47 -14i
You can work this out in the straight-forward way, or you can recognize that (6-i) is a common factor. In the latter case, you have ...
... = (6-i)(5 + 3-i)
... = (6 -i)(8 -i)
This product of binomials is found in the usual way. Each term of one factor is multiplied by each term of the other factor and the results summed. Of course, i = √-1, so i² = -1.
... = 6·8 -6i -8i +i²
... = 48 -14i -1
... =
_____
A suitable graphing calculator will work these complex number problems easily.
C(-8,2) and M(0,0) , since M is at the origin. Let x₁ and y₁ be the
coordinates of S →s(x₁ , y₁)
C(-8,2) and S(x₁ , y₁)
The coordinates of M, the midpoint of CS are M(x₂ , y₂)
a) x₂ = (-8 + x₁)/2 , but x₂ = 0, then :
0 = -4+x₁/2 and x₁ = 8
b) y₂ = (2+y₁)/2 , but y₂ = o, then:
0 = 2+ y₁/2 and y₂ = -2
Then the coordinates of S are S(8 , -2)
Answer:the total cost of the collar is $5.11
Step-by-step explanation:
To make a collar for her dog, she needs to buy some chain,a clasp, and a name tag.
The length of the chain that she wants to buy is 40 centimeters.
1000 centimeters = 1 meter
40 centimeters = 40/1000 = 0.04 meters.
One meter of chain costs $9.75. Therefore, 0.04 meters of chain would cost
0.04 × 9.75 = $0.39
The clasp is $1.29 and the name tag is $3.43. Therefore, the total cost of the collar would be
0.39 + 1.29 + 3.43 = $5.11
A function is positive if it lies above the x axis.
This function is positive before x = -4, i.e. over the interval 
It is negative elsewhere, i.e. over the interval 
So, the only correct option is the second one.