Tutor profile: David F.
How do I factor a quadratic equation of the form ax^2+bx+c=0?
To factor is to "un-FOIL" an equation like this one -- to write it in the form (x+p)(x+q)=0. But how to find p and q? First, look at the "c" term in the original equation. That's the product of p and q. So you've already narrowed it down significantly. Then look at "b." Assuming "a" is 1, b has to be the sum of p and q. So in the case of x^2-22x+96, we know that we're looking for two factors of 96 (bearing in mind that either or both could be negative) that add up to -22. The answer ends up being (x-6)(x-16)=0. Incidentally, this means that the solutions to this equation are 6 and 16, because if you plug in either of those for x, then you're multiplying by zero and you get zero, just like the equation says.
In the science section, what's the difference between the dependent and independent variable in an experiment?
If you don't know the terminology used in scientific experiments, you'll find the science section of the ACT a lot harder than it has to be. The phrase "independent variable" is a bit of a misnomer. It's actually the variable you directly control -- the one you manipulate in order to see what happens. So if you conduct an experiment to see what happens if you turn up the heat, then the temperature is your independent variable. The "dependent variable," on the other hand, is the result you watch for -- the point of the experiment. If you're trying to see if organisms grow faster in high heat, then the organisms' growth is your dependent variable.
I have a system of two equations and two variables. Should I solve it using substitution or elimination?
Good question -- and the answer is, it depends. If one of your variables is already solved for you -- for example, one of the equations is y=x-4 -- then the quickest and easiest thing to do is substitute that into the other equation. On the other hand, if you see that one of the variables has the same coefficient in both equations, or that you can easily make it so by multiplying one of the two equations, elimination is the way to go. For example: 3x-4y=10 5x+4y=22 That -4y, and 4y are screaming out to be eliminated. Add the equations together, top to bottom, and you get: 8x+0=32 8x=32 x=4
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