Answer:

Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
In this problem line AB and line BC are perpendicular
so

step 1
Find the slope AB
we have
A(p,4), B(6,1)
The formula to calculate the slope between two points is equal to

substitute the values


step 2
Find the slope BC
we have
B(6,1), and C(9,q)
The formula to calculate the slope between two points is equal to

substitute the values


step 3
Find the equation that relates p and q
we know that

we have


substitute



Answer:
A
Step-by-step explanation:
edge
Answer:
Step-by-step explanation:
We have 2 linear equations, and in both, the amount of merchandise you would have to purchase is "x", the unknown. We are asked to find that value of x.
The first equation is
C(x) = .30x + 90, which says that the cost of this plan is a fixed $90, and you pay 30% of the manufacturer's cost, x.
The second equation is
C(x) = .80x + 40, which says that the cost of this plan is a fixed $40, and you pay 80% of the manufacturer's cost, x.
If we want to know when the cost of these 2 are equal to each other, we set the equations equal to each other and solve for x:
.3x + 90 = .8x + 40 so
-.5x = -50 so
x = $100
The cost for each plan will be the same at this value of x, but we will plug in 100 for x in each just to make sure we did it right:
C(100) = .3(100) + 90
C(100) = 30 + 90
C(100) = 120 and
C(100) = .8(100) + 40
C(100) = 80 + 40
C(100) = 120
The value 18 will go in the first box
For the next two boxes, you'll type in

or (16/63)pi or something along those lines. The answer format will vary depending on how your teacher wants it.
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To get those values, I used the rule
If
z = a*(cos(b) + i*sin(b)) and w = c*(cos(d)+i*sin(d))
then
z*w = a*c*(cos(b+d)+i*sin(b+d))
In this case
a = 2
c = 9
so a*c = 2*9 = 18 goes in that first box
Then we compute b+d
b+d = (pi/9) + (pi/7)
b+d = (7pi)/63 + (9pi)/63
b+d = (16/63)pi
which goes in the last two boxes