<p>If (a+b)^1/2 = (a-b)^-1/2, which of the following must be true?</p>
<p>A) b=0
B) a+b=1
C) a-b=1
D) a^2+b^2=1
E) a^2-b^2=1</p>
<p>The answer is E, I don't know how though. Can anybody explain or show me how?</p>
<p>(a+b)^1/2 = (a-b)^-1/2
[(a+b)^1/2]^2 = [1/(a-b)^1/2]^2
(a+b) = 1/(a-b)
(a+b)(a-b)=1
...
after expanding:
a^2-b^2 =1 (E)</p>
<p>a lot.</p>
<p>Can any1 help me with this one:</p>
<p>In the x-y coordinate plane, the graph of x= y squared minus four (x=y^2-4) intersects line L at (0, p) and (5, t). What is the greatest possible value of the slope of L?</p>
<p>The answer is 1. But how? Simplifying in terms of y, I got y=sqrt(x+4). For this fxn, the points with the corresponding values of points given are (0, 2) and (5, 3). I found the slope between these two cause I didnt really know what to do; and I got 1/5. thats what i put as the answer, which is wrong. The right answer is 1, can anybody tell me how?</p>
<p>Thanks.</p>
<p>if you make the 2 negative the slope will equal 1</p>
<p>y= -2-(3) = -5 0-5= -5</p>
<p>how can you just make the 2 negative tho? isn't (0, -2) not in that fxn... it's (0,2) that is in the fxn.</p>
<p>when you square (-2) and (2) you still get four as both answers</p>
<p>when you solve for y, the equation becomes right side is the square root of (x + 4) as well as the negative square root of (x + 4). both work out when you plug it back into the original equation.</p>
<p>gotchya thanks a lot...</p>
<p>i got two more if anybody can help...</p>
<p>SAT Practice Test 1 in the collegeboard (big blue) book:
Section 6 (Math) Number 5
Section 9 (Math) Number 12</p>
<p>If you don't have the book and u want me to type them out, tell me. the second one has a graph so it might be harder to type out, but still i can try.</p>
<p>Section 6 (Math) Number 5</p>
<p>6 is greater than 5,4,3,2,1
5 is greater than 4,3,2,1
4: 3,2,1
3: 2,1
2:1</p>
<p>count them up and thats 15 out of a possible 36 (6*6) possibilities
A</p>
<p>Section 9 (Math) Number 12</p>
<p>2x<y<0</p>
<p>that means 2x and y are negative</p>
<p>so the opposite of (2x and y) would be positive (B)
and greater than the opposite of either 2x or y separately (A and E)</p>
<p>B</p>
<p>hopefully that answers them for you</p>
<p>Thanks a lot..</p>
<p>Now how about College Board (blue book) Practice Test Number 2...</p>
<p>Pg. 473
Sections 6, Number 8... the answer is E. 360-2a-3b... but how do you get that?</p>
<p>and</p>
<p>pg. 489
Section 9, Number 7... the answer is D... but how? y^z is 2^4, thats obvious. But doesn't x^-1/2 equal 1/sqrt(x) ??? apparently they say its 1/x^2 but i dont see how.</p>
<p>help from any1 would be greatly appreciated... thanks!!!</p>
<p>the OFFICIAL SAT book, right?</p>
<p>uh, okay. since i can't draw arrows on the diagrams, and because i don't know how to post a diagram, i'll try to explain this as best as i can.</p>
<p>the middle triangle has two different angles, a and b. there's also an unnamed one. we'll call that 180-a-b.</p>
<p>the triangle onthe bottom left is similar. the unnamed angle is 180-a-b.</p>
<p>now, the top triangle has angles b and c. so the unnamed one must be 180-b-c.</p>
<p>now add that all up. it should all the unnamed angles so far should equal 180.</p>
<p>(180-a-b)+(180-a-b)+(180-b-c) =180
540-2a-3b-c=180
540-180-2a-3b-c=180-180
360-2a-3b-c=0
360-2a-3b-c+c=0+c
360-2a-3b=c</p>
<p>TADA!</p>
<p>as for p. 489...assuming this is still the OFFICIAL SAT book...
so you already know that z=4 and y=2.</p>
<p>so...lessee....</p>
<p>(1/sqrt x) =1/3
3 * (1/sqrt x) = 3 * 1/3
sqrt x * (3/sqrt x) =1 *sqrt x
3 = sqrt x.
3 squared = sqrt x squared
9 = x
x +z =9+4=13.</p>
<p>hope this helps!</p>
<p>talk about stupid mistakes on my part...</p>
<p>thanks a lot, really appreciate it.</p>
<p>no probs!</p>
<p>^^</p>
<p>Help!</p>
<p>5.101001000100001...</p>
<p>The decimal number above consists of only ones and zeros to the right of the decimal point. The first one is followed by one zero, the second one is followed by two zeros, the third one and so on. What is the total number of zeros between the 98th and the 101st one in this decimal number</p>
<p>a.) 288
b.) 291
c.) 294
d.) 297
e.) 300</p>
<p>The correct answer is D and I don't know how to find it..... THANKS</p>
<p>OK, This is one of the quickest way.</p>
<p>5.101001000100001...</p>
<p>The 1's locations:</p>
<p>1, 3, 6, 10</p>
<p>The zeroes inbetween 1's:</p>
<p>1 2 3 </p>
<p>For 1st one (1) and 2nd one (3): there is 1 zeroes
For 2nd one (3) and 3rd one (6) : there are 2 zeroes
For 3rd one (6) and 4th one (10): there are 3 zeroes
.
.</p>
<p>Now u see the pattern: n represents the 1's placement.</p>
<p>For nth one and (n+1)th one : there is n zeroes inbetween
.
.
For 98th one and 99th one : 98 zeroes
For 99th one and 100th one : 99 zeroes
For 100th one and 101st one : 100 zeroes</p>
<p>So the answer is 297.</p>
<p>Thank you so much!!!</p>