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# How do you figure out the difference of two squares if the numbers aren't square? (answer)

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 following is...

Since Lauren has already provided an excellent answer, although without an illustration, here's one:     ^--  that is a quadrilateral     :) :) :)

# How to solve this word problem with an equation? (answer)

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      / /  /   /------------- Half for Painting     / /  /...

# what is the square root of 58 (answer)

Wyatt, 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 a somewhat...

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) Proof...

# the product of four consecutive even integers es 1680. what are the four numbers? (answer)

Juan, 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 next potential...

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                     2L + 2W = 22                     2(L + W) = 22...

# i need to see how to work a couple of these slope intercepts and parallel and perpendicular problems (answer)

Hi Amber, 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 (x1, y1) Slope-Intercept: y = mx + b We use slope-intercept when we know the slope m and the y-intercept b There is no...

# 4 divided by i (answer)

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 radical in the denominator. A very...

# A gas in a balloon expands from 2L to 3L against 2 atm of pressure, what is the change in temperature relative to the initial temperature? (answer)

The general equation governing changes in fixed-quantity gasses is   P1V1          P2V2 ---------  =  -------    T1            T2 This is what is known as the "combined gas law" because it covers the other known laws with separate names: Boyle's Law - constant temperature...

# Writing a system of equations and solving using elimination or substitution (answer)

Hi Tracy, 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" the...

Test: θ θ θ Θ

# solve triangle. b=14 c=18 angleB=50 degrees (answer)

Maria, 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 of the...

# how do you do algebra (answer)

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 of yours...

# In regards to the big bang heory, where did the matter come from to have the big bang? (answer)

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 Einstein's E=mc2). However, you also...

# how do i find where a function is discontinuous if the bottom part of the function has been factored out? (answer)

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)...

# What is a monomial? (answer)

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.  Thus, x2 + 3x + 2 is a polynomial, and is made...

# my math that i am doing i am having a hard time with +2-4 and its asking me to find the slope on my graph i dont know how to read a graph (answer)

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 two points (X1, Y1) and (X2, Y2) then the formula...

# a recipe calls for 3 cups of flour. all you have in the kitchen is a talespoon. if you need to triple the recipe,how many tablespoons of flour will need? (answer)

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. But when attempting to convert units, there is...

# why cant you divide by zero, wont it just be zero? (answer)

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 ÷ 3 = 2 because...