The last of my Practice SAT questions.

[Wendybird]

There are just a few more issues I had from the Practice SAT questions I had to skip or got wrong. Since the real tests is now only 9 days away, I figured I'd better just post them all at once, but there's not that many left now

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The first one I guess is just an order of operations question.
"x+3y=180. Solve for x.

x=180-3y
x=3(60-y)

Since y is an integer, it follows that x must be a multiplier of 3."

I follow this as far as x=180-3y, but I don't see what they did to get to x=3(60-y), and I'm not sure where the integer things comes in, although that may be because I didn't write down the question in my notes XD



The second one I mostly understand, but still feel like I'm missing a step that will trip me up on the final test.

"tx+12y= -3 is the equation of a line on the xy plane, and t is a constant. If the slope of the line is -10, solve for t.
Slope intercept form is y=mx+b. So:

tx+12y= -3
12y= -tx-3
y=(t/12)x-(1/4)" <---the things in parenthesis are fractions on my paper. I don't know how to type fractions otherwise. Also, this is the step that confuses me. I get that to get rid of the 12 on one side, both sides are divided by 12, but in the end didn't they only divide the t and 3 by 12, leaving the x? I didn't think it worked that way.

If I skip that step and take their word for it, I understand their reasoning to get the rest of the answer. " If the slope (m) is -10, then (-t/12) must equal -10. Since -120/12= -10, t must equal 120. " But without understanding how that one step works, I can't get the answer again on my own.

The last two are very short. Please excuse my messy replacement for exponents since I don't actually know how to type them.

1 - 500(0.81)^to the 0 power=500. Isn't anything to the 0 power supposed to be 0? And even if it weren't, wouldn't the 0.81 change th number from 500? I don't get this at all.

2 - (2r)^to the 3rd power/cubed = 8r^to the 3rd power/cubed. I understand that 2x2x2=8. But if you've already used the exponent, how is the 8 still cubed??? Obviously I'm missing something???

And that's it for my quandries from the Practice test. I figure even if I understand just a FEW more basic concepts, I can bring that math score up high than the 600 I got before. (Which is the bare minimum I need to get into the university I was eyeing, but I'd really rather get in by more than the skin of my teeth! XD)

 

[wjm11]

1 - 500(0.81)^to the 0 power=500. Isn't anything to the 0 power supposed to be 0? And even if it weren't, wouldn't the 0.81 change th number from 500? I don't get this at all.

2 - (2r)^to the 3rd power/cubed = 8r^to the 3rd power/cubed. I understand that 2x2x2=8. But if you've already used the exponent, how is the 8 still cubed??? Obviously I'm missing something???

1) Any number (except zero) raised to the zero power equals 1.

2) (2r)^3 = (2^3)(r^3) = 8(r^3)

 

[Wendybird]

Thanks to everyone that answered! Somehow, some way, even though I looked at them a few days ago and was still confused a bit, looking at them now, I'm pretty sure I understand all of them. The reasons I kept getting the same questions wrongs again and again was I was trying to solve for the wrong things, the wrong way. Or something like that. But I'm starting to get a grip on the workings of it, thankfully.

@Denis - Anything in quotes is the exact explanation from the SAT practice question, although paraphrased. So they were the ones calling it an integer, and as I said in the post, I probably should have copied the whole question as well as the explanation, but after a 4 hour practice test I was really pushing my patience just to write down all the ones I left blank or got wrong so I could study them, so I skipped a few things...

As for the magically disappearing minus/negative sign, after looking in my notes, that was a typo, sorry. Also the (2r)^3 confusion was just me giving two different names for something like I did in the sentence before this. Apologies. What I was screwing up was considering "2r" to be one number, so I was on applying the cube to the 2, and didn't understand that I was supposed to apply it to the r as well. Hence the 8r^3 answer. And thanks for the google link. I wouldn't have thought to google a rule I had no idea existed. (Anything^0=1)

@wjm11 - Thanks for posting the above mentioned rule and writing out the "simple" simplification. I hadn't understood that they weren't actually dividing the numbers by 3, but instead simplifying it. Which would explain why x didn't get divided by 3 too.

Anyway, the important thing is I understand it now, haha. Thanks again!