Hi Melanie,   In this problem, there are two types of terms: two terms with a "p" and one term that's just a number, the 12 on the right. Take the two terms with the p and pull the p out, or factor it.   -10p + 9p = 12 p(-10 + 9) = 12   If...

Hi Brittany,   When you roll a six sided die, there are 6 possibilities. A standard die means that its a fair die, or that the game is fair: all of the sides are equally likely. So, rolling a 2 has to have the same probability as rolling a 1, 3, 4, 5, or 6, so we divide the probability...

Just wanted to point something extra out. This really is just my own personal preference but its something to look out for that I think can make this problem a bit easier. Multiply every term by 10, which is to say the move the decimal places once to the right. (10)0.1(w+0.5) +(10)0...

This is a proportionality problem and you can write out an equation with an unknown if necessary. Problems like this will pop up on tests like the SAT's. The information given says that every 8 kids I talk to, 3 will prefer strawberry. So if I ask 16 kids, 6 will prefer strawberry, and if I ask...

Looks like a typo of some kind. I think it should read f(t) = ∫dτe-(t-τ)sin(τ)dτ, where the integration variable is the Greek letter tau and the first function is an exponential. I'm using tau since in physics torque is usually tau and I guess thats what you mean. But the first function should...

HI Gayla, You have √8 + √2. Now, when simplifying square roots, you want to get all of the perfect squares out of the square root. 2 cannot be written as the square of another integer but 8 = 2 * 22 and that 22 can be pulled outside. √8 + √2 = √(2*22)...

You can think of it like this" -4 = (-1)*4, so -4 * -4 = (-1)(4)(-1)(4) Your common sense about multiplication is stated in the commutative property of multiplication: multiply numbers in any order and you'll get the same answer. (-1)(4)(-1)(4) = (-1)(-1)(4)(4). I just rearranged...

The set of real numbers have a TON of properties depending on your level of expertise. I will point out two important ones: additive and multiplicative closure. If you add two numbers x1 + x2 , you always get a real number x3. You know those word problems that start like "the sum...

Hi Jenah, Think of distribution, when you distribute something to a group of people, you give everyone something. The same thing goes for the distribution property. We take the number outside the parenthesis and distribute, or give to, it to each term in the parenthesis. so 7(t - 4) = 7xt...

First, FOIL the left side. x2 + 2kx + k2 = x2 + ax + a Both sides have a factor of x2 so subtract it to remove it from the equation. 2kx + k2 = ax + a Now, I'm going to move everything over to the left by subtracting ax and a from both sides. 2kx...

Aravind, You have to specify a specific polynomial. There are a few formulas and techniques for specific cubic polynomials.  You can try guessing a root and then use polynomial long division/synthetic division to see if it divides evenly into the polynomial. If the remainder is 0, then...

Hi omar, First, lets make sure we know exactly what we need to find. Three consecutive integers, so there are three unknowns. We could start out by saying that each of these integers needs a label: x1, x2, and x3. But the key piece of information here is the word consecutive, meaning following...

Nope, distribute the x and -1, collect like terms together, and then plug everything into the quadratic formula.  Remember one thing about factoring quadratics: if you're stumped, the quadratic formula is always true.

I had my first child last summer and I would be on my back with a daisy in my hand and little x's over my eyes if it weren't for coffee.

Hi Demarco, I'd like to give you a thorough explanation of how to get the answer so you can understand why the rule Heather stated is true. Imagine you are cutting up a square into equal pieces. The square is a whole and we represent it by 1. If I divide 1 by 1/4, and use the reciprocal...

Ok, this one is a bit tricky to discuss without drawing a figure so bear with me.   The equation of a circle is (x -x0)2 + (y - y0)2 = r2 where (x0, y0) is the location of the circles center. We have three unknowns to find including the radius. Draw a bunch of circles...

Hi Manosh,  I'd like to give you some understanding of what the property is and why we use it.  First, think of a simple example. 3 x 7 = 21. But 7 can be decomposed into 2 + 5 so  3 x 7 = 3 x (2 + 5) = 21 In order for the equation to remain true, we have to...

Hi Elica, I'd like to give you a solution while pointing out something to look for in the future. We have the system x + y = 2    2x - y = -1 Let me move the y in the second equation over to the right and the -1 to the left. x + y = 2    2x + 1 = y Now,...

Think of it as adding two numbers 16 + 1/2 (When you say "16 and a half", using the conjunction and is a way of saying add the two numbers) You can't add them until they have the same denominator. In front of 16 is the implied 1, or 16(1). It may seem silly to write (1) since multiplication...

Jesse, the order doesn't matter. When manipulating equations, the most important thing to remember is that what you do to one side, you must do to the other. However, there is an easy way and a hard way. Let me make this suggestion so that you become comfortable with manipulating equations:...