solve the equation. Express radical in simplest form

Question

1.solve the equation. Express radical in simplest form

(4z-1)^2=9/16 

 

2. find the measures of angle whose supplement is 9times the measure of its compliment 

Answer 1

In the first problem, take the square root of each side.

Remember that the square root of 9/16 has both a positive and a negatuve solution (3/4 or -3/4)

This will give you:

4z-1=3/4 snd 4z-1=-3/4

Now you can solve for z

Answer 2

I'm not going to try to type out a solution to number one, but here's number 2.

 

2) To find the supplement of an angle X, you can do 180 - x.  The compliment is 90-x.  So...

180-x=9(90-x)

180 - x = 810 - 9x

8x = 630

x = 78.75

 

To check... the complement would be 11.75, the supplement would be 101.25, and 101.25 is 9 times 11.75

Answer 3

The way to solve either of these questions hinders on your understanding on what you need to do. The biggest tip to remember when solving this problem is 'whatever you do to one side of the equation, you have to do to the other'. Keeping this in mind, you first look at problem #1: (4z-1)^2=9/16 and ask yourself "what are you trying to solve?" In this case, Z. So how do we do this? The first thing to do is get ride of the square on the right side - ie. we have to 'undo' the square. What's the opposite of a square? The square root. Thus, you take the square root of both sides and continue on like Mrs. Jennifer said above.

The way to solve these kinds of problems hinders on what you understand and what you see needs to be done. A lot of math is actually working backwards and then asking yourself 'how do I get to the next step'.

 

For problem #2, you really need to know what Complimentary and Supplementary angles are. Without this knowledge memorized, you've really got no chance at getting the right answer.

So, as I'm sure you've figured out Complimentary Angles are angles that add up to 180º, while Supplementary Angles add up to 90º. So (lets take this step by step) if we know Complimentary Angle is 9 times more the Supplementary Angle (keep in mind it's the same X angle), than we can say

 

(180 - x) = 9(90 - x). And solve for X

 

The part which is confusing is how the word problem asks for X. If you didn't see this right away, get a hold of me and I'll explain the magic of turning English into Math Symbols. It makes all the difference when you have word problems!