Answer:
x=6
Step-by-step explanation:
Group Like Terms:
3x+x+30=10+2x+5x+2
Add similar elements 3x+x=4x:
4x+30=10+2x+5x+2
Add similar elements 2x+5x=7x:
4x+30=10+7x+2
Group like terms:
4x+30=7x+10+2
Add the numbers 10+2=12:
4x+30=7x+12
Subtract 30 from both sides:
4x+30-30=7x+12-30
Simplify:
4x=7x-18
Subtract 7x from both sides:
4x-7x=7x-18-7x
Simplify:
-3x=-18
Divide both sides by -3:
Simplify:
x=6
Hence, the correct answer is 6
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: