Answer:
Step-by-step explanation:
y=x^2-x+1
We want to solve for x.
I'm going to use completing the square.
Subtract 1 on both sides:
y-1=x^2-x
Add (-1/2)^2 on both sides:
y-1+(-1/2)^2=x^2-x+(-1/2)^2
This allows me to write the right hand side as a square.
y-1+1/4=(x-1/2)^2
y-3/4=(x-1/2)^2
Now remember we are solving for x so now we square root both sides:
The problem said the domain was 1/2 to infinity and the range was 3/4 to infinity.
This is only the right side of the parabola because of the domain restriction. We want x-1/2 to be positive.
That is we want:
Add 1/2 on both sides:
The last step is to switch x and y:
A. <span>–13 + 27 = 27 + (–13) is an example of the commutative property.
The commutative property states that a + b = b + a.</span>
2. Each side of a pentagon is the same size.
4cm x 5 = 20cm or 4cm+4cm+4cm+4cm+4cm = 20cm
3. Each side of a square is the same size.
13yd x 4 = 52yd or 13yd+13yd+13yd+13yd = 52yd
4. Add all sides together.
12m+12m+30m+30m = 84m
5. Again add all sides together.
16yd+16yd+4yd+4yd = 40yd
6. Each side of a square is the same size.
7in x 4 = 28in. or 7in+7in+7in+7in = 28in
7. Add all sides together.
2cm+2cm+3cm+3cm = 10cm
8. Each side of a rhombus is the same size. A rhombus has 4 sides.
23in x 4 = 92in or 23in+23in+23in+23in = 92in
9. A regular octagon has 8 sides and each side is the same size.
9cm x 8 = 72cm
Answer:
100 times
Step-by-step explanation: vibration per second: 50 times
vibration for 2 seconds; 50*2=100 times
