Answer:
The domain of the function (cd)(x) will be all real values of x except x = 2.
Step-by-step explanation:
The two functions are 
and d(x) = x + 3
So, (cd)(x) = 
Then, for x = 2 the function (cd)(x) will be undefined as zero in the denominator will make the function (cd)(x) undefined.
Therefore, the domain of the function (cd)(x) will be all real values of x except x = 2. (Answer)
Answer:
volume of box = l*b*h
= 8/9*5/12*3/10
= 1/9 cubic feet
Step-by-step explanation:
The dot product is used to determine the magnitude of the resultant vector of two component vectors. It is expressed as a·b. It does not literally mean that you multiply their values. Instead, you multiply their matrices. However, since we cannot find matrices, let's just find the resultant vector through theorems involving triangles. By cosine law:
R = √[a² + b² - 2abcos(3π/4)]
R = √[60² + 30² - 2*60*30*cos(3π/4)]
R = 83.94
Thus, a·b = 83.94
Let
x = base pay per month
y = commission per $1 of sales
Then the monthly pay for selling $100 of merchandise is
P = x + 100y
In one month, Alyssa earned $388 for selling $400 worth of merchandise.
Therefore
x + 400y = 388 (1)
In another month, she earned $520 for selling $1000 worth of merchandise.
Therefore
x + 1000y = 520 (2)
Subtract (1) from (2).
x + 1000y - (x + 400y) = 520 - 388
600y = 132
y = 0.22
From (1), obtain
x = 388 - 400y = 388 - 400*0.22 = 300
When Alyssa sells $3300 worth of merchandise, she earns
300 +0.22*3300 = $1026
Answer: $1026
