Solve the inequality, if possible. Write the solution set in interval notation.

Two angles are complementary. The measure of one angle is 46 degrees more than three times the measure of the other. Find the measure of each angle.

1) 
2)  

so 


 
therefore 

Simplify the following algebraic expression: (a) 2/( x-3) - 1/( x+3)

Differentiate the exponential function

Write the given equation in point-slope form

Simplify the given radical expression

assuming that cos(theta)=2/7 for an acute angle theta, find sin(theta)

Given:

the fastest way is to use the pythagorean identity:


which simplifies to...

Simplify with out using a calculator the square root of 704.

factorization can be done by successive division by the prime numbers:

Now we employ the properties of square roots:



:)

One number is 5 greater than another number. their sum is equal to 5 times their difference. Find the numbers.

1)x=y+5
2)x+y=5(x-y)

1) tells us x-y=5
therefore we can repalce x-y with 5 in 2)

new system:

x+y=25
x-y=5 

adding the two equations...

2x=30

x=15
so...

y=10

What is the inverse function of (2x-1)/(x-3)

so the inverse function is:

Solve: log3(x+3)+log3(x-3)=3

 <--other solution is extraneous

Solve the compound inequality |3x-9| < 15 AND |2x-3| > 5

1)
-15 < 3x-9 < 15
-15+9 < 3x < 15+9
-6 < 3x < 24
-2 < x < 8
(-2,8)

2)
2x-3 < -5 or 2x-3 > 5
2x < -2 or 2x > 8
x < -1 or x > 4
(-oo,-1)U(4,oo)


intersection:
(-2,-1) U (4,8)

Use rational exponents to rewrite as a single radical expression. ∛9 √2

Find the value of x: log6 (5x + 9)= 4

---

{x + y = 9, 1/x + 1/y = 1/2} Find x and y.

leads to

but 
so

this means


which leads to


so that  or 
then we can see:
{ (3,6), (6,3) }

The variables x and y satisfy the equation y=A(b^-x), where A and b are constants. The graph of ln y against x is a straight line passing through the points (0, 1.3) and (1.6, 0.9). Find the values of A and b, correct to 2 decimal places.

so this means

and so

Is this sequence geometric or arithmetic or neither: 3,5,9,15 ?

9-5=4
5-3=2
so it is not arithmetic

15/9=5/3

so it is not geometric either
... so neither

If a person invested a third of her money at 6% and two thirds at 9% and received $450 in interest, find the total money invested.