The two problems are almost identical: you have to set up a system, and then solve it.
In the first case, let 
and 
be, respectively, the number of girls and boys.
We know that 
(the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that 
(there are 61 students in total).
So, we have the system
We can use the first equation to substitute in the second
And then solve for :
For the second problem, let 
and 
be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system
And you can solve it in the very same way we solved the previous one.
Answer:
8m
Step-by-step explanation:
x = hypotenuse since they want the point of observation to the top of the tree
cos 60 = 4/x
x = 4 / cos 60
x = 8m
Answer:
$39,851.25
Step-by-step explanation:
If the sales increase at a rate of 9% per year, this means it will be 109% of the previous year's value since 100% + 9% = 109%
109% in decimal form = 109/100 = 1.09
Therefore, the exponential function is:
, where 
is the number of years
So when 
,
After 8 years, annual sales = $39,851.25
The x-coord. of the vertex is halfway between the given zeros. Here, it'd be halfway between x=3 and x=9, which comes out to x = 6 (answer).
Using the triangle of pascal we have that the expression equivalent to (x + y) ^ 6 is given by:
x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
Therefore, the coefficients of the expansion are given by:
1, 6, 15, 20, 15, 6, 1
Answer:
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1
