help with sat questions?

Question

a=1/x
b=9a
c=1/b
d=9c
e=1/d
x=
A) a
B) b
C) c
D) d
E) e


If b does not equal a, then (b/a-b) - (a/b-a) =
A) -1
B) 0
C) 1
D) (b-a)/(a-b)
E) (a+b)/(a-b)

If x^2 + y^2 =15 and xy= 5 , then x + y =
A) 5 only
B) -5 only
C) 5 or -5
D) 5 or 10
E) 10 or -10

17 minutes ago - 3 days left to answer. - 0 answers - Report

Answer 1

(1)
a = 1/x
b = 9a = 9*(1/x) = 9/x
c = 1/b = 1/(9/x) = x/9
d = 9c = 9*(x/9) = x
e = 1/d = 1/x

x = d, answer (D).

(2)
b/(a-b) - a/(b-a) =
b/(a-b) + a/(a-b) = // Since (b-a) * -1 = a-b
(b + a) / (a - b) =
(a + b) / (a - b)

Answer (E).

(3)
x^2 + y^2 = 15
xy = 5

You're trying to figure out x+y, and if you add twice the second equation to the first, you'll have a perfect square of (x+y) on the left:

x^2 + y^2 + 2xy = 15 + 2*5
x^2 + 2xy + y^2 = 25
(x+y)^2 = 25
sqrt((x+y)^2) = sqrt(25)
x+y = +/- 5

x+y is therefore the positive or negative square root of 25, which is 5 or -5. Answer (C).

Answer 2

Hey there!

Here's the first answer.

a=1/x --> Write the problem.
b=9(1/x) --> Since b is equal to 9a, substitute 1/x for a.
b=9/x --> Simplify the above equation.
c=1/(9/x) --> Since c is equal to 1/b, substitute 9/x for b.
c=x/9 --> Simplify the above equation.
d=9(x/9) --> Since d is equal to 9c, substitute x/9 for c.
d=x --> Simplify the above equation.

Since the question asks the value of x, the answer is d, and the multiple choice answer is D.

Here's the second answer.

(b/(a-b))-(a/(b-a)) --> Write the problem.
(b/(a-b))+(a/(a-b)) --> Since b-a is the same thing as -(a-b), factor out the -1 in the right side of the expression.
(b+a)/(a-b) --> Simplify the above expression.

Since (b+a)/(a-b) is the same thing as (a+b)/(a-b), the answer is (a+b)/(a-b) or E.

Here's the third answer.

xy=5 --> Write the problem.
2xy=10 --> Multiply 2 on both sides of the equation.
x^2+y^2=15 --> Write the problem.
x^2+2xy+y^2=25 --> Add 2xy into the left side of the equation, and add 10 to the right side of the equation.
(x+y)^2=25 --> Factor the above quadratic trinomial. Recall that x^2+2xy+y^2=(x+y)^2.
x+y=±5 --> Take the square root on both sides of the equation.

So the answer is 5 or -5, which in this case is C.

Hope it helps!