<p>i think this is from the online college board practice tests.</p>
<p>1) here's the link for the graphic : <a href="http://i36.tinypic.com/5305dx.jpg%5B/url%5D">http://i36.tinypic.com/5305dx.jpg</a>
In triangle MPQ above, the measure of angle M is 30 degrees and the measure of angle Q is 45 degrees. What is the length of segment MQ?</p>
<p>a) 15 b) 20 c) 5 radical 2 d) 5 radical 3 e) 5 radical 3 plus 5
the answer is e but i don't get how.</p>
<p>2)
z=x-y+4
z=y-w-3
z=w-x+5
Based on the system of equations above, what is the value of z?</p>
<p>a) 2 b) 3 c) 4 d) 6 e)12
the answer is a</p>
<p>3) Point P lines in plane M. How many circles are there in plane M that have center P and a circumfrence of 6(pi) inches?
a) none b) one c) two d) four e) more than four
the answer is b, one but i can't seem to visualize this properly</p>
<p>any help greatly appreciated thanks!</p>
<p>1) if you’ve taken precalc, you know that sinA/A = sinB/B = sinC/C</p>
<p>OR</p>
<p>you can just draw a line straight down and use get your sides lengths using right triangles.</p>
<p>2) the answer is not a. it’s d.</p>
<p>3) because the circle has a set circumference, it also means it has a set radius. Thus only one circle can have that center and occupy the same circle of points.</p>
<p>The answer is 2 for the 2nd question with 3 equations-a) not d).</p>
<ol>
<li>z=x-y+4</li>
<li>z=y-w-3</li>
<li>z=w-x+5</li>
</ol>
<p>Next, bring over the constants to the other side.
- z-4=x-y
- z+3=y-w
- z-5=w-x</p>
<p>Add equations 1 and 2 to get 2z-1=x-w</p>
<p>Add equations 1 and 3 to get 2z-9=w-y</p>
<p>Isolate w from the added equations 1 and 3. w=2z-9+y</p>
<p>Substitute this equation back into the added equations 1 and 2. 2z-1=x-2z+9-y</p>
<p>Isolate x-y. x-y=4z-10</p>
<p>Substitute this back into equation 1. 4z-10=z-4.</p>
<p>Subtract/add like terms. 3z=6</p>
<p>z=2</p>
<p>Ah right. my mistake, forgot to divide by 3 at the end.</p>
<p>For 2, I just added the three equations. x-y +4 +y-w-3+w-x+5 = 3z. Putting like terms together x-x -y+y -w+w + 4-3+5 =3z. You can see easily how all the variables zero out leaving you with 4-3+5=3z which is 6=3z. Divide by 3, and you’re done.</p>
<p>1) First of all, we know angle measure P = 105. Next, draw a line from point P to some point X on MQ such that PX is perpendicular to MQ (PX is an altitude of the triangle). By definition of an altitude, PXQ = 90 and therefore QPX = 45. PXM = 90 as well, and MPX = 60 (this all makes sense since 45+60=105). Now we have a 30-60-90 triangle and a 45-45-90 triangle. Length 10 is opposite the 90 degree angle, so PX = 5 (it is opposite the 30 degree angle) and MX = 5sqrt(3) (it is opposite the 60 degree angle). PX = XQ since triangle PXQ is isosceles, so XQ = 5.</p>
<p>MQ = MX + XQ
MQ = 5sqrt(3) + 5</p>
<p>2)
z=x-y+4
z=y-w-3
z=w-x+5</p>
<p>Whenever you see a weird system of equations like this, you almost always will need to add or subtract them from each other (don’t bother isolating variables, plugging one equation into another, etc.) Try adding them together</p>
<p>z+z+z = x-y+4+y-w-3+w-x+5
3z = x-x-y+y-w+w+4-3+5 <--------- Look ma, three variables will cancel out!
3z = 4-3+5
3z = 6
z = 2</p>
<p>3) Point P lines in plane M. How many circles are there in plane M that have center P and a circumfrence of 6(pi) inches?</p>
<p>Circumference 6pi inches means that the circle will have radius 3. The question is asking how many circles with center P and radius 3 are there in plane M. Can you draw any more than one circle with a certain center and a certain radius? Nope, you can only draw one.</p>
<p>Wonderful answer " Masterus2010 " , Thx , alot</p>
