<p>A restaurant has 19 tables that can seat a total of 84 people. Some of the tables seat 4 people and the others seat 5 people. How many tables seat 5 people?</p>
<p>What's the algebraic way to this rather than guess and check?</p>
<p>This is on page 415, number 6 of BB2, so if you need to see the diagram you can go but I don't think you need to.</p>
<p>In the xy-plane above, the equation of line l is x+3y=12. Which of the following is an equation of a line that is perpendicular to line ?
a) y=X+2
b) y=-3x+2
c) y=3x-6
d) y=(1/3) x+6
e) y= - (1/2)x-3</p>
<p>The equation of line l when put in y=mx+b form was peculiar and that got me confused. </p>
<h1>16</h1>
<p>A four-digit integer, WXYZ, in which W X Y Z each represent a different digit, is formed according to the following rules.
1. X=W+Y+Z
2. W=Y+1
3. Z=W-5
What is the four-digit integer?</p>
<p>Once again what's the more "algebraic" way to do this other than plugin from knowing that each digit can't be greater than 9 in the end? </p>
<h1>17, You'll probably need the diagram so I won't type the question in an attempt to shorten this wall of text. But would this just be to find the small "perforatted" triangle and knowing that it is also equilateral and the sides would be 10 each and then subtracting the 10 from AD(which is 20) which would mean AD minus the perforated and BE minus the perforated is 10 each so it's 10+10+20+20+30? Only problem i had with this solution is you had to assume the small perforated overlap triangle was also equilateral and I guess you could see but meh.</h1>
<h1>18 This was rated as 5 question but is it just legit to say that when x=3 it equals to zero therefore: a-1.2=3 would find the answer? Because I don't see how this is a hard difficulty question. If I'm wrong and I just got lucky here and it won't work everytime please tell me the appropriate way to do it.</h1>
<p>Thank you so much for your time!</p>
<p>P.S. Yes I know that sometimes the shortcuts via guess-and-check and plugin choices is faster but I just want the algebraic way for reinforcement and understanding</p>
<p>P.P.S Why isn't there a BB2 consolidated thread?</p>
<p>System of equations:
4x + 5y = 84
x + y = 19
Then substitute and simplify to solve for x and y</p>
<h1>6</h1>
<p>x + 3y = 12
3y = -x + 12
y = -(1/3)x + 12
The slope of the original line is -1/3. A line perpendicular to the original slope will have it’s opposite inverse (i.e. multiply it by -1, and then flip it over so the denominator is on top). The new line therefore has a slope of 3. So the answer is c.</p>
<h1>16</h1>
<p>Sorry, can’t help you on this one; I ended up plugging in at the end. I’m not sure if it is possible to solve algebraically, since there are 4 variables and only 3 equations.</p>
<p>I don’t have BB2, so I can’t say anything about 17 and 18. Sorry :(</p>
<p>Because W=Y+1, you can substitute Y+1 for W in the last equation to get Z=Y-4.</p>
<p>Substitute Y+1 into the first equation for W, and substitute Y-4 into the first equation for Z. You should get X=3Y-3.</p>
<p>Because X is the sum of the other numbers, we know that X has the greatest value. In order to get a reasonable value for X, Y must either be 3 (in which case X=6) or 4 (in which case x=9). However, because Z=W-5, we know that X must be larger than 6. </p>
<p>Therefore, X is 9 and Y must be 4. Substitute 4 for Y in the second equation and find W to be 5. Substitute 5 for W into the last equation and find Z to be 0.</p>
<p>yeah i messed up on 3 by divide the 12 over 3 to so i got y= (-x+12)/3
so i’m guessing you don’t divide the 3 by the y-intercept also? just the x(slope)</p>
<p>For #18, you did it just fine. The function g is zero at only x=3 or x=-3, therefore if g(cabbage) = 0, that must mean that cabbage=3 or cabbage=-3. Many function questions on the SAT are not that hard, but a lot of people have trouble with notation etc.</p>
<p>kk and for 17… will CD, DE, and EF always be equal to half of one full side of the larger equilateral triangles? If so what is the proof/reasoning/theorem behind this? Cuz this two equilateral overlapping triangles is often used on SATs and PSATs and i’d think it’d be worth mastering these.</p>
<p>You got the answer for #17, you’re just wondering why the small dashed triangle is equilateral? Remembering that the two big triangles are equilateral, ask yourself: what is the angle inside the small triangle at point D? At point E?</p>
<p>Yeah i got that afterwards what i don’t understand is what makes the sides of the smaller triangle DEX(we’ll call the X from when the bold line turns to dashed) half of the side of the larger equilateral triangles. DX and EX are both 10 while BC (the larger equilateral triangle) is 20. What makes it that the side of smaller equilateral formed by the overlapping the two larger equilateral triangles become half of the larger triangle.</p>
<p>What makes it half is that CD, DE, and EF are all the same length (10). The side of the top equil. big triangle is CE = CD+DE = 20, and the side of the bottom equil. big triangle is DF = DE+EF = 20. It doesn’t <em>have</em> to be that way: if the figure were to scale, you might have CE = 20 but DE = 6 even though all triangles are equilateral…</p>