What is the derivative of the equation f(x) = 3x^2 + 2x + 9 ?
To find the derivative, one must multiply the coefficient of each variable by the exponent and then subject one from the exponent in each term. Therefore the first term would be derived as 6x, the second as 2x^0, the third as 0. The reason the third term is 0 is because 9 has an assumed x^0 attached to it. Therefore the derivative is f'(x) = 6x + 2
There are two times as many blue marbles as black marbles, there are 10 orange marbles, and the total amount of marbles in the bowl is 40. How many blue marbles are in the bowl?
The first step to this question is creating an equation that mirrors the problem given. In this case, they tell us that there are "two times as many blue marbles as black marbles" which means that the equation to find the amount of blue marbles if you were given the amount of black is "2x" if "x" is the variable used to describe black marbles. They also tell us that there "are 10 orange marbles" and "the total amount of marbles in the bowl is 40". So the 40 marbles includes 10 orange, some amount of black, and some amount of blue (remember that blue is two times black). Therefore the equation would read 40 = 2x + x + 10 Now, to solve this equation you must remember that everything you do to one side of the equation you must also do to the other. So, get rid of the 10 to isolate the variable x by subtracting it from both sides. This makes the equation 30 = 2x + x Now, combine the variables. There is 2 x's plus one more x which makes the equation 30 = 3x Now divide by the 3 on both sides to isolate the variable, making the equation 10 = x So, if there are 10 black marbles and blue marbles are twice as much as black marbles, then there must be 20 blue marbles in the bowl. You can check this answer by adding up the amounts of these marbles that we found. 20 blue + 10 black + 10 orange = 40 marbles in total.
Natalie wants to make sure that her business's bank account matches what is written in her general ledger. The information given is that her beginning of the month bank balance was $100, her end of the month bank balance is $250, and her end of the month cash balance was $300. Along with this information, Natalie finds out that there is an outstanding check of $50 and a deposit in transit of $100. Does her bank balance reconcile with the cash balance in her general ledger?
The answer is yes! Her end of the month bank balance may be $50 less than what is shown in her cash balance, but that is explained by the outstanding check and deposit in transit. The outstanding check, once it is placed against your account will lower the balance to $200. The deposit in transit, when deposited into your account will then raise the account balance to $300 as shown in the cash balance of the general ledger.