What is the greatest common factor of 4k, 18k4, and 12?
2 answers:
Answer: The greatest common factor is 2.
Step-by-step explanation: We are given to find the greatest common factor of the following expressions:
<u>Greatest Common Factor:</u> The GCF of two or more numbers (expressions) is the greatest factor that divides all the numbers or expressions.
We have
Therefore, the greatest common factor will be
Thus, the required greatest common factor is 2.
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Answer:
Step-by-step explanation:
Your final answer is the standard form of a parabola. Since your equation has an x-squared term in it and not a y-squared term, your form will be
To get it into this form we will solve the quadratic for y and then set it equal to 0 so we can complete the square on it. Solving for y then setting y equal to 0:
so
We only need to complete the square on the x-terms, so we will move the constant back over to the other side of the equals sign:
The rule for completing the square is that the leading coefficient HAS to be a 1. Ours is 1/8, so we have to factor it out. When we do that we are left with:
To complete the square on the left, we take half the linear term, square it, and add it onto both sides. Our linear term is 2 (the number stuck to the x-term). Half of 2 is 1, and 1 squared is 1. So we add it into the parenthesis on the left. BUT we cannot discount the 1/8 sitting out front there. It is a multiplier. So what we actually added on the left is 1/8(1). That looks like this:
Now we will write the left side into its perfect square binomial (which was the whole reason for doing this!) and simplify the right at the same time:
Now we will set the whole thing back to equal y:
That's one form. But you need it in vertex form, so we add 3 to both sides:
and then multiply both sides by 8:
If you need to break it down further to include what your p value is, then:
Either that one or the one right above it should work.