Math Problems?

1) If (a+b)^1/2 = (a-b)^-1/2, which of the following must be true?


A) b=0


B) a+b=1


C) a-b=1


D) a^2+b^2=1


E) a^2-b^2=1





2) Set X has x members and set Y has y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k%26gt;0). Which of the following represents the number of members in set Z?





A) x+y+k


B) x+y-k


C) x+y+2k


D) x+y-2k


E) 2x+2y-2k





3) If x^2 + y^2 = 73 and xy = 24, what is the value of (x+y)^2





4) In the xy-coordinate plane, the graph of x=y^2-4 intersects line l at (0,p) and (5,t). What is the greatest possible value of the slope of l?





5) Exactly 4 actors try out for the 4 parts in a play. If each actor can perform any one part and no one will perform more than one part, how many different assignments of actors are possible?





If anyone can help me with any of these problems and show how they did it, I would greatly appreciate it. Thanks in advance.

Math Problems?
1)E


Set them equal


(a+b)^1/2 = (a-b)^(-1/2) *( since your exponent's negative, you can put it in the denominator and it turns positive like


1/(a-b)^(1/2)


square both sides to get


a+b = 1/(a-b)


Now cross multiply to get


(a+b)(a-b) = 1


FOIL to get


a^2 - ab +ab - b^2 = 1


cancel -ab+ab to leave you with


a^2-b^2 = 1





2) B I think, because all members in x and y = x+y, but we don't want the ones in both so subtract out k to get x+y-k


Not sure if that is right, seems too easy





3) for xy = 24 you have only a few options (if using integers) 1 and 24, 2 and 12, 3 and 8, or 6 and 4


but 3 and 8 also gives 3^2 + 8^2 = 73, so x=3 y=8


so (3+8)^2 = 11^2 = 121


You can also do this one algebraically though...





4) did you mean x = y^-2???





5) 4x3x2x1 = 24
Reply:1. (E)





2. (B)





3. (x+y)^2 = x^2+2xy+y^2 = 73+2(24) = 121





4. |t-p|/5





5. 4! = 24
Reply:1)E) a^2-b^2=1


2)B) x+y-k


3)97
Reply:1) a+b=1


2) x+y-2k


3) 121


5) 10
Reply:1. a+b=1


Break down the expression until you get sqr (a+b) / 1=1 / sqr(a+b). Then multiply both sides by sqr (a+b) to get 1=1/ sqr (a+b). Then multiply both sides by a+b to get a+b=1.


2.x+y=k


This is simple. Think of it as a venn diagram. An A side, a B Side, and a AB middle. So the entire contents would be a+b-ab.


3.121


Through the substitution property you find that x and y equal 8 and 3. Plug them back into the expression to check It doesn't matter whether x=8 or x=3. Then plug them in. (8+3)^2. 11^2. 121


4.?????? The equation doesn't appear to be any kind of mathematical shape.


5. 24


4!. 4x3x2x1
Reply:Lol im really bad at maths!
Reply:1. (E) a^2-b^2=1


(a+b)^1/2 = sqrt(a+b)


(a-b)^-1/2 = 1/sqrt(a-b)


1/sqrt(a-b) = sqrt(a+b) === cross multiply


1 = sqrt(a+b)*sqrt(a-b) === square both sides


1 = (a+b)(a-b)


1 = a^2-b^2





2. (B) x+y-k


all members of X and Y = x + y


all common members = k which are not found in Z


therefore Set of Z contains (x + y - k) members





3. (x+y)^2 = x^2+2xy+y^2 = (x^2+y^2)+2(xy) = 73+2(24) = 121





4. given: (0, p), (5, t) %26amp; x = y^2-4


slope = (x2-x1 / y2-y1)


slope = [t - p]/5-0 = [t - p]/5


for p: 0 = y^2 - 4, 4 = y^2, y = 2 = p


for t : 5 = y^2 - 4, 9 = y^2, y = 3 = t


substitute: [3 - 2]/5 = 1/5 is the maximum slope of l





5. its a factorial answer (!)


- actor 1 has a choice of 4 parts


- actor 2 has a choice of 3 parts


- actor 3 has a choice of 2 parts


- actor 4 has a choice of 1 parts





therefore = 4 * 3 * 2 * 1 = 4! = 24 possible assignments of the actors.

survey monkey