ
as you say, there is not one unique solution for this triangle. Using Law of Sines, we get:
sin C = 18 * sin(50) / 14 = 0.98491
There are two angles which satisfy this constraint: C = 80.035 and C = 180 - 80.035 = 99.965
From these two answers we can derive the rest...
Well, alaina, this is a very general question, and people spend whole careers on such questions.
At a fundamental level, Algebra is the study of variables - unknown quantities that we would like to solve for.
Here's an example: If you have a certain number of apples, and a friend...
The Big Bang theory posits that matter (and anti-matter) were both created as part of the Big Bang. In other words, matter didn't cause the big bang, matter was produced BY the big bang. This is a result of the equivalence of matter and energy (Albert
There is a simple process for determining discontinuities and zeros of rational functions (that is, a ratio of two polynomial functions):
First, fully factor the numerator and denominator to the smallest order polynomials that have real coefficients. So you should factor x2-4 to (x+2)(x-2)...
Well let's first answer the question of what is a "polynomial". The answer is a sum of terms that are composed of variables and/or constants that are multiplied together, and have non-negative exponents. A "monomial" is just one of these terms.
Another term often used to describe "slope" is "rise over run". What this means is that you choose two points on the graph of a line (any two will do), and you divide their "vertical distance" by their "horizontal distance".
So if you have...
Units (also called "dimensions") are funny things, aren't they?? They actually change the MEANING of the numbers that they are attached to... So "3 cups" is obviously not the same as "3 gallons". It's something most people take for granted.
Without going to the unnecessary point of considering advanced mathematics (calculus and beyond), division is just asking the question "how many times do you have to add the divisor (the number in the denominator) to get the dividend (the number in the numerator)??"
For example, 6...