Since the amount earned is 9% per year, you would earn 5.4 in the first year because 60*(9/100)
Add that to the money that is already in your account, and you get 65.4
This tells us that after the first year, you have 65.4 dollars in your account.
Now, the amount you would earn in the second year is 3.924 because 65.4*(9/100)
interest in first year + interest in second year = total
5.4 + 3.924 = 9.324
Since we are dealing with money, the smallest unit is a penny, which is the hundredth place. Rounding, you get 9.32
Note: I do all my calculations by hand you might want to check the answer.
Sorry if my answer is wrong.
This is a quadratic, and to find x in a quadratic, you can use the quadratic formula.
First, expand the equation:
Now, the equation is in
This tells us that
The quadratic formula is:
x=(-b +- sqrt(b^2-4ac))/2a
Now, plugging in the variables, you get:
x=(-11 +- sqrt(11^2-4*2*1))/2*2
x=(-11 +- sqrt(121-8))/4
x=(-11 +- sqrt(113))/4
Now you can find the two possible values of x. When you let the equation have a plus sign in front of the sqrt, you get:
When you let the equation have a minus sign in front of the sqrt, you get:
Now you have your two possible values of x.
The question asks for the sum of the possible values of x, so all you have to do is add the two values of x.
ANSWER FOR THE SUM OF THE ROOTS: -22/4 OR -5.5
I saw in the title that you wanted the product of the roots also, even though you didn't include that in the actual problem, so here it is.
All you have to do is multiply the roots.
Doing some math that you probably know how to do, you get:
ANSWER FOR THE PRODUCT OF THE ROOTS: 1/2 OR 0.5
All of the work above is the LONG way of doing it. There is actually an easier way that you can use after you understand how it works.
To find the sum of the roots, all you have to do is:
To find the product of the roots, all you have to do is:
Using this gives us the same answer:
Hopefully this helps, this is my third answer :)
Note: I do all my calculations by hand so my method should be correct but you should double-check my work.
First, you have to find how much each ticket costs. Bob has 20 dollars, and he spends 2/5 of it on the movie ticket. To find this, you can simply do 20*(2/5). You can also see that 1/5 of 20 dollars is 4 because 20/5=4. He used 2/5 which is double of 1/5 which means the ticket is 2*4=8. Using both methods, your answer will be, the movie ticket is 8 dollars.
Since the problem says that the tickets were the same amount of money, you can make the equation: 8=y*(4/15). The 8 stands for the price of the movie ticket, the y stands for how much money Bill has, and the 4/15 stands for the fraction of Bill's money spent on the movie ticket. As shown above, y*(4/15) will tell you how much 4/15 of y is.
Solving for y, you get 30. In conclusion, Bill has 30 dollars.
This is my FIRST every response to a question so hopefully this helps :)
(I do all my calculations on paper so you should probably solve the equations yourself to make sure I didn't make any silly mistakes.)