Find the roots of f(x) = x^2 + 6x + 9.
Answer: -3 To begin this problem, we must think of the FOIL method. We can apply this method in a backwards sense to solve this problem. When looking for roots in this equation, we want to factor out our equation into a format of (x +/- __)(x +/- __). In this case, we would look at the constant which is 9. Now, think of the multiplication factors that create the number 9. There would be the numbers 1, 3, and 9. [1x9 = 9 and 3x3 = 9]. There are no other numbers that could multiply to create the number nine. From these equations that create the number nine, look at what numbers would add together to make the coefficient of x, in this case, 6. We can see here that 3 and 3 add together to make 6. Lastly, look at the x squared variable. Since there is no coefficient, we know each of our roots would contain just x. Our two roots would be (x+3)(x+3). You can double check your answer by foiling it to make sure you end up with the original equation. To find the roots, set each parenthesis equal to zero. Here we would have x+3 = 0 for each parenthesis. Subtract 3 from both sides to get x = -3.
What is the process of transcription?
Transcription is a process of converting DNA into RNA. There are three steps to transcription - initiation, elongation, and termination. The initiation of transcription begins when RNA polymerase binds to a sequence of DNA, referred to as the promoter. RNA polymerase will then begin to unwind the double-stranded DNA molecule, creating single stranded DNA. Then, elongation will begin. One of the single-stranded DNA will act as a template for the RNA polymerase. RNA polymerase will read the strand and add on complementary bases to the 3' end. This causes the strand to grow from 5' to 3' end. Termination occurs when RNA polymerase reads a specific sequence called terminators that signal the RNA polymerase that transcription is complete.
Find the x intercept of the equation 4x - 12y = 10
To find the x-intercept, we know that the y-value must be equal to zero so that the point on the graph lies on the x-axis. To solve this, you enter 0 as the value for the y variable to get 4x - 12(0) = 10. You then further simplify the equation to 4x = 10. Since there is a coefficient in front of the x, which is the value of 4, you must divide both sides of the equation by 4. Always remember, what is done to one side of the equation must be done to the other. After dividing both sides, you are left with x = 10/4. You can reduce this to 5/2 if the answer must be simplified.